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System-level performance evaluation of microwave fiber optic links

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Order Num ber 9431163
System -level performance evaluation of microwave fiber-optic
links
Ackerman, Edward Irving, Ph.D.
Drexel University, 1994
UMI
300 N. Zeeb R&
Ann Aibor, MI 48106
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System-Level Perform ance Evaluation
of M icrowave Fiber-O ptic Links
A Thesis
Submitted to the Faculty
of
Drexel University
by
Edward Irving Ackerman
in partial fulfillment of the
requirements for the degree
of
Doctor of Philosophy
June 1994
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Thesis Approval Form
(.For Masters and Doctoral Students)
This thesis, entitled
S y s te m - L e v e l P e r f o r m a n c e E v a l u a t i o n ________
________________________o f M ic ro w a v e F i b e r - O p t i c L i n k s
___________
______________________________________________________________________
and authored
by_______ E d w ard I r v i n g _A ck erm a n _________ •;$ he re b y accepted and approved.
Signatures:
Chairman, Examining Committee:
Supervising Professor:
Committee Members:
Graduate Advisor:
D epartm ent H ead:
T1
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For James A. Ackerman
1928-1994
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A CKNOW LEDGM ENTS
I would very much like to thank all the people who provided so much assistance,
guidance, and support during the five years I needed to complete this work.
First and foremost, I feel greatly indebted to my advisor, Dr. Afshin Daryoush,
who first interested me in the subject of this work, for his patience, understanding, and
helpful advice throughout my course of study. Many other people affiliated with Drexel
University— especially Dr. Peter Herczfeld, Dr. Bill Jemison, Dr. Tsang-der Ni, Dr.
Arthur Paollela, and Dr. Reza Saedi—have also assisted me in ways too numerous to list
I am also grateful for all the help provided by my friends and co-workers at Martin
Marietta Laboratories in Syracuse, New York. Special thanks are owed to Dr. Walter
Butler, Tom Carroway, Theresa Costello, Barbara Craig-Adams, Dave Hogue, Anthony
Jacomb-Hood, Dr. Dumrong Kasemset, Dr. James Komiak, Dr. Luke Lester, John
MacDonald, Mary McCabe-Bunyea, Joelle Prince, Steve Wanuga, and Kelly Wypych for
the technical and administrative assistance they gave so consistently and enthusiastically. I
also owe favors to the following individuals for the helpful information they allowed me to
pry out of them about the devices purchased from their companies: Ron Scotti and Bill
Minford at AT&T Bell Labs; Ken Miller of British Telecom & DuPont; John Schlafer at
GTE Laboratories; Milton Chang at NewFocus.
I must express my sincere appreciation to the Ackerman, Belock, Daryoush,
Herczfeld, Jurand, Kudless, Litvin, Matthews, Ni, Rogers, Saedi, and Sestak households
for the hospitality they extended to me during my many trips to the Philadelphia area.
Finally, I will be forever thankful for the constant support and understanding shown by my
loving family and friends during these past few years.
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iv
TABLE O F CONTENTS
Page
L IS T
OF
T A B L E S .................................................................................................
ix
L IS T
OF
F IG U R E S .............................................................................................. xiv
A B S T R A C T ............................................................................................................... xx
1
2
I N T R O D U C T I O N ...........................................................................................
1.1 Optical Fiber Signal Distribution in Phased Arrays................................
1.2 Fiber-optic Link Architectures...................................................................
1.3 Objectives of the Thesis.........................................................................
1.4 O utline of the Thesis...............................................................................
R E V IE W O F L IT E R A T U R E ......................................................................
2.1
2.2
State-of-the-Art Fiber-optic Link Architectures......................................
Optical Carrier Modulation Techniques.................................................
D irect M odulation...........................................................................
External M odulation.......................................................................
2.3 D etection Techniques................................................................................
D irect (Intensity) Detection..........................................................
Microwave Interferometric Detection............................................
Optical Interferometric Detection..................................................
2.4 Fiber-optic Link Performance Optimization Techniques..........................
2.4.1 RF Impedance Matching Techniques...........................................
R esistive M atching..........................................................................
R eactive M atching..........................................................................
Pseudo-Reactive M atching.............................................................
A ctive M atching.............................................................................
2.4.2 Optical Device-to-Fiber Coupling Techniques.............................
2.4.3 Optical Feedback Isolation Techniques.......................................
2.5 Electronic and Photonic Devices for Fiber-optic Links............................
2.5.1 O ptical Fibers................................................................................
2.5.2 O ptical Sources....................................
Solid-State Lasers fo r External Modulation Links.........................
Semiconductor Diode Optical Sources.........................................
Semiconductor Light-Emitting Diodes..........................................
Semiconductor Laser Diodes........................................................
2.5.3 RF/O ptical M odulators..................................................................
Electro-optic M odulators...............................................................
Electro-absorption Modulators......................................................
M odulator Substrate Materials......................................................
M odulator Electrode Layout.........................................................
2.5.4 O ptical/RF D etectors.....................................................................
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1
1
5
7
8
9
10
15
16
21
25
26
26
29
32
32
34
34
35
36
36
39
42
42
45
45
46
49
50
54
54
57
58
59
60
3
Semiconductor p-i-n Photodiodes............................. ..................
Metal-Semiconductor (MS and MSM) Schottky Photodiodes.
Avalanche Photodiodes..................................................................
2.5.5 Optical A m plifiers.........................................................................
Doped Fiber Am plifiers................................................................
Semiconductor Laser Amplifiers...................................................
2.6 Existing Fiber-optic Link Performance Models.......................................
Semiconductor Laser Diode Modeling.........................................
External Modulator Modeling......................................................
Optical Detector Modeling...........................................................
Full Direct and External Modulation Link Modeling.......................
61
63
64
65
66
69
71
71
76
77
78
D EV ELO PM EN T O F ANALYTICAL M OD ELS...................................
80
3.1
Direct Modulation Fiber-optic Link......................................................... 80
3.1.1 Gain A nalysis................................................................................. 84
3.1.2 Noise A nalysis............................................................................... 88
3.1.3 Intermodulation Distortion Analysis............................................. 91
94
3.1.4 Linearity Analysis...................................................
3.1.5 Analog Link Performance: Dynamic Range Calculation................ 95
3.1.6 Summary of the Direct Modulation Fiber-optic Link Model
96
3.2 External Modulation Fiber-optic Link..................................................... 96
Lumped-Element Modulator Model............................................... 99
Traveling-Wave Modulator Model..................................................101
3.2.1 Gain A nalysis................................................................................. 106
Lumped-Element Modulator Model................................................ 107
Traveling-Wave Modulator Model................................................ 109
3.2.2 Noise A nalysis............................................................................... 109
Lumped-Element Modulator Model.................................................112
Traveling-Wave Modulator Model................................................ 112
3.2.3 Intermodulation Distortion Analysis.............................................. 112
Lumped-Element Modulator Model................................................ 113
Traveling-Wave Modulator Model................................................ 114
3.2.4 Linearity A nalysis......................................................................... 115
Lumped-Element Modulator Model................................................ 116
Traveling-Wave Modulator Model................................................ 117
3.2.5 Analog Link Performance: Dynamic Range Calculation................. 117
3.2.6 Summary of the External Modulation Fiber-optic Link Model
118
4
EXPERIM ENTAL VERIFICATION O F ANALYTICAL M ODELS
4.1
123
Link Performance Characterization Techniques......................................... 123
4.1.1 Small-Signal Gain Characterization............................................. 124
4.1.2 Noise Figure Characterization.......................................
124
4.1.3 Spurious-Free and Compression Dynamic Range Characterization.... 126
4.2 Direct Modulation Fiber-optic Link...........................................................127
4.2.1 Determination of Model Parameters..............................
127
4.2.2 Case 1: Small Percentage Bandwidth Surrounding a Low Microwave
F requency.............................................................................................132
Electro-optic Device Selection...................................................... 132
Electro-optic Device Characterization.............................................132
Electro-optic Device Modeling..................................................... 133
Optical Transmitter and Receiver Fabrication................................. 134
Optical Transmitter and Receiver Modeling....................................134
Link R esults..................................................................................... 136
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4.2.3 Case 2: Small Percentage Bandwidth Surrounding a High Microwave
F requency............................................................................................. 139
Electro-optic Device Selection...................................................... 139
Electro-optic Device Characterization.............................................139
Electro-optic Device Modeling..................................................... 140
Optical Transmitter and Receiver Fabrication................................. 140
Optical Transmitter and Receiver Modeling....................................141
Link R esults..................................................................................... 141
4.2.4 Case 3: Large Percentage Bandwidth.............................................145
Electro-optic Device Selection........................................................ 145
Electro-optic Device Characterization.............................................145
Electro-optic Device Modeling..................................................... 146
Optical Transmitter and Receiver Fabrication................................. 146
Optical Transmitter and Receiver Modeling....................................149
Link R esults..................................................................................... 149
4.2.5 Observation: Dependence of Performance Parameters Upon Laser
Bias C urrent..................................................................................... 153
Dependence o f Insertion Gain Upon Laser Bias........................... 153
Dependence o f Noise Figure Upon Laser Bias............................... 154
Dependence o f Dynamic Range Upon Laser Bias......................... 157
4.2.6 Concluding Rem arks...................................................................... 157
4.3 External Modulation Fiber-optic Link..................................................... 158
4.3.1 Determination of Model Parameters............................................. 159
4.3.2 Case 1: Small Percentage Bandwidth Surrounding a Low Microwave
F requency............................................................................................. 162
Electro-optic Device Selection...................................................... 162
Electro-optic Device Characterization.............................................163
Electro-optic Device Modeling..................................................... 163
Optical Transmitter and Receiver Fabrication................................. 164
Optical Transmitter and Receiver Modeling....................................165
Link R esults..................................................................................... 165
4.3.3 Case 2: Small Percentage Bandwidth Surrounding a High Microwave
F requency............................................................................................. 168
Electro-optic Device Selection...................................................... 170
Electro-optic Device Characterization.............................................171
Electro-optic Device Modeling..................................................... 171
Optical Transmitter and Receiver Fabrication................................. 172
Optical Transmitter and Receiver Modeling....................................173
Link R esults..................................................................................... 173
4.3.4 Case 3: Large Percentage Bandwidth.............................................174
Electro-optic Device Selection...................................................... 177
Electro-optic Device Characterization.............................................177
Electro-optic Device Modeling:.................................................... 178
Optical Transmitter and Receiver Fabrication................................. 178
Optical Transmitter and Receiver Modeling....................................179
Link R esults..................................................................................... 180
4.3.5 Observation: Dependence of Performance Parameters Upon Modulator
Bias V oltage.................................................................................... 183
Dependence o f Insertion Gain Upon Modulator Bias.................... 183
Dependence o f Noise Figure Upon Modulator Bias....................... 186
Dependence o f Dynamic Range Upon Modulator Bias.....................186
4.3.6 Concluding Rem arks...................................................................... 191
5
C O M PA R ISO N
OF
A R C H IT E C T U R E S .................................................. 193
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5.1
Characteristics of Electro-optic Devices Used in Future Direct Modulation
Fiber-optic Links........................................................................................... 194
5.1.1 Semiconductor Laser Development Trends.................................... 194
Improved gain-bandwidth product (Fano's limit achieved)................196
Strong suppression o f all but a single cavity mode......................... 197
Very small active region volume..................................................... 200
Very large photon density and probability o f stimulated emission.......200
Minimum steady-state conduction-band electron density................ 201
Maximum in-cavity photon lifetime.............................................. 202
Likely device param eters................................................................. 202
Critical damping o f relaxation oscillations......................................203
Minimum threshold current............................................................. 204
Maximum laser-to-fiber coupling efficiency....................................205
5.1.2 Photodetector Development Trends......................
206
Improved gain-bandwidth product (Fano's limit achieved)............... 208
Very fast and efficient traveling-wave photodetectors...................... 209
Maximum fiber-to-detector coupling efficiency............................... 210
Minimum dark current............................................................
211
5.2 Characteristics of Electro-optic Devices Used in Future External Modulation
Fiber-optic Links........................................................
212
Improved gain-bandwidth product (Fano's limit achieved)............... 216
Perfect velocity matching.............................................................. 219
Maximum voltage-length product................................................ 219
Suitable compromise between gain and dynamic range.................. 220
Efficient coupling to integrated semiconductor laser diode............. 221
5.3 Direct vs. External Modulation: Crossover Frequency for a Given Percentage
B andw idth......................................................................................................... 222
5.3.1 Predictions Made Using Characteristics of Currently Available
Electro-optic Devices........................................................................222
5.3.2 Predictions Made Using Characteristics of Future Electro-optic
Devices, with Expected Improvements Based on Analysis of Physical
M odels................................................................................................. 230
5.4 CPU-level vs. T/R-level Data Mixing....................................................... 234
5.4.1 Predictions Made Using Characteristics of Currently Available
Electro-optic Devices........................................................................235
5.4.2 Predictions Made Using Estimated Characteristics of Future Electrooptic D evices................................................................................... 238
6
SU M M A R Y
L IS T
OF
AND
C O N C L U S IO N S ........................................................... 240
R E F E R E N C E S .................................................................................... 242
APPENDIX A:
DETERMINATION OF ELECTRO -O PTIC DEVICE
EQ U IV A LEN T C IR C U IT M O D ELS............................... 251
APPENDIX B:
DETERMINATION OF TH E ELECTRO -O PTIC
D EV IC E FREQ U ENCY R ESPO N SES............................ 262
APPENDIX C:
DETERMINATION O F LASER RELATIVE
IN T E N S IT Y N O IS E ....................................................... 272
A PPENDIX D:
ANALYTICAL M ODEL O F L-BAND (900 MHz)
D IR E C T M OD U LA TIO N L IN K ....................................278
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APPENDIX E:
ANALYTICAL M ODEL O F Ku-BAND (12.0 GHz)
D IR E C T M O D U LA TIO N L IN K ...................................282
A PPENDIX F:
ANALYTICAL M ODEL O F S/C-BAND (3-6 GHz)
D IR E C T M OD U LA TIO N L IN K ...................................286
A PPENDIX G:
ANALYTICAL M ODEL O F L-BAND (900 MHz)
EX TER N A L M OD U LA TIO N L IN K .......................... 290
A PPENDIX H:
ANALYTICAL MODEL O F M ILLIM ETER-W AVE
(32.5 GHz) EXTERNAL M ODULATION LIN K
294
APPENDIX I:
ANALYTICAL M ODEL O F WIDEBAND
M ICROW AVE (6-12 GHz) EXTERNAL
M O D U L A T IO N L IN K .................................................... 298
APPENDIX J :
L IS T
OF
SY M B O LS........................................................ 302
V I T A ............................................................................................................................. 314
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LIST OF TABLES
T able
Page
T able 2.1
Comparison of the expected performance of fiber-optic links—CPUlevel data mixing architecture vs. T/R-level data mixing architecture. 14
T able 2.2
Comparison of the expected performance of fiber-optic links—direct
modulation of a semiconductor laser vs. external modulation of a highpower solid-state laser with a Mach-Zehnder interferometric modulator. 22
T able 2.3
Comparison of currently available optical sources for direct modulation
fiber-optic links.................................................................................. 47
T able 2.4
Comparison of currently available optical waveguide modulators for
external modulation fiber-optic links.......................................... 55
T able 2.5
Comparison of currently available optical detectors for direct and
external modulation fiber-optic links.......................................... 62
T able 3.1
Summary of analytical model for small-signal gain and noise figure of a
direct modulation link...................................................................... 97
Table 3.2
Summary of analytical model for spurious-free and compression
dynamic range of a direct modulation link..................................... 98
T able 3.3
Summary of small-signal gain and noise figure performance of an
external modulation link................................................................... 119
Table 3.3 (a) Summary of analytical model for small-signal gain and noise figure of
an external modulation link employing a lumped-element electro-optic
m odulator............................................................................................... 119
Table 3.3 (b) Summary of analytical model for small-signal gain and noise figure of
an external modulation link employing a traveling-wave electro-optic
m odulator............................................................................................... 120
T able 3.4
Summary of spurious-free and compression dynamic range performance
of an external modulation link........................................................ 121
Table 3.4 (a) Summary of analytical model for spurious-free and compression
dynamic range of an external modulation link employing a lumpedelement electro-optic modulator....................................................... 121
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X
Table 3.4 (b) Summary of analytical model for spurious-free and compression
dynamic range of an external modulation link employing a travelingwave electro-optic modulator.......................................................... 122
Table 4.1
Methods for determining all parameters needed to predict direct
modulation link performance using model set forth in Chapter 3 (Fig.
3.1 and Tables 3.1 and 3.2).......................................................... 128
Table 4.2
Summary of the L-band direct modulation link performance at f=900
MHz. Measured and modeled results are given at laser bias currents of
20 mA, 27 mA, and 44 mA. Spurious-free and compression dynamic
ranges are quoted for a resolution bandwidth of 1 MHz................... 138
Table 4.3
Summary of the Ku-band direct modulation link performance at f=12
GHz. Measured and modeled results are given at laser bias currents of
50 mA, 60 mA, and 70mA. Spurious-free and compression dynamic
ranges are quoted for a resolution bandwidth of 1 MHz................... 144
Table 4.4
Summary of the S/C-band direct modulation link performance at f=3.0,
4.5, and 6.0 GHz. Measured and modeled results are given at laser bias
currents of 30 mA, 50 mA, and 70 mA. Spurious-free and compression
dynamic ranges are quoted for a resolution bandwidth of 1 MHz.
152
Table 4.5
Methods for determining all parameters needed to predict external
modulation link performance using model set forth in Chapter 3 (Fig.
3.2 and Tables 3.3 and 3.4).......................................................... 160
Table 4.6
Summary of the L-band external modulation link performance at f=900
MHz. Measured and modeled results are given at modulator bias
voltages of -1.5 V, -2.5 V, -3.0 V, -3.8 V, ^ . 0 V, -4.5 V, -4.8 V,
and -5.0 V. Spurious-free and compression dynamic ranges are quoted
for a resolution bandwidth of 1 MHz...............................................169
Table 4.7
Summary of the millimeter-wave external modulation link performance
at f=32.5 GHz. Measured and modeled results are given at one
modulator bias voltage (-3.0 V). Spurious-free and compression
dynamic ranges are quoted for a resolution bandwidth of 1 MHz
176
Table 4.8
Summary of the broadband microwave external modulation link
performance at f= 6,9, and 12 GHz. Measured and modeled results are
given at one modulator bias voltage (-2.V). Compression and spuriousfree dynamic ranges are quoted for a resolution bandwidth of 1 MHz... 182
T able 5.1
Summary of analytical model for the prediction of future direct
modulation link performance.......................................................... 213
Table 5.1 (a) Summary of analytical model for predicting small-signal insertion gain
of a future direct modulation link.................................................... 213
Table 5.1 (b) Summary of analytical model for predicting noise figure of a future
direct modulation link........................................................................214
Table 5.1 (c) Summary of analytical model for predicting dynamic range of a future
direct modulation link........................................................................215
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Table 5.2
Summary of analytical model for the prediction of future external
modulation link performance........................................................... 223
Table 5.2 (a)
Summary of analytical model for predicting small-signal insertion gain
of a future external modulation link................................................. 223
Table 5.2 (b) Summary of analytical model for predicting noise figure o f a future
external modulation link.................................................................... 224
Table 5.2 (c) Summary of analytical model for predicting dynamic range of a future
external modulation link.................................................................... 225
Table A.1
Example of how the one-port scattering parameter S n of the
semiconductor laser in the narrowband 900 MHz direct modulation link
was de-embedded from the measured scattering parameter S’n of the
device in its test fixture: (a) Measured parameters; (b) Results of
calculations using measured parameters of (a) in equations (A-13)
through (A -19)..........................................................................
255
Table A.2
Scattering parameters of the semiconductor laser diode and p-i-n
photodiode in the L-band direct modulation link described in section
4 .2 .2
256
Table A.3
Scattering parameters of the semiconductor laser diode and p-i-n
photodiode in the Ku-band direct modulation link described in section
4 .2 . 3 ...........................................................................................................257
T able A.4
Scattering parameters of the semiconductor laser diode and p-i-n
photodiode in the S/C-band direct modulation link described in section
4 .2 . 4 ...........................................................................................................258
Table A.5
Scattering parameters of the traveling-wave electro-optic modulator and
p-i-n photodiode in the L-band external modulation link described in
section 4.3.2......................................................................................... 259
T able A.6
Scattering parameters of the lumped-element electro-optic modulator and
p-i-n photodiode in the millimeter-wave external modulation link
described in section 4.3.3.................................................................. 260
T able A.7
Scattering parameters of the traveling-wave electro-optic modulator and
p-i-n photodiode in the wideband (6-12 GHz) external modulation link
described in section 4.3.4.................................................................. 261
Table B .l
Calculation of the frequency responses for the devices in the L-band
direct modulation link described in section 4.2.2: (a) calculation of the
semiconductor laser frequency response from measured E -0 data; (b)
calculation of the p-i-n photodetector response from the measured O-E
d a ta ............................................................................................................ 266
Table B.2
Calculation of the frequency responses for the devices in the Ku-band
direct modulation link described in section 4.2.3: (a) calculation of the
semiconductor laser frequency response from measured E -0 data; (b)
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calculation of the p-i-n photodetector response from the measured O-E
d a ta ............................................................................................................ 267
Table B.3
Calculation of the frequency responses for the devices in the S/C-band
direct modulation link described in section 4.2.4: (a) calculation of the
semiconductor laser frequency response from measured E -0 data; (b)
calculation of the p-i-n photodetector response from the measured O-E
d ata........................................................................................................... 268
Table B.4
Calculation of the frequency responses for the p-i-n photodetector in the
L-band external modulation link described in section 4.3.2 from
measured O-E data............................................................................269
Table B.5
Calculation of the frequency responses for the p-i-n photodetector in the
millimeter-wave external modulation link described in section 4.3.3
from measured O-E data...................................................................270
Table B.6
Calculation of the frequency responses for the p-i-n photodetector in the
wideband (6-12 GHz) external modulation link described in section
4.3.4 from measured O-E data....................................................... 271
Table C.1
Calculation of the relative intentity noise of the semiconductor laser used
in the L-band direct modulation link described in section 4.2.2 from RF
noise power measurements............................................................. 274
Table C.2
Calculation of the relative intentity noise of the semiconductor laser used
in the Ku-band direct modulation link described in section 4.2.3 from
RF noise power measurements........................................................275
Table C.3
Calculation of the relative intentity noise of the semiconductor laser used
in the S/C-band direct modulation link described in section 4.2.4 from
RF noise power measurements........................................................276
Table C.4
Calculation of the relative intentity noise of the NdrYAG laser used as a
CW optical source in the three external modulation links described in
Chapter 4 from RF noise power measurements...............................277
Table D .l
Calculation of the L-band direct modulation link's performance using
the model rendered in section 3.1 (Fig. 3.1 and Tables 3.1 and 3.2).... 280
Table D.l (a) Frequency-independent device parameters necessary for calculation of
the L-band direct modulation link performance................................280
Table D. 1(b) Frequency-dependent device parameters necessary for calculation of the
L-band direct modulation link performance. Parameter values are
rendered for frequencies between 500 MHz and 1.5 GHz in 100 MHz
s te p s ........................................................................................................ 281
Table E.1
Calculation of the Ku-band direct modulation link's performance using
the model rendered in section 3.1 (Fig. 3.1 and Tables 3.1 and 3.2).....284
Table E.1 (a) Frequency-independent device parameters necessary for calculation of
the Ku-band direct modulation link performance..............................284
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Table E. 1 (b) Frequency-dependent device parameters necessary for calculation of the
Ku-band direct modulation link performance. Parameter values are
rendered for frequencies between 11 and 13 GHz in 100 MHz steps.... 285
T able F .l
Calculation of the S/C-band direct modulation link’s performance using
the model rendered in section 3.1 (Fig. 3.1 and Tables 3.1 and 3.2)..... 288
Table F .l (a) Frequency-independent device parameters necessary for calculation of
the S/C-band direct modulation link performance..............................288
Table F. 1 (b) Frequency-dependent device parameters necessary for calculation of the
S/C-band direct modulation link performance. Parameter values are
rendered for frequencies between 2 and 7 GHz in 250 MHz steps
289
Table G .l
Calculation of the L-band external modulation link's performance using
die model rendered in section 3.2 [Fig. 3.2 and Tables 3.3 (a) and 3.4
(a )]
292
Table G .l (a) Frequency-independent device parameters necessary for calculation of
the L-band external modulation link performance..............................292
Table G. 1 (b) Frequency-dependent device parameters necessary for calculation of the
L-band external modulation link performance. Parameter values are
rendered for frequencies between 0.5 and 1.5 GHz in 100 MHz steps.. 293
T able H .l
Calculation of the millimeter-wave external modulation link's
performance using the model rendered in section 3.2 [Fig. 3.2 and
Tables 3.3 (b) and 3.4 (b)].............................................................. 296
Table H.1 (a) Frequency-independent device parameters necessary for calculation of
the millimeter-wave external modulation link performance.................. 296
Table H.1 (b) Frequency-dependent device parameters necessary for calculation of the
millimeter-wave external modulation link performance. Parameter
values are rendered for frequencies between 25 and 35 GHz in 500
M Hz step s............................................................................................. 297
Table 1.1
Calculation of the wideband (6-12 GHz) external modulation link's
performance using the model rendered in section 3.2 [Fig. 3.2 and
Tables 3.3 (b) and 3.4 (b)].............................................................. 300
Table 1.1 (a)
Frequency-independent device parameters necessary for calculation of
the millimeter-wave external modulation link performance................ 300
Table LI (b)
Frequency-dependent device parameters necessary for calculation of the
wideband external modulation link performance. Parameter values are
rendered for frequencies between 5 and 15 GHz in 500 MHz
ste p s ........................................................................................................ 301
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xiv
LIST O F FIGURES
F ig u re
F igure
Page
1.1 Important fiber-optic link input/output signal relationships.................
3
Figure 1.1 (a) Generalized block diagram of a fiber-optic link for microwave/
millimeter-wave communications applications...................................
3
Figure 1.1 (b) Graphical representation of fiber-optic link performance parameters
(gain, noise figure, compression-limited dynamic range and spuriousfree dynamic range)..........................................................................
3
Figure
1.2 Architectures for achieving fiber-optic T/R interfaces to a phased array..
6
Figure 1.2 (a) CPU-level data mixing architecture.................................................
6
Figure 1.2 (b) T/R-level data mixing architecture...................................................
6
Figure
2.1 Fiber-optic link architecture block diagrams....................................
11
Figure 2.1 (a) CPU-level data mixing architecture. The single-sideband mixing of an
intermediate-frequency or baseband signal (with frequency fnO with a
local oscillator (at frequency fLo) generates and de-constructs the RF
signal (fLO+flF)................................................................................. 11
Figure 2.1 (b) T/R-level data mixing architecture. The high-frequency LO and IF data
signals interface with the remote end of the link separately to construct
and de-construct the desired RF signal........................................... 11
Figure
2.2 Fiber-optic link block diagrams......................................................
17
Figure 2.2 (a) Direct modulation fiber-optic link. The modulating signal is impressed
directly onto the DC current that forward-biases the light-emitting diode
(LED) or laser diode source........................................................... 17
Figure 2.2 (b) External modulation fiber-optic link. An optical source generates a
constant-level lightwave signal that is mode-coupled into an optical
fiber, and modulation of the optical carrier is achieved via an external
modulator placed upon this waveguide........................................... 17
Figure
2.3 Optical power output vs. electrical current input relationship for directly
modulated semiconductor LED and semiconductor laser diode
18
Figure
2.4 Optical power output vs. electrical voltage input relationship for MachZehnder interferometric electro-optic modulator............................... 24
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XV
Figure 2.5
External modulation link architecture employing a balanced receiver for
cancellation of the laser’s RIN (after [23])...................................... 27
Figure 2.6
Alternative external modulation balanced receiver link architecture which
minimizes noise figure by combining the two complementary outputs of
a Y-branch electro-optic modulator in such a way that the signal power
is increased while the detrimental effect of the optical noise is wholly or
partly negated...................................................................................... 30
Figure 2.7
De-embedding to determine an electro-optic device's reflection
coefficient TDevice from measured reflection coefficient TMeasured- Twoport voltage-current transmission matrices of the intermediary elements
(bias tee, connector, and transmission line) can be obtained using the
Thru-Reflect-Line (TRL) technique (after [28])............................... 33
F igure 2.8
Fiber-to-device coupling techniques most often employed in highperformance fiber-optic links........................................................... 38
Figure 2.8 (a) Butt-coupling technique for device-to-fiber optical power coupling
38
Figure 2.8 (b) Optical coupling via a combination of spherical and GRIN lenses
38
Figure 2.8 (c) Optical coupling via a single plano-convex lens which approximates the
function of a spherical and GRIN lens combination......................... 38
Figure 2.8 (d) Optical coupling via a tapering of the fiber’s cladding......................
38
Figure 2.8 (e) Optical coupling via a hemispherical microlens formed at the fiber tip...
38
Figure 2.8 (f) Optical coupling via a hemispherical microlens formed at the tip of a
lengthened core region..............’...................................................... 38
Figure 2.9
Optical isolator operation................................................................. 41
Figure 2.9 (a) Optical isolator forward mode. Light entering the input polarization
filter becomes linearly polarized in the vertical plane at 0°. This
vertically polarized light then enters the Faraday rotator, which rotates
the plane of polarization 45° clockwise so that it can exit the output
polarization filter............................................................................... 41
Figure 2.9 (b) Optical isolator reverse mode. Retropropagating light becomes
polarized at 45° upon passing through the output polarization filter. The
light then enters a Faraday rotator, which rotates the plane of
polarization 45° clockwise so that it will be completely extinguished by
the input polarizer............................................................................. 41
F igure 3.1
Analytical model of direct modulation fiber-optic link......................
81
Figure 3.1 (a) Equivalent circuit of semiconductor laser-based optical transmitter.
81
Figure 3.1 (b) Equivalent circuit of p-i-n photodiode-based optical receiver.
81
Figure 3.1 (c) Signal flow diagram of semiconductor laser-based optical transmitter...
81
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Figure 3.1 (d) Signal flow diagram of p-i-n photodiode-based optical receiver.
F igure 3.2
81
Analytical model of electro-optic modulator in external modulation fiber­
optic lin k .............................................................................................. 100
Figure 3.2 (a) Equivalent circuit diagram of lumped-element electro-optic modulatorbased optical transm itter.....................................................................100
Figure 3.2 (b) Equivalent circuit diagram of traveling-wave electro-optic modulatorbased optical transm itter.....................................................................100
Figure 3.2 (c) Signal flow diagram of lumped-element or traveling-wave electro-optic
modulator-based optical transm itter...................................................100
Figure 4.1
Experimental set-up for measuring the small-signal insertion gain of a
microwave fiber-optic link.................................................................125
Figure 4.2
Experimental set-up for measuring the output noise power from a
microwave fiber-optic link to determine its noise figure......................125
Figure 4.3
Experimental set-up for measuring the two-tone intermodulation
distortion of a fiber-optic link to determine its dynamic range
125
F igure 4.4
Experimental set-up for measuring the microwave frequency response
of electro-optic devices for use in fiber-optic links.............................130
Figure 4.4 (a) Set-up for measuring the frequency response of a directly-modulated
semiconductor laser or an external modulator with a CW optical source. 130
Figure 4.4 (b) Set-up for measuring the frequency response of an optical detector
130
Figure 4.4 (c) Set-up for measuring the relative intensity noise of an optical source.... 130
F igure 4.5
Experimental L-band direct modulation link. The optical transmitter
module is shown on the upper right, and at the lower left is the optical
receiver m odule.................................................................................... 135
Figure 4.6
Insertion loss of the L-band direct modulation fiber-optic link. The
measured result is shown along with the performance predicted in
Appendix D using the model rendered in section 3.1..........................137
F igure 4.7
Insertion loss of the Ku-band direct modulation fiber-optic link. The
measured result is shown along with the performance predicted in
Appendix E using the model rendered in section 3.1........................ 142
Figure 4.8
Experimental S/C-band (3-6 GHz) optoelectronic transceiver. The
microwave signal enters transceiver package at an SMA connector
(upper left of photo) and is fed through a reactive matching network to
semiconductor laser. The modulated optical signal is coupled through a
spherical lens, optical isolator, and GRIN lens to an optical fiber pigtail
(upper right). The modulated optical signal enters transceiver package
through optical fiber pigtail at the lower right and is reflected onto the
photosensitive back-facet of the photodetector. The de-modulated
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microwave signal is fed through a pseudo-reactive matching network to
the SMA connector at the transceiver output (lower left)..................... 148
F igure 4.9
Insertion loss of the S/C-band direct modulation fiber-optic link. The
measured result is shown along with the performance predicted in
Appendix F using the model rendered in section 3.1........................ 150
F igure 4.10 Sources of noise contributing to the measured output noise floor (at
f=12 GHz) of the experimental Ku-band direct modulation link, plotted
as a function of both the laser diode bias current above threshold and the
optical power detected in the optical receiver.................................. 155
F igure 4.11 Experimental L-band external modulation link. The optical transmitter
consisting of the solid-state laser, optical polarization controller, and
matched lumped-element electro-optic modulator is shown on the left,
and at the upper right is the optical receiver module containing the
reactively matched, fiber-pigtailed, reverse-biased p-i-n photodiode
166
F igure 4.12 Insertion loss of the L-band external modulation fiber-optic link when
the modulator is biased at Vb=0. The measured result is shown along
with the performance predicted in Appendix G using the model rendered
in section 3.2.................................................................................... 167
F igure 4.13 Insertion loss of the millimeter-wave external modulation fiber-optic link
when the modulator is biased at Vb=0. The measured result is shown
along with the performance predicted in Appendix H using the model
rendered in section 3.2.................................................................... 175
F ig u re 4.14 Insertion loss of the wideband (6-12 GHz) external modulation fiber­
optic link when the modulator is biased at Vb=0. The measured result is
shown along with the performance predicted in Appendix I using the
external modulation link model rendered insection 3.2.................... 181
F igure 4.15 Gain and noise figure of the 900 MHz external modulation link at f=900
MHz as a function of the modulator bias voltage. Measured and
analytically determined values are shown....................................... 184
Figure 4.16 Compression and spurious-free dynamic range of the experimental
external modulation link at f = 900 MHz as a function of the modulator
bias voltage. Measured and analytically determined values are shown.. 185
F ig u re 4.17 Sources of noise contributing to the measured output noise floor (at
{=900 MHz) of the experimental L-band external modulation link,
plotted as a function of both the modulator bias voltage and the optical
power detected in the optical receiver...............................................187
F igure 4.18 Calculated spurious-free dynamic range of the experimental L-band
external modulation link as a function of the modulator bias voltage,
plotted for several assumed levels of available optical power............... 189
F igure 5.1
Projected improvements in the state of the art of future semiconductor
la se rs......................................................................................................... 195
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Figure 5.2
Projected improvements in the state of the art of future p-i-n
photodiodes............................................................................................ 207
F igure
5.3 Projected improvements in the state of the art of future electro-optic
external m odulators.............................................................................217
Figure
5.4 Predicted insertion gain and spurious-free dynamic range of fiber-optic
links as a function of the center frequency in the link band, assuming the
use of the conventional CPU-level data mixing architecture and devices
consistent with the current state of the art........................................ 227
Figure 5.4 (a) Performance is shown for both direct and external modulation links, as
calculated using the expressions in Tables 3.1 and 3.2, respectively, and
assuming link design optimization at a single frequency (Bandwidth=0
% of center frequency)................................................................... 227
Figure 5.4 (b) Performance is shown for both direct and external modulation links, as
calculated using the expressions in Tables 3.1 and 3.2, respectively, and
assuming a 10% link bandwidth (Bandwidth=10% of link center
frequency)............................................................................................... 228
Figure 5.4 (c) Performance is shown for both direct and external modulation links, as
calculated using the expressions in Tables 3.1 and 3.2, respectively, and
assuming an octave link bandwidth (Bandwidth=70% of link center
frequency)...............................................................................................229
Figure 5.5
Predicted insertion gain and spurious-free dynamic range of fiber-optic
links as a function of the center frequency in the link band, assuming the
use of the conventional CPU-level data mixing architecture with future
state-of-the-art devices..................................................................... 230
Figure 5.5 (a) Performance is shown for both direct and external modulation links, as
calculated using the model and assumptions summarized in Tables 5.1
and 5.2, respectively, and assuming link performance optimization at a
single frequency(Bandwidth=0% of link center frequency)................. 231
Figure 5.5 (b) Performance is shown for both direct and external modulation links, as
calculated using the model and assumptions summarized in Tables 5.1
and 5.2, respectively, and assuming link performance optimization
across a 10% bandwidth (Bandwidth=10% of link center frequency).... 232
Figure 5.5 (c) Performance is shown for both direct and external modulation links, as
calculated using the model and assumptions summarized in Tables 5.1
and 5.2, respectively, and assuming link performance optimization
across an octave bandwidth (Bandwidth=70% of link center frequency) 233
F igure 5.6
Example of how, using the T/R-level data mixing architecture with
suitable choice of LO frequency, the anticipated performance of future
straightforward (CPU-level mixing) external modulation links can be
approached currently.......................................................................... 236
Figure A .l Technique for measuring the one-port scattering parameter S'n of a oneport electro-optic device in a microwave test fixture.......................... 252
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F igure A.2 Schematic diagram of test fixture characterization model.................... 252
Figure B .l Experimental set-up for measuring the microwave frequency responses
of electro-optic devices: (a) Set-up for measuring the frequency
response of a directly-modulated semiconductor laser; (b) Set-up for
measuring the frequency response of an optical detector.....................265
Figure D .l Analytical model of direct modulation fiber-optic link optimized across a
narrow bandwidth at L-band (900 MHz): (a) Equivalent circuit of
semiconductor laser-based optical transmitter; (b) Equivalent circuit of
p-i-n photodiode-based optical receiver; (c) Signal flow diagram of
semiconductor laser-based optical transmitter; (d) Signal flow diagram
of p-i-n photodiode-based optical receiver........................................279
Figure E.1
Analytical model of direct modulation fiber-optic link optimized across a
narrow bandwidth at Ku-band (12 GHz): (a) Equivalent circuit of
semiconductor laser-based optical transmitter; (b) Equivalent circuit of
p-i-n photodiode-based optical receiver; (c) Signal flow diagram of
semiconductor laser-based optical transmitter; (d) Signal flow diagram
of p-i-n photodiode-based optical receiver........................................ 283
F igure F. 1 Analytical model of direct modulation fiber-optic link optimized across a
broad bandwidth at S-C bands (3-6 GHz): (a) Equivalent circuit of
semiconductor laser-based optical transmitter; (b) Equivalent circuit of
p-i-n photodiode-based optical receiver; (c) Signal flow diagram of
semiconductor laser-based optical transmitter; (d) Signal flow diagram
of p-i-n photodiode-based optical receiver........................................ 287
Figure G .l Analytical model of external modulation fiber-optic link optimized
across a narrow bandwidth at L-band (900 MHz): (a) Equivalent circuit
of electro-optic modulator-based optical transmitter; (b) Equivalent
circuit of p-i-n photodiode-based optical receiver; (c) Signal flow
diagram of electro-optic modulator-based optical transmitter; (d) Signal
flow diagram of p-i-n photodiode-based optical receiver.....................291
Figure H.1 Analytical model of millimeter-wave external modulation link optimized
across a narrow bandwidth surrounding a millimeter-wave freuqency
(32.5 GHz): (a) Equivalent circuit of electro-optic modulator-based
optical transmitter; (b) Equivalent circuit of p-i-n photodiode-based
optical receiver, (c) Signal flow diagram of electro-optic modulatorbased optical transmitter, (d) Signal flow diagram of p-i-n photodiodebased optical receiver........................................................................ 295
Figure 1.1
Analytical model of external modulation fiber-optic link optimized
across a wide microwave bandwidth (6-12 GHz): (a) Equivalent circuit
of electro-optic modulator-based optical transmitter; (b) Equivalent
circuit of p-i-n photodiode-based optical receiver; (c) Signal flow
diagram of electro-optic modulator-based optical transmitter; (d) Signal
flow diagram of p-i-n photodiode-based optical receiver.................... 299
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XX
A BSTRA CT
System-Level Performance Evaluation of Microwave Fiber-Optic Links
by
Edward Irving Ackerman
under the supervision of
Dr. Afshin S. Daryoush
Future generations of phased array radar systems as well as steerable
communication antennas will require feed and distribution to many hundreds—possibly
thousands— of solid-state MMIC radiating elements. In phased arrays operating at
millimeter-wave frequencies, backplane interface and signal distribution methods will need
to fulfill strict performance criteria. The metallic waveguides and coaxial cables currently
used as phased array backplane interconnects will be unable to meet these stringent
requirements. At millimeter-wave frequencies, where array backplane congestion is a
major problem, distribution of the RF and digital control signals using optical fiber offers
significant weight and crosstalk immunity advantages.
To realize all the benefits of optical fiber signal distribution in a phased array, the
single most critical development is the high-performance RF fiber-optic link. Some radar
and communication systems, however, have such stringent transmit and/or receive
performance goals which may not be easily met with conventional fiber-optic links.
Fulfilling such difficult performance criteria requires prudent link architecture design.
Before choosing a fiber-optic link design approach, it would benefit the phased
array antenna system designer to possess a means of determining what RF performance
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could be expected. To do this, the designer needs a means of verifying that the mixing,
modulation, and detection methods and the devices selected will result in a link with highfidelity performance at the RF design frequencies. This work provides just such a design
tool
In order to identify how best to leverage the advantages of optical fiber signal
distribution in a microwave or millimeter-wave phased array, this thesis will investigate the
optical link architectures that offer the maximum potential for achieving high-performance,
low-profile array backplane interfaces. To assist the designer in the choice of signal mixing
technique, modulation scheme, and electronic and photonic components that will yield the
best combination of fiber-optic link characteristics (i.e., gain, noise figure, dynamic range,
etc.) over a given frequency band, accurate link modeling techniques are set forth, verified
experimentally, and then employed to evaluate the suitability of the various architectures to
specific applications.
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1
CHAPTER 1
IN TRO D U CTIO N
Described in this thesis are models for predicting the microwave and millimeterwave performance of the fiber-optic links in optically controlled phased array antennas.
This introduction to the thesis explains the use of fiber-optic links in phased arrays in order
to establish the significance of this work, and sets forth the objectives of the work
described in the chapters that follow. Finally, an outline of the thesis is provided at the end
of this chapter to familiarize the reader with the order in which information is presented in
the remainder of the work.
1 .1
O ptical F iber Signal D istribution in Phased A rrays
Future generations of phased array radar systems as well as steerable
communication antennas will require feed and distribution to many hundreds—possibly
thousands— of solid-state MMIC radiating elements. In phased arrays operating at
millimeter-wave frequencies, backplane interface and signal distribution methods will need
to meet strict performance criteria. These include: high (greater than 60 dB) isolation from
both electromagnetic interference and crosstalk between module or subarray feeds; analog
frequencies of operation into the millimeter-wave range with bandwidths of an octave or
more; dramatic reduction in size and weight relative to present fielded arrays; and low RF
insertion loss.
The metallic waveguides and coaxial cables currently used as phased array
backplane interconnects will be unable to meet these stringent requirements. Conventional
waveguides, including coaxial cables, are heavy and bulky; moreover, the isolation
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2
between adjacent cables can be as low as 20-30 dB, depending on the type of cables and
their spacing. Coax is also extremely lossy—an 18 GHz signal, for example, attenuates
2300 dB/km in cable with a 2.2 mm outer diameter [1]. Furthermore, as higher-frequency
phased array operation is pursued, element spacing becomes increasingly tight, making
waveguide congestion and crosstalk at the array backplane serious design concerns.
At millimeter-wave frequencies, where array backplane congestion is a major
problem, distribution of the RF and digital control signals using optical fiber offers unique
advantages. These include [2]:
•
Small size (nominally 125 pm outer diameter) for reduced congestion at the
array backplane;
•
High durability (tensile strength > 105 lb/in2), supreme flexibility (minimum
bend radius < 1 in.), and negligible weight;
•
Immunity to the electromagnetic interference that pervades a densely-packed
millimeter-wave environment;
•
Low loss (attenuation < 0.5 dB/km); and
•
Suitability for implementing true-time-delay and other beamsteering and
signal processing functions in the optical domain.
To realize all the benefits of optical fiber signal distribution in a phased array, the
single most critical development is the high-performance analog fiber-optic link. In this
thesis, a "fiber-optic link" is considered a two-port electronic device in which a highfrequency analog (microwave or millimeter-wave) signal is relayed from input to output via
an optical fiber. Although the link can be defined—perhaps more accurately—as a network
of electronic and photonic devices, it is important to note that both its input and output are
electronic because this helps to specify what is meant by "high-performance."
A block diagram of a fiber-optic link is shown in Fig. 1.1 (a). At the input to this
network (port 1), a microwave or millimeter-wave signal modulates a stream of photons
(the optical carrier) that is launched into an optical fiber; at the other end of the fiber, the
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Port 1
Modulation
Optical
Signals
Transmitter
(fj, f2) |
+
—
Input Noise
Carrier
/\A/►
( j
Fiber-Optic Link
Port 2
• 1
Modulation
Optical
Signals
Receiver
I
( f p f 2>
+
Intermodulation
Products
( 2 ^ , 2 ^ )
+
Output Noise
(a)
outjnt
ii
out,lCP
PinjcP7 f
BO
o u u R X -P in,TXx G
D.
^outRX
= knT B G NF
NF
Spurious-Free Dynamic Range,
Input Power (dBm)
at fundamental signal frequencies
, f2
(b)
Figure 1.1
(a) Generalized block diagram of a fiber-optic link for microwave/
millimeter-wave communications applications.
(b) Graphical representation of fiber-optic link performance parameters
(gain, noise figure, compression-limited dynamic range and spuriousfree dynamic range).
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4
modulating signal is retrieved from the optical carrier and electronically coupled to the
output of the link (port 2). The analog performance of the link, as for any other microwave
or millimeter-wave two-port device, can refer to any of several figures of merit. Usually
the most critical of these are: G, the insertion gain (or loss); NF, the noise figure; CDR, the
compression-limited dynamic range; and SFDR, the spurious-free dynamic range.
The meaning of these performance parameters is illustrated in Fig. 1.1. The
insertion gain, G, is defined as the ratio of optical receiver output power P 0ut,RX to optical
transmitter input power Pm,TX at some signal frequency (given as fi in the figure); thus:
( 1- 1)
Noise figure, NF, is the extent to which the signal-to-noise power ratio (S/N) degrades
between the input and output of the optical link:
NF -
(S/N)out
ksTBG '
( 1-2 )
where kg is Boltzmann's constant, T is the absolute Kelvin temperature, and B is the
instantaneous receiver bandwidth. Therefore, the insertion gain and noise figure determine
N0ut,RX» the noise power at the output of the link’s optical receiver [see Fig. 1.1 (b)]:
N0Ut,RX = kB T B G N F .
(1-3)
The output noise determines the low end of the range of usable signal powers at the output
of the link. The upper end of the dynamic range is limited by the nonlinearity of the active
devices in the link, which, for large input powers, causes both compression of the output
signal amplitude and generation of unwanted signals at harmonic and intermodulation
frequencies. The compression-limited dynamic range is here defined as the range of input
signal powers for which the output signal power is above the noise floor Nout,RX and is
compressed by less than 1 dB relative to the small-signal response; thus:
p Dp _ 1-259 P quUCP _ Pin.ICP
N0Ut<Rx
kB T B NF ’
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(1-4)
5
where Pin,icp and Pout,lCP are the input and output signal powers at the point where the
output power at frequency fi is compressed by 1 dB (a factor of 1.259).
Another means of specifying the dynamic range of a system is to determine the
range of input powers at some fundamental frequency for which all spurious signals at
harmonic and intermodulation frequencies are below the noise power at the output of the
link. The highest-level and most problematic spurious signals present at the output of a
link are usually the third-order intermodulation products resulting from the nonlinear
mixing of two closely-spaced components of the fundamental signal. That is, if the
spacing of two fundamental frequencies fi and f 2 is smaller than the receiver resolution
bandwidth B, then it is likely that one or both of the third-order intermodulation product
frequencies (2fi-f2 and 2f2—fi) will also be present at the receiver. Defining
Pin,int
and
Print int as the input and output powers at the third-order intercept [where the fundamental
signal and third-order intermodulation product signal have equal output powers—see Fig.
1.1 (b)], the spurious-free dynamic range is given by the following expression:
( P out.int \ -s _ I
N ouuRx )
1.2
P in .in t
\
\kB T B NF/
Fiber-optic Link Architectures
Some radar and communication systems have stringent transmit and/or receive
performance goals which may not be easily met with conventional fiber-optic links. When
a phased array is operating in transmit mode, for instance, the links must deliver highpower, distortion-free RF waveforms to the subarrays to minimize the amount of
amplification and processing that needs to occur at the module level. In the receive mode,
the links must relay a wide dynamic range of signals from the array to the controller.
Various system architectures therefore use mixers to up- and down-convert the
signals at the input and output of links in an effort to optimize the overall system
performance at the desired RF frequencies. In the straightforward CPU-level data mixing
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6
O
T/R
Switch
"
Fiber-Opdc Link
T/R
Switch *
<
RF
* C
to+fff
TJ
Fiber-Opdc Link
T/R Module or Subarray
Central Processing Unit
(a)
‘ LO
TJ
Fiber-Opdc Link
TJ
T/R
Switch
" T
Central Processing Unit
Fiber-Opdc Link
LO
m l - /O n - - ^
Switch
TJ
Fiber-Opdc Link
np
RF
X
fLO+ fIF
T/R Module or Subanay
(b)
Figure 1.2
(a) CPU-level data mixing architecture.
(b) T/R-level data mixing architecture.
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7
approach, illustrated in Fig. 1.2 (a), the RF signal transmitted to the phased array by the
transmit link is constructed at the central processing unit (CPU) by mixing the baseband or
intermediate frequency (IF) signal with a local oscillator (LO) signal of a suitably high
frequency. The receive RF waveform delivered from the array by a separate receive fiber­
optic link is similarly decomposed at the CPU.
In the CPU-level data mixing architecture it is difficult to optimize the performance
of the transmit and receive links across very wide RF bandwidths, and to alleviate this
problem the architecture shown in Fig. 1.2 (b) has been proposed. In this architecture the
transmit and receive links operate at the IF frequencies, and the RF signals are constructed
from and deconstructed into the IF and LO components at the individual T/R modules or
subarrays of the phased array antenna. This architecture is called T/R-level data mixing. It
is inherently more complex than the CPU-level architecture, typically requiring a separate
link for relaying the narrowband LO signal to each T/R module or subarray.
Before choosing to design a fiber-optic interface to a phased array backplane using
the T/R-level data mixing architecture, it would benefit the system designer to possess a
means of determining what performance improvement relative to CPU-level mixing (if any)
could be expected. Moreover, prudent design of the individual links in either architecture
requires a means of verifying that the modulation methods and devices selected will result
in high-fidelity performance. A purpose of this work is to provide just such a design tool.
1.3
Objectives of the Thesis
In order to identify how best to leverage the advantages of optical fiber signal
distribution in a microwave or millimeter-wave phased array, this thesis will investigate the
optical link architectures that offer the maximum potential for achieving high-performance,
low-profile array backplane interfaces. Over a desired frequency band, in order to predict
what choice of signal mixing technique, modulation scheme, and electronic and photonic
components will yield the best combination of fiber-optic link characteristics (i.e., gain,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
8
noise figure, dynamic range, etc.), accurate modeling techniques are needed. In the
chapters that follow such models will be set forth, verified experimentally, and then
employed to evaluate the suitability of the various architectures to specific applications.
1.4
Outline of the Thesis
In Chapter 2, the review of literature, the present state of the art in fiber-optic link
technology is evaluated. Specific mixing techniques, electro-optic modulation methods,
and electronic devices are examined with regard to their potential for improving the ability
of fiber-optic links to function as RF signal relays in phased array backplanes. To quantify
this potential, several currently available models purport to predict the performance of fiber­
optic links; the extent to which these models succeed is also evaluated in Chapter 2.
Addressing the shortcomings of the existing models, Chapter 3 proposes a new
method for accurately predicting all fiber-optic link performance parameters relevant to
phased array systems.
Chapter 4 presents the measured performance characteristics of six highperformance fiber-optic links that use different optical modulation methods over a number
frequency bands. These experimental results are compared to the performance predicted by
the proposed models in order to assess the usefulness and accuracy of this modeling
procedure.
Using the known characteristics of state-of-the-art devices, in Chapter 5 link
performance is calculated as a function of frequency band and link architecture to provide a
benchmark for selecting the optimum fiber-optic link architecture to meet any given set of
system specifications. Future component developments are also predicted in Chapter 5,
and the models are used to show the effect of these developments upon link performance,
resulting in revised link architecture assessments.
Chapter 6 concludes the thesis with a discussion of the most relevant findings in
this thesis, including some recommendations for the direction of future work.
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9
CHAPTER 2
REVIEW OF LITERATURE
Achieving the benefits of optical fibers—reduced size and weight, full EMI
immunity, and the feasibility of efficient and compact optical processing schemes—in a
microwave or millimeter-wave phased array antenna for radar or communications scenarios
hinges upon the design of high-performance fiber-optic links. When replacing bulky
metallic waveguides with compact optical fibers, the insertion loss and noise figure (signalto-noise ratio degradation) should be minimized over the bandwidth of interest to ensure
that the links can reliably relay signals having the broadest possible range of powers.
To make prudent architecture selection for a given system it is necessary to be able
to accurately model a microwave or millimeter-wave fiber-optic link’s performance. In
Chapter 1, the efficiency, noise, and linearity of the fiber-optic link were discussed and
defined in terms of electronic system parameters such as gain, noise figure, and dynamic
range. Because the fabrication of a fiber-optic link consumes both time and money, the
ability to predict the performance of a designed link before fabrication has been sought by a
number of researchers. Such a modeling technique would verify the prudence of link
architectures, components, and other features selected by the designer. To accomplish this,
the model must consistently and quantifiably account for all phenomena and features of the
link which may contribute to its insertion gain/loss, noise figure, dynamic range, and
bandwidth. Furthermore, it should apply to the devices and techniques which a designer is
most likely to use in the pursuit of high performance.
The fiber-optic link architectures which are worth modeling (i.e., those which are
likely to yield high performance) must first be identified, along with the devices and other
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10
link features that should be accounted for in any useful link model. Therefore, in section
2.1 of this chapter RF-IF signal mixing architectures are examined in order to select those
which will be compared using the models set forth in Chapter 3. State-of-the-art
modulation and detection techniques, link performance optimization techniques (impedance
matching, fiber-to-device coupling, and feedback isolation methods), and state-of-the-art
devices (optical fibers, sources, modulators, detectors and optical amplifiers) are discussed
in sections 2.2-2.5 to determine which of these the new models need to cover. Finally, in
section 2.6, current fiber-optic link performance models are reviewed to assess the extent to
which they accommodate these high-potential architectures, components, and features.
2.1
State-of-the-Art Fiber-optic Link Architectures
When an optically controlled phased array antenna is operating in transmit mode,
the fiber-optic links must deliver high-power, distortion-free RF waveforms to the transmit
modules or subarrays to minimize the amount of amplification and processing that needs to
occur at the module level. In the receive mode, the links must relay a wide dynamic range
of signals from the array to the controller.
Various system architectures use mixers to up- and down-convert the signals at the
input and output of links in an effort to optimize the overall system performance at RF
frequencies. Most methods of mixing baseband or intermediate frequency (IF) information
with a high-frequency local oscillator (LO) to translate it into the desired RF band are
conceptually equivalent to either the CPU-level data mixing or the T/R-level data mixing
architecture.
Figure 2.1 shows detailed block diagrams for the CPU-level and T/R-level mixing
architectures. The fundamental differences between these two architectures are the location
at which RF-IF mixing is performed (as suggested by their names) and the typical number
of links in each architecture. Note from the illustration that, whereas CPU-level data
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11
^0+fIF
<Shrl
T/R
Switch
o
t
T/R
Switch
Fiber-Optic Link
^ D + f IF
O
"
RF
fo+fIF
--------------------------------------------
<
'
Fiber-Optic Link
T/R Module or Subarray
Central Processing Unit
(a)
LO
Fiber-Optic Link
T/R
Switch
T/R
Switch
Central Processing Unit
Fiber-Optic Link
T/R Module or SubaiTay
(b)
Figure 2.1 (a) CPU-level data mixing architecture. The single-sideband mixing of an
intermediate-frequency or baseband signal (with frequency fiF ) with a
local oscillator (at frequency f ^ ) generates and de-constructs the RF
signal (^o+ f ^ ).
(b) T/R-level data mixing architecture. The high-frequency LO and IF data
signals interface with the remote end of the link separately to construct
and de-construct the desired RF signal.
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mixing requires two fiber-optic links to achieve bi-directional T/R interface to an array,
mixing at the T/R module level usually requires three.
In the CPU-level data mixing architecture [Fig. 2.1 (a)], the single-sideband mixing
of an intermediate-fiequency or baseband signal (with frequency fjp) with a local oscillator
(at frequency fLo) generates the transmit RF signal (fLo+flF)- This signal is usually
imposed on the optical carrier by either directly modulating the output of a semiconductor
laser or LED, or by externally modulating an optical source using an electro-optic
modulator. The same LO can be used to down-convert the received RF signal.
In the T/R-level data mixing architecture [Figure 2.1 (b)], the high-frequency LO
and transmit IF data signals are separately imposed on two opdcal carriers, and are mixed at
the remote end of the link to construct the desired IF-modulated LO. Thus the performance
of the LO link need only be optimized at a single frequency (fLo). and the IF data can be
generated efficiently and with low noise by a semiconductor laser or modulator that is
impedance-matched to yield high transducer gain across the lower-frequency data
bandwidth. This architecture can result in improved link performance, especially in cases
where the desired RF frequency band is exceedingly high, broad, or both.
Currently, devices such as semiconductor lasers, electro-optic interferometric
modulators, and p-i-n photodetectors which exhibit high efficiency, low noise, and wide
linear operating regimes at modest microwave frequencies are commercially available.
Therefore, at these frequencies the straightforward CPU-level data mixing architecture is
likely to yield as good a system performance as the more complex T/R-level mixing
architecture. When CPU-level data mixing is employed, the maximum RF frequency of the
system is limited to the maximum modulation bandwidth of the LED, laser, or modulator.
For a direct modulation link using a semiconductor laser as a modulated optical source, it is
likely that the laser will be operating at or near its highest-noise frequencies, resulting in
narrow dynamic range for the CPU-level mixing architecture.
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13
For arrays operating at millimeter-wave frequencies above the rated bandwidths of
commercially available electro-optic devices, it is expected that higher-performance
interfaces will be obtained using a T/R-level data mixing architecture. Compared to the
CPU-level mixing scenario, mixing at the T/R module level typically requires an additional
fiber (see Fig. 2.1); also, all modules or subarrays fed by separate LO and IF links must
have RF coherency established via phase-locking. The payoff, however, lies in the fact
that much higher modulation frequencies can be attained by using the nonlinearities of the
laser diode, modulator, detector, or mixer. That is, at the T/R module a millimeter-wave
transmit RF signal can be constructed by mixing the optically-fed IF signal with an n111order harmonic of the optically fed microwave LO (using the mixer's nonlinearity both to
up-convert and to mix); in receive mode, a subharmonic of the RF signal from the array can
be mixed with the LO to generate the IF data retrieved optically from the module. In this
fashion, both the LO and IF links can be operated at modest microwave frequencies where
electro-optic devices exhibit efficient, low-noise, highly linear performance characteristics.
Based only on these assumptions, the relative advantages expected from these two mixing
architectures are listed in Table 2.1; in Chapter 5 the models set forth in this thesis will be
used to verify or nullify each of these expected characteristics.
Employing the T/R-level data mixing scheme, Koffman et aL have demonstrated a
dynamic range 22 dB greater than what was achieved using the same commercial link in a
CPU-level mixing architecture [3]. Further demonstrations of T/R-level data mixing by
Polifko and Daryoush [4] and by Ogawa and Kamiya [5] have proven the viability of two
T/R-level mixing configurations for feeding a 10 GHz RF signal to a transmit subarray. In
the first of these configurations one of the harmonics generated in a link was filtered at the
detector output and fed into a nonlinear mixer which also served as the detector for the IF
link (a MESFET or HEMT could accomplish this) to generate the RF remotely [4]. In the
second configuration, the IF data was detected by its own photodetector and mixed in a
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Advantages
CPU-level Data Mixing
Only one link needed per T/R module or
subarray
Disadvantages
Maximum operating frequency limited to
laser bandwidth (for direct modulation)
Directly modulated semiconductor laser
operating at frequencies where RIN is
high
T/R-level Data Mixing
Laser diode and other active device
nonlinearities can be leveraged to
subharmonically injection lock the LO,
resulting in much higher maximum
operating frequency
Two separate links required per T/R
module or subarray
Coherency needed among all T/R-level
LO's
Table 2.1 Comparison of the expected performance of fiber-optic links—CPU-level data mixing architecture vs. T/R-level data
mixing architecture.
15
nonlinear detector/mixer (again, a MESFET or HEMT) with one of the harmonics of the
LO link frequency [5].
Several additional methods of producing carrier frequencies beyond the
fundamental modulation response of laser diodes or electro-optic modulators have been
proposed and investigated. These methods include: mode locking of laser diodes;
generating millimeter-wave beat frequencies between two wavelength-tunable lasers
(superheterodyning); and using the laser diode's, modulator's, or detector's nonlinearity to
up-convert signals [6]. Such methods all involve feeding a signal of one frequency into a
modulatable source or external modulator and retrieving a different frequency from the
detector—i.e., using the link not only for relaying of a signal but for frequency conversion
as well. Optical links as frequency converters is a broad and interesting topic which
requires considerably different modeling, measurement, and characterization techniques
than do the RF communication links that are the focus of this work. Therefore, the only
RF-IF mixing architectures which will be modeled and compared in this work are those in
which each link is modeled and evaluated for how effectively it duplicates its input signal at
the output (at the same frequency as the input signal).
After new fiber-optic link performance models are set forth in Chapter 3 and
verified experimentally in Chapter 4, the CPU-level and T/R-level data mixing architectures
will be compared in Chapter 5. At any frequency, the performance characteristics of the
RF link in the CPU-level mixing architecture and of the IF link in the T/R-level mixing
architecture can be predicted using the models along either with known characteristics of
currently available devices or with the expected characteristics of future devices.
2 .2
Optical C a rrie r M odulation Techniques
Selection o f a technique for imposing a microwave modulation signal upon an
optical carrier involves considerations of electro-optic transducer efficiency, noise,
linearity, size, and cost Modulation methods include direct modulation of a semiconductor
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16
LED or laser diode and external modulation of an optical source using an electro-optic or
acousto-optic device. Figure 2.2 shows block diagrams of direct modulation and external
modulation fiber-optic links. Both modulation techniques are described in this section of
the literature review.
Direct Modulation
Direct modulation [Fig. 2.2(a)] is so named because the modulating signal is
impressed directly onto the DC current that forward-biases a semiconductor diode optical
source. The diode is a p-n junction constructed from doped III-V semiconductor layers
with a bandgap energy corresponding to a wavelength which will propagate in an optical
fiber with minimal loss and dispersion. When this junction is forward-biased, electrons
and holes are injected into the p and n regions, respectively.
In a semiconductor light-emitting diode (LED), spontaneous emission is the chief
source of photon emissions, even when the injection current is high enough to excite a
large population of electrons to the conduction band energy. A laser is created by setting
up conditions in the diode to favor stimulated emission over spontaneous emission. This
results in optical radiation that is both high-gain (due to the large number of photon
emissions which one photon can stimulate before it leaves the diode or is absorbed) and
coherent (due to the phase equality of the incident and stimulated photons). The minimum
injection current at which stimulated emission dominates over spontaneous emission is
known as the device's laser threshold current IthBoth LEDs and laser diodes feature an output optical power P0ut,op that is related to
the bias current I I , and hence modulation of the DC bias current produces direct
modulation of the optical carrier. This relationship is illustrated in Figure 2.3, which plots
the optical power emitted from a typical semiconductor LED and laser diode as a function
of the forward bias current II- A laser diode behaves exactly like an LED at bias currents
below the threshold Ith» and this concept is also illustrated by Fig. 2.3—that is,
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Optical Transmitter
Input
Signal
Optical Receiver
Modulated Optical
Semiconductor
Input
LED or
Electrical ►
Laser
Diode
Circuit
Optical Transmitter
earner (\J\^
u
Input
Electrical
Circuit
Electio-optic
External
Modulator
Output
► Electrical
Circuit'
Optical Fiber
Optical Receiver
Modulated Optical
W - CaiIier'\A/»Input
Signal
Optical
Detector
Output
Signal
Optical
Detector
Output
Electrical
Circuit
Output
Signal
Optical Fiber
Optical
Source
Figure 2.2 (a) Direct modulation fiber-optic link. The modulating signal is impressed directly onto the DC current that forwardthe light-emitting diode (LED) or laser diode source.
(b) External modulation fiber-optic link. An optical source generates a constant-level lightwave signal that is modecoupled into an optical fiber, and modulation of the optical carrier is achieved via an external modulator placed upon
this waveguide.
Optical Power Output Pout,op(mW)
Po u t,raTlL ^ L
w
CW Optical
Power
P
=n
RF-modulated
Optical Power
I
out,op 'LED L
Threshold
Current
RF Signal
Current
Electrical Current Input IL (mA)
Figure 2.3
Optical power output vs. electrical current input relationship for
directly modulated semiconductor LED and semiconductor laser diode.
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19
Pout,op = t i l e d ® I I .
(2 -1 )
where 1 ) l e d ( I ) , the current-dependent relationship between bias current and output optical
power, is called the external differential quantum efficiency of the directly modulated
optical source below its lasing threshold. That is, for lL<Ith» both the LED and laser diode
have the following differential quantum efficiency:
t il e d ®
=
t i l e d + ti' l e d
I I + tT 'l e d I I + tT ' l e d I I + -------
(2 -2 )
For LEDs in which the P-vs.-I characteristic has been optimized for maximum linearity, the
nonzero-order terms of the quantum efficiency are made as small as possible, and thus for
all but the largest bias currents a quasi-linear relationship is assumed:
Pout.op -
t il e d
II •
(2 -3 )
An LED's quantum efficiency is typically quite poor—on the order of 0.01 mA/mW.
For lL>Ith» the LED continues to obey this relationship, while the laser diode
differential quantum efficiency increases dramatically and is expressed with a separate set
of terms:
Pout,op =
t il ®
( I I — Ith),
(2 -4 )
where
til® = T|l + t | l
(II - I th ) + t |" l ( I I
-
Ith)2
+ v T l (II - 1*? + -----
(2-5)
As for LEDs, for a laser diode in which the P-vs.-I characteristic has been optimized for
maximum linearity, the nonzero-order terms of the quantum efficiency are made as small as
possible, and thus for all but the largest bias currents a quasi-linear relationship can often
be assumed—i.e.,
Pout,op = t i l ( I I — Ith) •
(2 -6 )
Laser external differential quantum efficiency of 0.25 mW/mA or greater is typical, even at
relatively high bias currents (nearly 100 mA).
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20
Direct modulation of a semiconductor diode optical source is currently the most
compact and cost-effective means of constructing an optical transmitter. LED and laser
diode output beam sizes are reasonably compatible with the spot sizes of optical fibers.
This, combined with excellent modulation efficiency at moderate microwave frequencies,
has enabled minimal insertion loss and even small levels of RF gain to be achieved using
direct modulation of a semiconductor laser in narrowband microwave fiber-optic links [715]. For instance, Wanuga et al. achieved an insertion gain of 2.7 dB and Blauvelt et a l
measured -7 dB of insertion loss across narrow (<20%) bandwidths at 2 GHz and 9 GHz,
respectively [7,8]. Even across very broad bands, impressive fiber-optic link gainbandwidth products have been obtained using direcdy modulated laser diodes. Daryoush et
aL, for instance, demonstrated a direct modulation fiber-optic link with 30 dB insertion loss
across an octave bandwidth at L-band (500-1000 MHz) [9].
The maximum dynamic range which can be achieved from a direct modulation link
is limited by the relaxation oscillation frequency of the semiconductor laser diode. The
relaxation oscillation frequency is the rate at which the laser's response to a step in the
modulation current oscillates before settling (or "relaxing") at its final value. The
oscillation shows up as a modulation of the output optical power unrelated to the intended
modulation signal, and the amplitude of this noise is maximum at the relaxation oscillation
frequency. To minimize the noise figure and maximize the dynamic range of a direct
modulation link, it is best to use a laser diode with a relaxation frequency that is much
greater than the maximum frequency at which the laser is to be modulated. For state-ofthe-art multiquantum well lasers, maximum relaxation oscillation frequencies of 18-24 GHz
have been measured [16].
Fiber-optic links using directly modulated semiconductor lasers have exhibited
acceptable noise figures and high dynamic range at lower microwave frequencies. Wanuga
et al., for example, measured a noise figure of 31 dB and a 72 dB^MHz2^ spurious-free
dynamic range for a direct modulation link operating across a 15% bandwidth at 2 GHz
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21
[7]. At higher microwave frequencies the laser noise generally increases and the gain
decreases somewhat, resulting in narrower dynamic range.
Table 2.2 summarizes the advantages and disadvantages of the direct modulation
technique. The table also compares these findings to parallel trends in fiber-optic links
employing the external modulation technique described next
External Modulation
In an external modulation link [Fig. 2.2(b)], an optical source (such as a
semiconductor LED, semiconductor laser diode, or diode-pumped solid-state laser)
generates a constant-level lightwave signal that is mode-coupled into an optical waveguide.
Modulation of the optical carrier is achieved via an external modulator placed upon the
optical waveguide, which electronically controls one or more properties of the waveguide
to impose an RF modulation signal upon the light therein.
In an electro-optic modulator, the Pockels effect is exploited in order to induce a
change in the optical waveguide's refractive index proportional to the applied electric field
intensity. The electro-optic effect thus enables phase modulation of the optical carrier. To
convert the phase modulation to amplitude modulation, a number of different techniques,
involving different configurations of the electronic and photonic waveguides, have been
demonstrated. Described in section 2.5.3 are three such approaches— polarization,
interferometric, and directional coupler electro-optic modulators. Another phenomenon
sometimes used to achieve external modulation is the Franz-Keldysh effect, in which the
absorption coefficient of a partially absorptive optical medium is changed electronically. In
an electro-absorption modulator, such exploitation of the Franz-Keldysh effect results in
modulation of the amplitude of an optical carrier.
Most external modulation links reported in the literature have used interferometric
electro-optic modulators fabricated in LiNbC>3 or GaAs [17-20]. For these and other
electro-optic external modulators the relationship between the optical output power and the
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Advantages
Direct Modulation
External Modulation
Table 2.2
Disadvantages
Simpler Architecture—Fewer
components necessary, lower cost
Larger minimum noise figure
Smaller components than those
necessary for external modulation link
Dynamic range limited by high noise
figure
Lower noise figure than possible with
direct modulation when solid-state laser
is optical source
More complex architecture—more
components required, higher cost
Higher dynamic range than possible
with direct modulation
Low noise figure achieved only with
solid-state laser (larger and more
expensive than semiconductor lasers)
Comparison of the expected performance of fiber-optic links—direct modulation of a semiconductor laser vs.
external modulation of a high-power solid-state laser with a Mach-Zehnder interferometric modulator.
to
to
23
applied voltage V m may be represented as shown in Fig. 2.4, where Pin,op is the
unmodulated optical power available at the electrodes of the modulator and Vn is the
voltage required for 100% modulation. Vm is generalized as an RF modulation voltage of
amplitude vm and frequency f applied to a DC bias voltage Vb- It is convenient to define
Vb=0 as the quarterwave bias point (where the output power is half the maximum and the
power-vs.-voltage relationship is most linear), so that the relationship in Fig. 2.4 can be
expressed as follows:
(2.7)
where
VM = Vb + vm sin to t,
(2-8)
and to = 2 t: f.
In an external modulation link the modulation efficiency, and hence the microwave
gain, depends upon the strength of the effect employed to modulate the light. When
exploiting the electro-optic effect, efficiency is dictated by the electro-optic coefficient of the
modulator material—that is, how much the refractive index of the waveguide changes for a
given electrical potential applied across it.
Equation 2-7 shows that to achieve maximum microwave efficiency it is also
important to have a very high-power optical source. Using LiNbC>3 interferometric electro­
optic devices to modulate high-power solid-state Nd:YAG lasers has produced narrowband
microwave fiber-optic links with high microwave gain. Betts et al. [17] reported 11 dB of
gain for such a fiber-optic link optimized for narrowband (<10% bandwidth) operation at
60 MHz . A microwave gain of 6.4 dB was achieved for a similarly constructed
narrowband link at 900 MHz [21]. Larger band widths at low frequencies have been
achieved at the cost of dramatically reduced performance due to the resistive matching
technique employed in matching the lumped-element modulator’s high RF impedance to 50
£2. External modulation at higher microwave and millimeter-wave frequencies often
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Optical Power Output P
in,op
*
= P.
opt,ext
in,op
, * V1
i
2 V
Electrical Voltage Input VM (Volts)
V = V, + vwsin cot
vm
Figure 2.4 Optical power output vs. electrical voltage input relationship for Mach-Zehnder interferometric electro-optic modulator.
to
4^
necessitates using a traveling-wave type modulator, which is inherently a broaderbandwidth device (as is discussed in section 2.5.3). A modulator with such a travelingwave electrode structure was used by Betts et al. to achieve an external modulation fiber­
optic link with 35 dB of insertion loss at 20 GHz [20].
As is true for direct modulation links, the largest contribution to signal-to-noise
ratio degradation in an external modulation link is usually the noise from the optical source
that falls within the microwave or millimeter-wave passband of the link. At most
microwave and millimeter-wave frequencies, the solid-state lasers that can be used as
optical sources in external modulation links have much lower noise output than
semiconductor laser diodes. Thus the available dynamic range is generally larger for
external modulation links than for direct modulation links, especially at frequencies near the
relaxation oscillation frequency of a semiconductor laser. Some microwave fiber-optic
links that use an LiNb0 3 external modulator to modulate the light from a high-power solidstate laser have demonstrated very broad dynamic range. Betts et al. achieved spuriousfree dynamic ranges of 71 dB^MHz2^3 and 68 dB^MHz2^3, respectively, for their 60 MHz
and 20 GHz narrowband external modulation links [17,20].
Table 2.2 shows a comparison of the performance expected from direct and external
modulation links. This comparison will be updated in Chapter 5 of this work after the new
link performance models have been presented, proven valid over the frequency ranges in
question, and used to predict the performance of links using next-generation photonic
components.
2.3
Detection Techniques
Detection in fiber-optic links is usually accomplished in the depletion region formed
at the reverse-biased junction of the p- and n-doped layers of a semiconductor diode, in
which an electron-hole pair is generated for each absorbed photon. In section 2.5.4 of this
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chapter, devices for performing optical detection are compared.
Three detection
architectures being investigated for current and/or future use in microwave fiber-optic links
are briefly discussed in this section of the literature review.
Direct (Intensity) Detection
In the direct detection architecture, a photodetector receives a stream of incident
photons (the optical carrier) that has been intensity-modulated with a microwave or
millimeter-wave signal, and converts it into a stream of electrons (current) modulated by the
same signal. The direct detection configuration is sometimes called intensity detection
because the amplitude of the photocurrent is proportional to the intensity of the incident
photons. In the sense that the incoming signal has an amplitude that is varying with the
microwave frequency (which is slow compared to the optical frequency), the phase of the
microwave output signal is preserved; however, the optical phase is not preserved in a
direct detection link. All incident optical carrier noise is also converted to photocurrent
when direct detection is employed; therefore, any noise which falls within the optical
receiver’s microwave or millimeter-wave spectral bandwidth will adversely affect the link’s
output signal-to-noise ratio.
Microwave Interferometric Detection
A number of researchers [22-25] are pursuing a microwave interferometric
detection technique which uses a balanced receiver to reject excess optical noise. This
method, shown in Fig. 2.5 (after Madjar and Malz [23]), could allow perfect cancellation
of the intensity noise generated by the optical source, resulting in decreased noise figure
and increased dynamic range compared to external modulation links employing direct
detection. As shown in the figure, optical power from a laser is divided equally between
two fibers by means of an optical power divider. In one of the fibers the light is not
modulated, while in the second branch an optical modulator is used to impress the RF
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Laser
Optical
Power
Divider
Optical
Detector
RF Out
RF In
Optical
Modulator
Optical Transmit Module
o
Optical
Detector
Optical Receive Module
Figure 2.5 External modulation link architecture employing a balanced receiver for cancellation of the laser's RIN (after [23]).
signal upon the optical carrier. The receiver uses two identical optical detectors. The
output signals of the two detectors feed into an RF combiner, where the quadrature
arrangement causes optical noise from the two detectors to interfere destructively at
microwave frequencies. Optional amplitude and phase adjusters facilitate equalization of
the insertion loss and delay in the two branches.
It is important to note that to achieve substantial laser noise cancellation using this
architecture, the amplitude of the optical carrier must be substantially similar in the two
paths, and any delay difference between the two paths must be very small compared to the
microwave signal period (not the optical carrier period, which would require much more
strict control). Under ideal balancing conditions the output of the first optical detector is
proportional to the laser noise, while the output of the second detector is proportional to the
sum of the RF signal and the laser noise. Thus, the out-of-phase combiner cancels out the
laser's noise contribution, and the output of the balanced receiver consists of the
microwave signal, thermal noise, and the shot noise generated by the two uncorrelated
photodetectors.
Ideal balancing conditions are always difficult to maintain because of environmental
effects on the components. To compensate, Madjar and Malz included amplitude and phase
adjusters in their recommended link architecture. They showed analytically that to achieve
20 dB reduction of the laser's relative intensity noise, either amplitude balancing of ±0.5
dB with perfect phase balance or perfect amplitude balance with ±6 degrees of phase
balance is required [23].
By combining the two complementary outputs of a Y-fed coupler electro-optic
modulator in a balanced receiver optimized for 900 MHz operation, a fiber-optic link noise
figure of 13.5 dB was demonstrated at this frequency [25]. This is among the lowest
published noise figure measurements for a fiber-optic link at any frequency, and is an
improvement of almost 10 dB relative to any result at or above this frequency. Figure 2.6
shows the architecture of this link, which is similar to the one described by Madjar and
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Malz, except for the use of a Y-fed coupler modulator in place of the optical power divider
and single-output modulator combination. The balanced receiver module in this link uses
identical reverse-biased p-i-n photodiodes to convert the two incoming optical intensity
noises to identical photocurrents. Thus the correlated optical intensity noise photocurrents
are equal in amplitude but 180° out of phase at their connection point, where they interfere
destructively. To prevent the modulation from canceling (along with the optical noise) in
the balanced receiver, the optical carriers in the two fibers are RF-modulated 180° out of
phase relative to one another using a Y-fed balanced bridge electro-optic modulator. In one
output fiber of this modulator, there is no phase difference between the modulated light and
the input RF signal; in the other output fiber, an RF phase shift of 180° (re radians) is
incurred. Therefore, the two components of the signal interfere constructively at the
connection point in the balanced receiver. As in the Madjar-Malz configuration, the output
of this balanced receiver consists of the microwave signal, thermal noise, and the shot
noise generated by the two uncorrelated photodetectors.
Optical Interferometric Detection
If care is not taken to maintain adequate optical signal amplitude throughout the
fiber, it may be difficult for an optical receiver employing the direct detection technique to
distinguish the optical signal from its own noise floor, which is set by the thermal and
quantum (shot) noise of the detector and any amplifiers in the receiver. Signal sensitivity
can be improved by 10 to 20 dB or more using a coherent optical detection configuration
[26], which interprets both the intensity and the phase of incoming optical carrier. In an
optical receiver designed for coherent detection, a local oscillator generates a continuous
signal at or close to the carrier frequency of the received optical signal. This technique was
designed to increase the maximum length of a fiber-optic link and thereby minimize the
number of repeaters necessary; it may, however, also serve to improve the performance of
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Optical
Polarization
Controller
Nd:YAG
Laser Source
O O)
C C S
RF In
Optical Transmit Module
p-i-n Photodiode
p-i-n Photodiode
Impedance
Matching
Circuit
RF Out
Balanced Receiver Module
Figure 2.6 Alternative external modulation balanced receiver link architecture which minimizes noise figure by combining the two
complementary outputs of a Y-branch electro-optic modulator in such a way that the signal power is increased while the
detrimental effect of the optical noise is wholly or partly negated.
the short-haul fiber-optic links in optical beamformers for phased arrays, which can often
introduce up to 20 dB of optical attenuation [27].
In a homodyne detection receiver, where the LO and received signal are tuned to the
same frequency, the local semiconductor laser oscillator must lock onto the phase of the
incoming signal, necessitating an optical phase-locked loop. By mixing the weak received
field with a local oscillator field, the detected signal can be sufficiently increased and
filtered so that noise in subsequent amplification becomes negligible and the physical limit
of detectability (i.e., shot noise) can be approached.
A heterodyne system tolerates a difference between the incoming signal and LO
frequencies. It therefore does not offer as large an improvement in sensitivity over direct
detection as homodyne detection does, but it is less complex than homodyne detection in
that it does not require locking of the LO phase to the received signal phase. Heterodyne
detection does still require, however, that the receiver include a highly stabilized low-noise
oscillator, which is not needed for direct detection.
The extra componentry required for homodyne or heterodyne detection techniques
dictates an increased cost for a fiber-optic link employing either of these coherent detection
architectures. Furthermore, the success of these techniques depends on maintaining a very
high degree of temperature stability throughout the fiber-optic links. Because the current
trend in fiber-optic link development is a focus on the reduction of cost without loss of
performance, interferometric detection techniques have not generally been considered for
the links that comprise an optical phased array backplane interconnect The fiber-optic link
models set forth in this thesis therefore only apply for the case of direct (intensity)
detection.
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2 .4
Fiber-optic Link Performance Optimization Techniques
Before the state of the art in fiber-optic link device technology is examined in a later
section of this chapter, in this section some widely used techniques for improving the
microwave and millimeter-wave performance of fiber-optic links are reviewed.
2.4.1
RF Impedance Matching Techniques
It is important to match the microwave impedance of the optical source (in a direct
modulation link) or modulator (in an external modulation link) and the optical detector to
the system impedance—usually 50 £2—in order to minimize reflections of RF power at the
link input and output. RF reflections reduce the link’s signal-relaying efficiency and may
also hamper the performance of any pre- or post-link signal-processing components
(mixers, amplifiers, phase-shifters, etc.).
Obviously, to pursue this performance optimization approach one must first know
the impedance of a device at the frequencies at which matching to 50 £2 is going to be
attempted. Since it is usually not possible to connect an optical source, modulator, or
detector directly to the ports of a microwave network analyzer, the transducers' microwave
impedance must first be extracted from the measured one-port scattering parameters of the
test fixtures in which they are housed. Measurement of a device's microwave one-port
scattering parameter using a network analyzer requires the interposition of a bias tee, an RF
connector, and a length of microstrip or coplanar transmission line. The two-port circuit
parameters of each of these intermediary components are thus em bedded within the
measured one-port S-parameters of an electro-optic device in such a test configuration. The
two-port circuit parameters of each intermediary element must therefore be determined and
subsequently de-embedded from the measured scattering parameter values in order to
recover the true scattering parameter of the device.
Standard through-reflect-line (TRL) methods [28] have been used to repeatably
determine the two-port circuit parameters of intermediary components. Figure 2.7 shows
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Test Fixture for Measurements
Electro-optic Device
RF Connector
X
Connector Network
Bias Tee
Device Test Fixture
n
n
^ Device
Measured
Calculate Tj^^as follows:
i + r,Device
l + r Measured
1 “ ^M easured
1
AB
x [ " l
X
,CDjbiaste [CDJ, onnector C D pi
a b
I
1 * ^Device
1
Figure 2.7 De-embedding to determine an electro-optic device's reflection coefficient
^Device ^rom measured reflection coefficient rM
easured. Two-port
voltage-current transmission matrices of the intermediary elements (bias
tee, connector, and transmission line) can be obtained using the ThruReflect-Line (TRL) technique (after [28]).
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how the voltage-current transmission matrices (ABCD matrices [29]) of the intermediary
elements are de-embedded from the measured reflection coefficient of a semiconductor
device in its fixture (TMeasured) to obtain the device's true reflection coefficient (JDevice)Once a device's microwave scattering parameter has been de-embedded from
measured data, a physically realistic equivalent circuit model is developed. To transform
the device's microwave impedance to 50 £2, an impedance-matching circuit must be
designed to combine the circuit elements of the device's model with external elements in
such a way that the dominant resistive element in the device's equivalent circuit is matched
to 50 £2 over the desired frequency band.
Resistive Matching
Since the dominant resistive elements in the equivalent circuit model of most
electro-optic transducers (semiconductor LEDs or lasers, lumped-element external
modulators, or photodetectors) usually have values less than 50 £2, a common practice has
been to add a resistor in series such that the total is 50 £2. Resistive matching accomplishes
a minimization of reflections over a broad RF bandwidth, but only at the expense of
reduced efficiency. That is, a large fraction of the RF power in the link is dissipated in the
matching resistors) rather than being delivered to the link output. In the transmitter of their
2-4 GHz analog link, Bechtle and Siegel employed a 47 £2 resistor in series with the laser
diode in order to resistively match it to the 50 £2 system over a broad bandwidth. This
minimized reflections, but the dissipation of power in the resistor led to a 12 dB increase in
insertion loss. No attempt was made to impedance match in the receiver [30], so
reflections in their link led to an even greater loss of signal power.
Reactive Matching
Across the chosen range of RF frequencies, impedance-matching circuits can be
designed and constructed using purely reactive elements, which maximizes the link's
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35
efficiency at that frequency. The use of reactive matching networks in the design of the
transmitter and receiver would have resulted in at least 10 dB less loss and a better dynamic
range for the Bechtle-Siegel link [30]. Similarly, reactive matching would have led to
higher dynamic range in the analog link of Pan et a l [31]. Stephens and Joseph improved
the performance of their direct modulation link by reactively matching the laser diode to the
electrical system, and achieved an insertion loss of 36.4 dB and a spurious-free dynamic
range of 44 dB across the 4.1-4.7 GHz band [32]. Furthermore, by employing reactive
matching in both the transmitter and receiver modules, they were able to increase the
dynamic range to 60 dB over the 2.85-3.15 GHz band [33]. These are only a few of many
links for which microwave performance has been improved by replacing resistive matching
circuits with reactive ones [7-14,17-20].
There exists a distinct trade-off between the minimum acceptable return loss in 2min
to be realized and the bandwidth Af over which impedance matching is to be performed.
This compromise is expressed by Fano [34] as follows:
(2-9)
A f Qext
where fo is the frequency at band center and Qext is the external quality factor of the device
to be matched to a 50 £2 system. Fano's rule tells the link designer if the entire desired
bandwidth can be achieved using purely reactive matching networks.
Pseudo-Reactive Matching
If Fano's equation indicates that the desired return loss cannot be achieved over the
full desired bandwidth via reactive matching, pseudo-reactive matching is often a viable
compromise. By adding a small resistive element in series or a large resistive element in
parallel to a device, its quality factor can be reduced by just enough to enable reactive
components to finish the job of fulfilling the return loss and bandwidth criteria of the
impedance matching circuit. Pseudo-reactive matching of the high-Q reverse-biased
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36
photodetector was pivotal in achieving a low insertion loss across an octave bandwidth in
the 500-1000 MHz direct modulation link reported by Daryoush et a l [9].
The models set forth in Chapter 3 of this thesis are valid for direct and external
modulation links in which any of the above-mentioned impedance-matching techniques
(i.e., resistive, reactive, or pseudo-reactive matching) are employed.
Active Matching
Techniques for matching the electro-optic transducer impedances to 50 £2 using
compatible active devices—such as MESFETs, HEMTs, or BJTs—are also currently being
explored for their potential benefit to matching bandwidth and integratability. For instance,
a reverse-biased p-i-n photodetector’s impedance is very similar to the gate-to-source
impedance of a transistor which is often used as a post-detector amplifier. Therefore, a
wider matching bandwidth could be achieved if one matched these devices directly to each
other instead of trying to transform both the detector output and post-amplifier input to 50
£2. Active matching thus involves using the MESFET, HEMT, or BJT itself as both an
impedance transformer and a pre- or post-amplifier in a fiber-optic link. Moreover, such
active devices take up less space in a circuit than do passive impedance matching elements.
Models of microwave transistors have been fully developed by other researchers
[35-37]. The link models described in Chapter 3 could accommodate the insertion of any
of these two-port devices between an electro-optic transducer and its 50 £2 microwave
access port. The addition of models for these devices to the fiber-optic link models is
facilitated by the signal flow diagram/cascaded S-parameter foundation on which the fiber­
optic link models rest, as is described in Chapter 3 of this work.
2.4.2
Optical Device-to-Fiher Coupling Techniques
Section 2.4.1 discussed how to maximize the efficiency with which the microwave
signal is coupled to and from the electro-optic devices. To achieve a high-efficiency Fiber­
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optic link, optical source-to-waveguide, waveguide-to-waveguide, and waveguide-todetector coupling efficiencies must also be maximized. Efficient coupling between two
optical fiber waveguides or between a fiber and the optical waveguide in an external
modulator is easily attained if their core sizes and index profiles closely match; otherwise,
one of the device-to-fiber coupling techniques described in this section must be applied in
order to minimize optical losses in the link.
Figure 2.8 illustrates several methods of device-to-fiber coupling. Shown in Fig.
2.8 (a) is the straightforward butt-coupling technique. The numerical aperture of optical
fiber is usually on the order of 0.1. Thus for semiconductor lasers, which have large
maximum output divergence angles (>30°, typically), it is exceedingly difficult to obtain
laser-to-fiber coupling efficiencies as high as 10% using this method, even when coupling
into large-core multimode fiber. To improve this efficiency, Fig. 2.8 (b) and (c) show two
device-to-fiber coupling methods in which very efficient (>50%) optical coupling—even
from a semiconductor laser to a single-mode fiber with an 8 pm core diameter—can be
achieved. A combination of spherical and gradient-index (GRIN) lenses, as shown in Fig.
2.8 (b), or a GRIN lens having a specially curved front facet [Fig. 2.8 (c)], can be used.
In either case, the first convex lens surface collimates the source's divergent output beam
and the cylindrical GRIN lens focuses this collimated beam down to the fiber spot size
gradually so that most light enters the fiber core at angles which can propagate via total
internal reflection in the fiber.
Shown in Fig. 2.8 (d), (e), and (f) are three techniques which use micro-etched
fiber tips to increase the efficiency of the butt-coupling technique. These techniques can
yield coupling efficiencies as high as the external lens techniques shown in Fig. 2.8 (b) and
(c), but they have the advantages of requiring less space, fewer components, and fewer
surfaces from which undesirable reflections can occur.
Fig. 2.8 (d) shows a technique in which the fiber's cladding region is tapered
gradually away such that the outer diameter at the tip is equal to the core diameter. The
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38
Electro-optic
Device _ _
Optical Fiber
Cladding
Core
Cladding
Active Region
Electro-optic
Device
Cylindrical Gradient Index Lens
Spherical Lens
Optical Fiber
Cladding
Core
Cladding
Active Region
Electro-optic
Device
Cylindrical Plano-Convex
Gradient Index Lens
Optical Fiber
Cladding
Core
Cladding
Active Region
(C)
Optical Fiber
Electro-optic
Device _ _
Cladding
Core
Cladding
Active Region
Optical Fiber
Electro-optic
Device ___
Cladding
Core
Cladding
Active Region
Electro-optic
Device .___
Optical Fiber
j
Cladding
Core
^ Cladding
Active Region
Figure 2.8 (a) Butt-coupling technique for device-to-fiber optical power coupling.
(b) Optical coupling via a combination of spherical and GRIN lenses.
(c) Optical coupling via a single plano-convex lens which approximates the
function of a spherical and GRIN lens combination.
(d) Optical coupling via a tapering of the fiber's cladding.
(e) Optical coupling via a hemispherical microlens formed at the fiber tip.
(f) Optical coupling via a hemispherical microlens formed at the tip of a
lengthened core region.
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effective numerical aperture of the fiber is thus gradually increased and thus the tapered
fiber can accept light from a wider range of input angles relative to the core axis. Optical
coupling to a tapered fiber end is more position-sensitive, however, than when an
ordinarily cleaved fiber end is butt-coupled to a device.
A hemispherical microlens formed at the fiber tip magnifies the core so that more
optical power can be coupled into it in a less position-sensitive manner. This configuration
is shown in Fig. 2.8 (e). Optical coupling to a single-mode fiber using a hemispherical
microlens is quite angle-sensitive and is limited to about 30%.
If, however, the
homogeneous core region is lengthened to effectively place the edge of the regular coreand-cladding fiber at the focal plane of the microlens [as shown in Fig. 2.8 (f)], the
coupling efficiency can be increased to 54% [38].
At the fiber-detector interface, any of these same techniques can be used to improve
coupling efficiency, although in the case of a single-mode fiber and a 25-, 35-, 50-|i.m or
larger detector active area diameter, nearly 100% coupling efficiency can be obtained using
the straightforward butt-coupling technique.
Optical coupling efficiency throughout a fiber-optic link is also improved if all
boundaries at which reflections can occur are coated with transparent materials that have
dielectric constants selected to minimize reflections. Minimizing optical reflections
throughout the link is vital not only from an efficiency standpoint, but also because of the
effect of optical feedback on laser performance, as is discussed in the following section.
2.4.3
Optical Feedback Isolation Techniques
Optical feedback arises from any and all optical reflection points in the link,
including those at the fiber-air, fiber-fiber, and detector-air interfaces, as well as at the faces
of any lenses used to couple light between fibers and devices. Optical power reflected back
into the laser cavity (from fiber endfaces at either end of the link and in connectors) couples
with the lasing modes, thereby causing their phases to vary. This produces a modulated
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40
noise spectrum with periodicity determined by the roundtrip delay of the light from the laser
to the reflecting point and back again. Depending on this roundtrip time, reflections can
create noise peaks in the microwave or millimeter-wave frequency region where the link is
intended to have low noise [39].
Distributed feedback (DFB) lasers, which are described in the next section of this
chapter, are especially sensitive to reflections. Lasing action in DFB lasers is not achieved
using reflective surfaces and therefore reflections set up an unwanted Fabry-Perot cavity,
creating optical feedback in competition with the optical feedback the device was designed
to set up for itself.
There are several techniques which have been widely used to minimize the amount
of optical power reflected back to the optical source in the link. One of these techniques
involves depositing anti-reflective coatings on the lens and detector surfaces. Additionally,
at fiber-air-fiber interfaces index-matching gel can be used to minimize Fresnel reflections.
Minimizing the optical feedback from fiber-air interfaces involves cleaving or
polishing the fiber endface at an angle sufficiently large relative to the axis normal to ensure
that any reflected light will be deflected at too great an angle to propagate back to the optical
source.
In cases where any or all of the above techniques provide inadequate protection for
the optical source, a miniature optical isolator is sometimes used between the optical source
and the fiber. This device consists of two linearly polarizing waveplates at either end of a
Faraday rotator. The Faraday rotator consists of a rod of magneto-optic material with its
ends polished flat and parallel. The rod is configured adjacent to a magnet such that the
lines of magnetic flux are along the axis of the rod and thus parallel to the direction of the
light propagation. By virtue of the Faraday effect, plane-polarized light entering the
magneto-optic material is rotated as the light propagates through the rod. Figure 2.9 shows
how such an isolator works. In forward mode [Fig. 2.9 (a)], light entering the input
polarizer becomes linearly polarized. This polarized light enters the Faraday rotator, which
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45
45
Forward
" Mode
►
Input
Polarizer
Output
Polarizer
Faraday
Rotator
(a)
45
90
90
/
Reverse
Mode
Input
Polarizer
Output
Polarizer
Faraday
Rotator
(b)
Figure 2.9 (a) Optical isolator forward mode. Light entering the input polarization filter becomes linearly polarized in the vertical
plane at 0°. This vertically polarized light then enters the Faraday rotator, which rotates the plane of polarization 45°
clockwise so that it can exit the output polarization filter.
(b) Optical isolator reverse mode. Retropropagating light becomes polarized at 45° upon passing through the output
polarization filter. The light then enters the Faraday rotator, which rotates the plane of polarization 45° clockwise so
that it will be completely extinguished by the input polarizer.
rotates the plane of polarization clockwise by 45°. The light then passes through the output
polarizer, which has a transmission axis at this same 45° angle relative to the input
polarizer. In the reverse mode [Fig. 2.9 (b)]» light reflected from a point further along in
the link becomes polarized at the 45° angle of the output polarizer when entering the
isolator. The light then passes through the Faraday rotator, which causes another 45° of
polarization rotation, still in the clockwise direction [40]. The light is now polarized at 90°
relative to the input polarizer and therefore cannot get through i t Devices of this type
routinely provide reverse isolation of -20 to -30 dB with forward optical insertion loss on
the order of 1 dB [41].
2 .5
Electronic and Photonic Devices fo r Fiber-optic Links
From the discussions of available modulation and detection techniques (sections 2
and 3 of this chapter), it is apparent that optical fibers, optical sources, modulators, and
photodetectors all need to be investigated with regard to maximizing the efficiency and
linearity of a fiber-optic link while minimizing the noise. Within each category of devices,
the types of these components that should be modeled—that is, those that are most likely to
yield the best link performance—will be identified in this section of the literature review.
Also included in this section is a discussion of optical amplifiers. Although they are
not an essential part of the fiber-optic link itself, optical amplifiers seem destined to become
mainstays in many systems—including optical beamformers—requiring signal processing
in the optical domain.
2.5.1
Optical Fibers
In an optical fiber, several important material parameters vary with optical
wavelength. The wavelengths at which optical fibers feature optimum performance have
therefore driven the design of all other components in fiber-optic links. It is for this reason
that they are discussed before the other components.
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One wavelength-dependent phenomenon is attenuation of the optical signal in the
fiber. Attenuation mechanisms in a fiber include absorption, scattering, and radiative
losses of the optical energy. Even for Si02 fibers made using the vapor-phase axial
deposition (VAD) process, in which structural imperfections, density variations, and
impurities (e.g., water and transition metal ions) are minimized, attenuation of less than 1
dB/km occurs only in the 700 nm to 1.80 pm window. At X=1.30 |im, the attenuation in
VAD single-mode glass fibers due to intrinsic absorption is, however, minimal—less than
0.S dB/km.
Optical confinement in fibers results from total internal reflection within a core that
is surrounded by a cladding having a lower refractive index. Therefore, along with the
optical wavelength used, the fiber's refractive index profile also determines many of its
waveguiding properties. One such property is signal distortion due to dispersion effects in
the fiber. Dispersion causes light pulses to broaden in time as they traverse the length of
fiber. After a certain amount of overlap has occurred, adjacent peaks and valleys in the
microwave signal that modulates the optical carrier can no longer be individually
distinguished at the receiver. The signal is thus distorted. Dispersion therefore determines
the limit the information capacity of the fiber, and this limit is expressed as the fiber's
bandwidth-distance product
Dispersion can be either intermodal or intramodal. Intermodal dispersion is a result
of each waveguide mode in the fiber having a different group velocity at any single optical
wavelength [39]. Intermodal dispersion can be a significant limitation to high-frequency
performance. For a step-index multi-mode fiber the various distortion effects tend to limit
the bandwidth-distance product to about 20 MHz-km. In graded-index multimode fibers
the radial refractive-index profile can be carefully tailored to equalize the group velocity of
all optical modes so that pulse broadening due to intermodal dispersion is minimized at a
specific operating wavelength. This has led to bandwidth-distance products as high as 2.5
GHzkm. If the product of the signal frequency and fiber length required for a given link
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exceeds this figure, significant distortion of the signal will be perceived by the receiver if a
multi-mode fiber is used. Therefore, to prevent this distortion single-mode fiber must be
used instead.
A penalty that is paid when choosing a single-mode fiber is the increased difficulty
of coupling optical power into the smaller core of the fiber. The benefit of single-mode
fiber, however, is its bandwidth-length product, which can exceed 100 GHz-km [39].
The desire to operate at very high frequencies has thus led most investigators to employ
single-mode fibers in their optical links.
Intramodal dispersion causes pulse spreading even within a single mode. It is a
result of the group velocity being a function of the wavelength. Signal distortion due to
intermodal dispersion therefore increases with the spectral width of the optical source. For
light-emitting diodes the spectral width is typically about 5 percent of the central
wavelength, whereas laser optical sources have much narrower spectral widths (due to
greater spectral coherence), with typical values of 1 to 2 nm [39]. For most glass single­
mode fibers, the pulse broadening due to intramodal dispersion is quite dramatic near 800
nm (-100 ps/nm-km), smaller around 1.55 |im (-10 ps/nm-km), and zero near 1.30 |im.
For this reason, most fiber-optic links designed for communications at high frequencies
and/or across long distances operate at A,=1.30 or 1.55 |0.m, and it is around these
wavelengths that the development of photonic components (sources, modulators, and
detectors) has recently centered.
The models presented in this thesis will address the use of single-mode fiber only.
Most fiber-optic links for phased-array interconnects will use single-mode optical
waveguides because optical signal processing and beamforming components like optical
amplifiers, modulators and switches operate optimally only when their optical inputs have
only one mode. In the lengths of single-mode fiber used in optical signal distribution and
beamforming systems for phased array antennas, the effects of distortion are negligible and
therefore do not warrant modeling.
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45
2.5.2
Optical Sources
Whether an optical source functions only as a source, as in an external modulation
link, or as both a source and modulator, as in a direct modulation link, large optical power
and low noise are desirable for high-fidelity link operation. These needs are best served
when a laser is used.
The concept of extending maser techniques to the infrared and optical regime was
first documented by Schawlow and Townes in 1958 [42]. Laser action is the result of
three key processes—photon absorption, spontaneous emission, and stimulated emission.
Whereas light is emitted in either of the latter two processes, generation of a coherent light
beam requires that the emitted photons be in phase with one another, which only occurs if
stimulated emission dominates over spontaneous emission. To set up this condition
requires a degree of population inversion. That is, the number of electrons excited to the
conduction energy band must exceed the number remaining in the valence band by a certain
minimum—or "threshold"—amount
Solid-State Lasers fo r External Modulation Links
In an external modulation link, the most logical choice for an optical source is a
high-power fiber-pigtailed laser emitting within the optimum range of optical wavelengths.
The most commonly used lasers in high-performance external modulation links are made
from Nd+-doped YAG material (X=1.06 or 1.30 pm). At microwave and millimeter-wave
frequencies, this type of laser has low relative intensity noise (RIN). RIN is the ratio of the
noise modulating the laser output at some RF frequency to the unmodulated carrier power.
Because of the high efficiency of the absorption process in the Nd+-doped YAG
crystal and the efficiency of the semiconductor diode laser pump source, the overall
efficiency of a diode-pumped Nd:YAG laser can be as high as 15-20%, resulting in high
output power from a relatively small crystal. Optical power levels as high as 75 mW in a
single longitudinal mode and up to 175 raW in multiple modes can be achieved from a laser
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46
that fits into a 2"-diameter cylinder that is 6" in length. Relative intensity noise is generally
very high at the relaxation oscillation frequency (which is usually between 100 kHz and 1
MHz) but is near the shot noise limit (-161 dB/Hz for a detected X=1.30 pm optical power
of 3.5 mW) at microwave frequencies.
The size of a diode-pumped solid-state laser remains a major disadvantage.
Advanced models housed in TO-5 cans are being developed, which will reduce the size
significantly. This type of laser may then be integrated with an external modulator in one
common assembly, enabling smaller and more efficient external modulation fiber-optic
links in the future. For the time being, however, the semiconductor light-emitting and laser
diodes developed for direct modulation links are much smaller.
Therefore, a
semiconductor diode optical source is used in an external modulation link if size is a major
concern, at the expense of reduced optical power output Table 2.3 compares the relative
advantages and disadvantages of various optical sources commonly used in external and
direct modulation links.
Semiconductor Diode Optical Sources
In a direct modulation link, a semiconductor device must serve as both source and
modulator, which makes both modulation efficiency and linearity design concerns, along
with the standard concern of noise. The directly modulated optical source is most often a
semiconductor diode with a bandgap energy corresponding to the optimum fiber
wavelength. Depending on its design, this semiconductor device is called a light-emitting
diode (LED) or a laser diode.
The light-emitting region of both LEDs and laser diodes consists of a p-n junction.
When this junction is forward-biased, electrons and holes are injected into the p and n
regions, respectively. This p-n junction is thus known as the active or recombination
region. The injected minority carriers can recombine either radiatively, in which case a
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Type of Optical Source
Optically Pumped
Solid-State Lasers
Disadvantages
Advantages
High power from laser
Expensive
Low noise at microwave
frequencies__________
Large
Very inexpensive
Low maximum modulation speed
Highly linear
Low efficiency and power output
Easy to fabricate
Significant modal noise
''Semiconductor Diode Optical Sources
Light-Emitting Diode (LED)
Stripe-Contact Ridge Waveguide
Laser
Low RF parasitics
Buried Heterostructure Laser
Most stable optical mode
Large RF parasitics.
Harder to fabricate than ridge laser
Distributed Feedback (DFB) Laser
Single longitudinal mode
Most difficult to fabricate
Low noise
Vertical Cavity Surface Emitting
Laser (VCSEL)
Potential for high speed
Difficult to remove heat
Circular emission pattern for
better optical fiber coupling
Lower output power available
unless array of VCSELs is used
Table 2 3 Comparison of currently available optical sources for direct modulation fiber-optic links.
$
48
photon of energy hv is emitted, or nonradiatively, whereupon the recombination energy is
dissipated in the form of heat [39].
Directly modulated source design goals include high electron-photon conversion
efficiency (quantum efficiency), large maximum optical power, high-frequency modulation
capability, low noise, and small emission beam divergence. The quantum efficiency is
proportional to the fraction of electron-hole pairs injected into the active region that
recombine radiatively. This is maximized by confining the charge carriers to the active
region of the p-n junction where radiative combination is most likely to take place. Optical
confinement also prevents absorption of the emitted radiation by the material surrounding
the junction.
To achieve carrier and photon confinement, semiconductor layer
configurations such as homojunctions and single- and double-heterojunctions have been
widely investigated. The most effective of these predominantly in use at this time is the
double-heterojunction device because of the two different alloy layers on each side of the
active region. Both the carriers and the optical field are confined in the central active layer
by this sandwich structure of differently-composed alloy layers. The bandgap differences
among adjacent layers confine the charge carriers, while the differences in the indices of
refraction of adjoining layers confine the optical field to the central active layer. This dual
confinement leads to both high efficiency and high power radiance [39].
Semiconductor material used for the active layer of optical sources usually have a
direct band gap. In a direct bandgap semiconductor, electrons and holes can recombine
directly across the band gap without needing a third particle to conserve momentum; thus,
only in direct-bandgap material is the radiative recombination sufficiently high to produce
an adequate level of optical emission. Although none of the normal single-element
semiconductors (group IV elements) are direct-bandgap materials, many binary, ternary,
and quartemary compounds are. The most important of these are the so-called IH-V
materials (such as GaAs) and various ternary and quartemary combinations of the binary
compounds (such as AlGaAs and InGaAsP, respectively) [39].
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Fiber characteristics such as attenuation and dispersion drive the choice of
semiconductor material for high-efficiency and low-noise potential. As mentioned in
2.5.1, loss and dispersion in a single-mode fiber are lowest at the 1.30 and 1.55 p.m
wavelengths. Consequently, high-frequency semiconductor light-emitting and laser diode
development in recent years has focused on InGaAsP-based devices.
Semiconductor Light-Emitting Diodes
In a semiconductor LED, photons are emitted when electrons in the conduction
energy band spontaneously decay to the valence energy band. The two basic LED
configurations being used for fiber-optics are surface emitters and edge emitters. In the
surface emitter the plane of the active light-emitting region is oriented perpendicularly to the
axis of the fiber.
In surface-emitting LEDs, although the gain coefficient is high under normal
driving conditions, the light is emitted from the active layer with a short—0.5 to 1.0 pm—
trip through the gain medium. Surface-emitting LEDs provide an output power of 1 to 2
mW for a 25 |im diameter active area at a driving current of 50-100 mA. They provide a
larger tolerance on fiber alignment than edge-emitting LEDs and lasers, and are therefore a
popular source choice for use in short-haul, low-frequency (<100 MHz) links.
In contrast, the light in edge-emitting LEDs experiences a much longer path of 150
to 300 p.m. The edge emitter consists of an active junction region, which is the source of
the incoherent light, and two guiding layers. The guiding layers both have a refractive
index which is lower than that of the active region but higher than the index of the
surrounding material. This structure forms a waveguide channel that directs the optical
radiation toward the fiber core.
Because of the larger region in which spontaneous emission is encouraged by the
forward bias, the output power of edge-emitters can be much higher than that of surfaceemitters [43]. Although optical feedback in edge-emitting LEDs is suppressed so that laser
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oscillation is prevented, super-luminescence or amplified spontaneous emission may occur.
In LEDs no lasing threshold is present, and the light output increases monotonically with
increasing current up to a large maximum. This gives edge-emitting LEDs a linearity
advantage over surface-emitting LEDs and some laser diodes.
As highlighted in Table 2.3, there are many reasons why neither type of
semiconductor LED is selected as the optical source in a high-performance fiber-optic link
for microwave signal feeds in a phased array antenna. The frequency response of an LED
is limited by its diffusion capacitance because of the storage of injected carriers in the active
region of the diode [39]. In addition, the LED’s maximum optical output power and
quantum efficiency are both much lower than in a semiconductor laser, in which photons
stimulate the emission of more photons. Moreover, because of the random phase
(incoherency) of spontaneously emitted photons, both the spectral linewidth and angular
beamwidth are much broader for an LED than for a laser, which makes fiber coupling
difficult and increases the dispersion effects in the fiber. Understandably, then, LEDs are
generally not used for direct modulation at frequencies above 100 MHz, although this limit
can be extended somewhat by optimizing the device and drive circuit
Semiconductor Laser Diodes
In a semiconductor laser the necessary population inversion is achieved by injecting
electrons into the material at the device contacts to fill the lower energy states of the
conduction band. The required feedback is achieved by creating a Fabry-Perot cavity or by
distributing the feedback along the length of the active region using a refractive or acoustooptic grating, as will be described later in this section. Strong confinement of both the
charge carriers and the optical wave to a well-defined active region helps maintain the
population inversion.
At low forward bias currents only spontaneous radiation is emitted, and thus both
the spectral range and the lateral beam width of this emission are broad like that of an LED.
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51
A dramatic and sharply defined increase in the power output occurs at the lasing threshold.
As this transition point is approached, both the spectral range and the emitted beam width
narrow, and the rate at which emitted optical power increases with respect to increasing
forward bias current becomes much larger. Above the threshold for stimulated emission
the carrier lifetime in a laser is very short (thus allowing high modulation rates), the spectral
emission narrows, the beam becomes more directional, and the external quantum efficiency
is high [44].
As far as material choices for high-performance semiconductor lasers are
concerned, GaAs and the related ternary and quartemary III-V compounds were the first
direct-bandgap semiconductors to successfully lase, and thus have undergone the most
development.
Other attractive properties of these materials are their emission
wavelengths—which fall within the 700 nm to 1.80 (im window for low-loss transmission
in an optical fiber—and their compatibility with GaAs MMIC manufacturing.
To achieve low threshold current, which is vital for power-efficient, low-noise, and
high-linearity operation of a Fabry-Perot semiconductor laser, a heterojunction is used
rather than a homojunction for carrier and photon confinement in the transverse dimension.
A viable heterojunction is formed by joining two layers of semiconductors with equal lattice
constants but differing bandgap energies. Whereas the threshold current density is quite
high in a homojunction diode laser (-100 kA/cm2 for GaAs), heterojunction devices feature
threshold current densities that are as low as 4 kA/cm2, making CW operation possible at
room temperature. The reduced threshold in a heterojunction device appears because the
different alloys that comprise the transverse layers have significantly different refractive
indices, providing an optical waveguide structure that increases the probabilities for both
stimulated emission and absorption, while reducing photon leakage from the active region.
Additionally, the bandgap of the inactive region's material is different, so that there is no
positive feedback to stimulate emission anywhere but in the active region. Thus, in
heterojunction devices the gain is strictly confined to the active region [44].
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For efficient and low-noise operation of a semiconductor laser-based fiber-optic
link, single-mode operation of the laser is sought The lateral modes in an edge-emitting
semiconductor laser depend upon the dielectric profile in the plane of the junction and thus
upon the technique used for definition of the junction area. If the width of the constricted
region is sufficiently narrow, high-order modes cannot reach threshold and the result is a
mode-stabilized laser. The boundaries of the active region in the lateral direction can of
course be formed by etching. However, they are better defined using stripe contacts,
enabling a narrower active region which supports only a single mode and concentrates the
output beam to a smaller radius, thereby improving the maximum achievable laser-to-fiber
coupling efficiency. Furthermore, the existence of inactive material beyond the lateral
boundaries of the active region fosters the dissipation of heat generated by inevitable
nonradiative carrier recombinations, thus improving the device's reliability. Stripe-contact
ridge-waveguide lasers of this type have the additional advantages of easy fabrication and
low RF parasitics, with the major disadvantage being modal noise. These features are
listed in Table 2.3.
While the stripe geometry defines a region of high gain within which the electronhole recombination is effectively confined, constriction of the resulting optical radiation is
even more thoroughly accomplished by creating a "buried heterojunction" in the lateral
dimension. Here, the active region is enclosed laterally by an inactive region of a different
material which not only forms a dielectric step that produces strong guidance of the optical
radiation similar to that within a single mode fiber, but also confines the electrons and holes
by establishing a step in the energy band gap [45]. As listed in Table 2.3, buried
heterostructure lasers have lower threshold currents and a more stable optical mode at high
output powers, with the disadvantages of more complex fabrication and larger RF
parasitics.
The introduction of the quantum size effect into the Fabry-Perot laser active medium
has enhanced the differential gain factor and increased the modulation bandwidth of buried-
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heterostructure lasers [46-48]. In single-quantum-well (SQW) lasers, the active layer is
one stack of thin (-10 nm) low-bandgap layers sandwiched between higher-bandgap
barrier layers. Multi-quantum-well (MQW) devices have demonstrated higher efficiency
out to high frequencies, with the addition of a strained layer to the quantum well structure
yielding even higher frequencies at which this high efficiency is maintained [49-51]. Lester
et aL [16] have fabricated lasers with graded-index separate-confinement heterostructure
(GRINSCH) multiquantum wells, resulting in a measured relaxation oscillation frequency
of 18 GHz and a 23.5 GHz 3-dB bandwidth.
Impressive performance has also been demonstrated by applying these quantumwell buried-heterostructure active region designs to a laser where feedback is not achieved
using reflective facets. In distributed-feedback (DFB) lasers, lasing action is achieved by
means of periodic variations of the refractive index and/or active layer thickness
incorporated into the multilayer structure along the longitudinal direction of the chip, similar
to the effective grating caused by an acoustic standing wave in a Bragg cell. This structure
exhibits nearly complete suppression (30 dB in a typical DFB) of all but a single
longitudinal mode. Because of the reduced opportunity for beating of two or more optical
frequencies, DFBs generally exhibit lower noise and higher linearity at microwave
frequencies. These advantages are delineated in Table 2.3.
Recently there has also been increased interest in vertical cavity, surface-emitting
lasers (VCSELs), which create an optical beam that is nearly circular and can therefore be
coupled to an optical fiber more easily for higher efficiency [52-56]. Another major
advantage of VCSELs compared to edge-emitting lasers is that they can be more easily
integrated into MMICs than edge-emitting lasers, which typically must be cut from a wafer
and soldered or epoxied to the edge of an optical transmitter circuit.
Geels and Coldren at UC Santa Barbara incorporated wavelength-selective
distributed Bragg reflector (DBR) mirrors on the facets of a VCSEL active region
composed of three 8-nm InGaAs quantum wells separated by 10-nm GaAs barriers in a
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cavity having a width of one wavelength. They achieved 2 mW of output power for a 6
|im x 6 pm device with a threshold current of 0.5 mA [57].
Most commercially available semiconductor lasers are edge-emitting devices which
achieve optical feedback by virtue of either a Fabry-Perot or a distributed-feedback
longitudinal structure. The direct modulation link model discussed in Chapter 3 of this
work will therefore be most applicable when one of these devices is used as the optical
source, but the model is also valid for each of the other types of optical sources listed in
Table 2.3.
2.5.3
RF/Optical Modulators
In an external modulation link the design of the modulator is critical. The chief goal
is to achieve high-efficiency and linear RF modulation at the frequencies of interest. High­
speed routing of an optical beam from one path to another can be accomplished by
electronically controlling one or more properties in an optical waveguide. Table 2.4
compares the performance of several types of devices which exploit different phenomena to
modulate light
Electro-optic Modulators
Most commercially available external modulators are electro-optic modulators,
which use the linear electro-optic (Pockels) effect to induce a refractive index change
proportional to the applied electric field intensity in the optical waveguide. The electro­
optic effect because it alters the refractive index, allows the microwave signal to modulate
only the phase of the optical carrier. To convert this to intensity modulation an additional
process must occur in the modulator. Table 2.4 compares three different phenomena that
have been leveraged to result in optical intensity modulation in an electro-optic modulator.
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Type of Modulator
Advantages
Disadvantages
Most development effort has
concentrated on electro-optic
modulators
Phase modulation needs to be
converted to amplitude modulation
Polarization
High extinction ratio possible
Poor modulation efficiency
Interferometric
Most electro-optic modulator
development effort has concentrated
on interferometric technique
Extinction ratios typically only 20-30 dB
Directional coupler
Reversed Ap design provides high
efficiency
Performance most sensitive to
integrated-optic waveguide length
discrepancies
Straightforward intensity modulation
(requiring no additional manipulation of
signal)
Background material absorption loss at
zero bias
Electro-optic
Electro-absorption
Table 2.4 Comparison of currently available optical waveguide modulators for external modulation fiber-optic links.
It is possible to add polarizing elements to convert electro-optic phase modulation to
intensity modulation. Such polarization modulators usually have their optical waveguide
oriented such that input light is linearly polarized at an angle 45° off the principle axes of the
crystal, creating two equally strong but orthogonal polarizations in the waveguide (TE and
TM modes). After propagating through the modulated portion of the guide, the phases of
the two modes are modulated differently resulting in elliptically polarized light, which can
be converted to an intensity modulation if a polarizing element is added at the output of the
waveguide.
Polarization-selective waveguide modulation of this type has been
demonstrated to high frequencies (>20 GHz), albeit with poor modulation efficiency [58].
One of the most common electro-optic intensity modulator configurations is the
interferometric configuration. In this configuration, the input light is equally divided into
two waveguides. The refractive indices of one or both of these waveguides are modulated
via the electro-optic effect The light from the separate guides is then re-combined, and the
relative phase difference determines the intensity of the coherently combined field, thereby
changing phase modulation in the interferometer arms to intensity modulation at the output
Another type of electro-optic modulator is the directional coupler modulator, which
uses the electro-optically induced index change to alter the waveguide propagation constant,
thus affecting the phase match between two evanescently coupled waveguides. With no
applied bias, the device is arranged so that light in one waveguide couples completely via
evanescent mode interaction into the other waveguide. When fully biased the propagation
coefficients in the two waveguides are sufficiently different to inhibit the coupling. Unlike
the interferometric modulator, this directional coupler transfer function is not periodic with
applied voltage and therefore requires an exact tailoring of the coupler length to match the
inter-guide mode coupling coefficient Reversed A{3 directional coupler modulators operate
similarly, but the modulation voltage is applied to one of the two electrodes in two or more
sections with alternating polarity in order to allow for compensation of waveguide length
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errors which often occur in fabrication. Directional coupler modulators are most sensitive
to such errors [59].
Electro-absorption Modulators
Instead of the electro-optic effect, which modulates the refractive index and
therefore requires additional manipulation of the optical carrier before intensity modulation
is achieved, it is possible to modulate the absorption coefficient of a partially absorptive
optical media like GaAs. This phenomenon is the Franz-Keldysh effect, which can be
implemented in an integrated source-modulator on GaAs. There is, however, nonnegligible background material absorption loss at zero voltage bias. Thus there have been
only a few reports of high-frequency modulation exploiting this effect [59]. Moss et al.
estimated from the capacitance of the electrodes of their single-quantum-well GRINSCH
ridge-waveguide electro-absorption modulator that its 3 dB bandwidth would exceed 20
GHz [60], but did not verify this experimentally. Rolland et al. measured a 3 dB
bandwidth of >11 GHz for their InGaAsP (1.30 Jim) electro-absorption modulator [61].
Multi-quantum well structures can also improve the modulation characteristics of
electro-absorption external modulators by enabling high-speed, low-voltage operation
because of the large magnitude of their Franz-Keldysh effect. Kotaka et al. achieved a 3
dB bandwidth of 16 GHz for their InGaAs/InAlAs MQW modulator operating at the 1.55
pm optical wavelength [62].
Most modulator development effort has concentrated on electro-optic devices of the
interferometric and directional coupler types. A goal in electro-optic modulator design is to
maximize the amount of phase shift for a given drive voltage, or equivalently, to minimize
the voltage required for the needed phase shift. A figure of merit for external modulators is
V„, the voltage required to achieve 180° (7t radians) of phase shift In a lumped-element
electrode modulator, this voltage is inversely proportional to the length Le of the electrodes.
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58
High modulation bandwidth is of course desirable as well, and this also scales as 1/Le, so
the trade-off between bandwidth and drive voltage is readily apparent It is usually wise to
use a modulator with the longest electrode length that still permits modulation to the highest
frequency needed, but is too long for modulation at higher frequencies [63]. Acceptable
bandwidth, drive voltage and size can be obtained by maximizing n03 rij» where no is the
optical refractive index and nj is the electro-optic tensor of the substrate material.
Modulator Substrate Materials
Development of commercial electro-optic waveguide modulators has centered
primarily on LiNbC>3. Although LiTa0 3 is similar, process technology for the former
material is much more advanced. To make use of the largest electro-optic tensor (r33,
which has a magnitude of 30xl0*12 m/V), LiNbC>3 devices must be either z-cut and ypropagating (using the TM mode) or x-cut and y-propagating (using the TE mode).
LiNb 0 3 has a refractive index reasonably close to that of glass fiber cores—about 2.2.
Thus the electro-optic effect’s figure of merit is no3-r33=320xl0*12 m/V. For planar
stripline electrodes on LiNb 0 3 , the z-cut effective dielectric constant at microwave
frequencies is 18.1, resulting in a refractive index of 4.25 for the electrodes [59].
GaAs has only one significant electro-optic coefficient tensor, r4 i, with magnitude
1.43xl(H2 m/V—nearly 20 times smaller than that of LiNbC>3. A typical optical refractive
index is 3.4 (at 1.30 |im). Because of the larger index of refraction, GaAs has a fairly
large electro-optic figure of merit no3 r4i=58xl0-12 m/V, only about 5 times smaller than
that of LiNbC>3. The effective stripline dielectric constant is about 7 at microwave
frequencies, corresponding to a microwave refractive index of roughly 2.6 [59].
There’s a trade-off in choosing the material. Ideally, in GaAs the velocities of
optical and RF waves are better matched, imparting greater potential bandwidth; however,
LiNb0 3 is more transparent It is unlikely that present-day LiNb0 3 modulators can easily
be integrated with existing GaAs MMICs. Although GaAs has a smaller electro-optic
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59
coefficient and requires higher microwave drive powers, it has high bandwidth capability
and allows true integration with GaAs MMIC technology.
Another category of materials being investigated thoroughly for use in external
modulators is the wide range of polymer materials. These may prove to have the best
combination of efficiency and bandwidth because their microwave and optical dielectric
constants are within a few percent of one another. Success in this material technology
depends upon rinding a structure with a large electro-optic tensor and thus a workable
trade-off between electrode length and switching voltage.
Modulator Electrode Layout
The potential modulation bandwidth of waveguide modulators depends on the
electrode type and geometry, as well as upon the substrate dielectric constant. For as large
as possible a modulation bandwidth from a lumped-element modulator it is necessary to
keep the capacitance per unit length of the electrodes fairly low, which necessitates a
relatively large electrode gap/width ratio. However, the absolute upper limit to the
bandwidth is the electrical transit time cutoff frequency, so there is no sense in increasing
the gap/width ratio past a certain ratio (about 1 for both LiNbC>3 and GaAs) [63].
Traveling-wave electrode structures do not have this cutoff frequency because the
electrodes are not acting as a capacitor but rather as a transmission line terminated in some
impedance. Instead, modulation speed is limited by the difference between the optical
carrier and RF modulation wavefront velocities. If a phase-reversal technique is not used,
therefore, the optical phase in the waveguide will differ from the RF phase by 180° after a
certain length, resulting in 3 dB of frequency response degradation. Therefore, for any
modulator with electrode length Le the 3 dB bandwidth is given by [64]:
Af3dB = —r—^ = = — - ,
JtPo-V E efflL e
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(2-10)
60
where nQ is the optical refractive index, eeff is the effective dielectric constant of the
transmission line formed by the traveling-wave modulator electrodes, Le is the length of the
electrodes, and c is the free-space speed of light.
Several researchers have demonstrated impressive combinations of large bandwidth
and low switching voltage. Alfemess et al. [65] demonstrated a LiNb0 3 waveguide
traveling-wave modulator with an asymmetric coplanar strip electrode, which operated at
X=1.32 [lm and exhibited a 3-dB modulation bandwidth of 7.2 GHz with a switching
voltage of 4.5 V. Gee et a l [66] demonstrated a traveling-wave type LiNbC>3 modulator
for 830 nm wavelength operation, achieving a 3-dB bandwidth of 17 GHz and a 7 V
switching voltage.
The models set forth in Chapter 3 focus on the lumped-element and traveling-wave
electro-optic modulators of the interferometric Mach-Zehnder type, which is the most
prevalent The modification of this model to account for other types of modulators which
may gain prevalence in future applications is addressed in Chapter 5.
2.5.4
Optical/RF Detectors
At the output end of an optical link there must be a receiving device which interprets
the information contained in the optical signal. A detector senses the optical power incident
upon it and converts the variation of this optical power into a correspondingly varying
electric current. Photodetectors are used in this way for envelope detection of microwave
intensity-modulated optical signals in direct as well as external modulation fiber-optic links.
In normal operation of a photodetector, a sufficiently large reverse-bias voltage is
applied across the device so that the intrinsic region is fully depleted of carriers. When an
incident photon has an energy greater than or equal to the band gap energy of the
semiconductor material, the photon can give up its energy and excite an electron from the
valence band to the conduction band. This process generates free electron-hole pairs
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known as photocarriers. The photodetector is normally designed so that these carriers are
generated mainly in the depletion region where most of the light is absorbed. The high
electric field present in the depletion region due to the reverse bias causes electrons and
holes to separate and be collected across the reverse-biased junction from one another.
This gives rise to a current flow in an external circuit
It is important that the optical detector perform this photonic-to-electronic transition
of the RF signal with high efficiency and low noise over a large linear range of powers.
When selecting a photodetector for high-efficiency, two important characteristics to
consider are its responsivity t|d and its response speed. These parameters are principally
determined by the doping profile and the type of material used in making the photodetector.
Responsivity is directly proportional to the external quantum efficiency rm>, which depends
on the material band gap, the operating wavelength, and the doping and thickness of the
device's depletion region. In a practical photodiode, 100 incident photons generate
anywhere from 30 to 95 electron-hole pairs. To ensure that the quantum efficiency is
closer to 95% than 30%, the depletion layer must be thick enough to permit a large fraction
of the incident light to be absorbed. However, the thicker the depletion layer, the longer it
takes for photogenerated carriers to drift across the junction. Since the carrier drift time
determines the response speed of the device, a compromise has to be made between
response speed and quantum efficiency [67].
The most promising types of photodetectors for high-performance microwave/
millimeter-wave fiber-optic links in the 800 nm to 1.55 |im wavelength range are the
semiconductor p-i-n photodiode, MSM (Schottky) photodiode, and semiconductor
avalanche-photodiode (APD). These detector types are compared in Table 2.5.
Semiconductor p-i-n Photodiodes
The p-i-n photodiode consists of p and n regions separated by a very lightly pdoped (n) or an undoped "intrinsic" (i) region. It is the most efficient type of optical
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Type of Detector
Advantages
Disadvantages
p-i-n photodiode
Most efficient: t]>0.8
Transit time and absorption effects
together limit the maximum efficiencybandwidth product: t\ f3dB<26 GHz
Avalanche photodiode
High gain-bandwidth products
possible (up to 30 GHz)
Added avalanche noise
High bias voltage required
MSM Schottky photodiode
Very fast (f3 dB > 40 GHz)
Efficiency not as great as p-i-n's
Table 2.5 Comparison of currently available optical detectors for direct and external modulation fiber-optic links.
detector, with its only main disadvantages being its limited bandwidth-efficiency product
and the difficulty of achieving monolithic integration with other circuit elements (due to its
thick layer structure). An InGaAs p-i-n diode utilizes direct bandgap optical absorption as
the mechanism for converting modulated ^=1.30 pm optical signals into electronic signals.
It requires low operating voltage (5-20 V), and can feature high responsivity (>0.9
mA/mW), large modulation bandwidth (>15 GHz), and low additional noise arising from
dark current. Analogous to a forward-biased semiconductor p-n junction's optical
emission, illumination of a p-i-n photodetector can occur at either the surface or the edge.
Very efficient surface-illuminated p-i-n photodetector performance has been
demonstrated, even at very high modulation frequencies. Makiuchi et al., for instance,
reported a cutoff frequency of 31 GHz for a surface-illuminated planar InGaAs/InP p-i-n
photodiode at a -10 V bias voltage. The photodiode had a capacitance o f0.054 pF, a dark
current of about 3 pA, and an external quantum efficiency of 74% at the 1.55 pm
wavelength [68].
Metal-Semconductor (MS and MSM) Schottky Photodiodes
A photodetector formed by the depleted region at a metal-semiconductor Schottky
junction is fast because of the very narrow depletion width. It is, however, very difficult to
effectively couple infrared (X=1.30 pm or 1=1.55 pm) light into such a device. That is, the
depletion region cannot be significantly widened to produce a more useful compromise
between efficiency and speed, such as that which is obtained by tailoring the intrinsic layer
width in a semiconductor p-i-n photodiode. Furthermore, MS and MSM photodiodes have
increased noise due to the higher surface leakage (dark) current generated at the metalsemiconductor boundaries. It is therefore not surprising that these devices are generally not
used unless very high (>20 GHz) modulation frequencies demand the use of a detector
having an ultra-narrow depletion region.
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64
Ozbay et al. demonstrated a GaAs Schottky photodiode with a full-width-at-halfmaximum (FWHM) temporal response of 2.0 ps, corresponding (via a Fourier transform)
to a 3-dB bandwidth of 150 GHz. They measured a responsivity of 0.15 AAV to X=532
nm light, corresponding to an external quantum efficiency of 33% [69]. By introducing a
buried n-type doped layer completely depleted of carriers, which reduces the hole transit
time, Borroughes e t al. demonstrated a technique for enhancing the bandwidth of metalsemiconductor-metal photodetectors without reducing responsivity. A 3-dB bandwidth of
10 GHz was measured [70].
Avalanche Photodiodes
An avalanche photodiode (APD), another commonly used photodetector, internally
multiplies the primary signal photocurrent. This is intended to increase the receiver
sensitivity since the photocurrent is multiplied before encountering the rest of the receiver
circuitry and its associated thermal noise. In order for carrier multiplication to take place,
the photogenerated carriers must traverse a region in which a very large electric field is
present In the high-field region a photogenerated electron or hole can gain enough energy
so that during collisions with bound electrons it ionizes them. This carrier multiplication
mechanism is known as impact ionization. The newly generated carriers are also
accelerated by the electric field and often gain enough energy to cause further impact
ionization, giving rise to a phenomenon called the avalanche effect [71].
By separating the absorption, grating, and multiplication regions, Holden et al.
were able to achieve a gain-bandwidth product of 40 GHz from their InP/InGaAsP/InGaAs
avalanche photodiode for 1.00-1.60 |im light [72], Using a similar structure, Kasper and
Campbell achieved a gain-bandwidth product of 70 GHz [71]. Because of the thick
ionization region, transit time effects limit the frequency response of the APD, and it is
therefore not likely that the gain-bandwidth product can be raised significantly beyond 70
GHz.
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65
Since the avalanche multiplication process in an APD is statistical in nature, its
contribution to a fiber-optic link's noise figure has been found to exceed even that of the
laser's RIN at frequencies below 2.5 GHz [30]. Furthermore, unlike the p-i-n the APD's
current output is highly dependent upon the biasing voltage and upon the temperature, and
therefore feedback is required to stabilize both voltage and temperature when using an
APD. Not surprisingly, then, the p-i-n and MSM photodiodes are employed much more
frequently than APDs are, since the additional DC power consumption by the APD often
does not buy any increase in the sensitivity of the receiver at all because of the excess noise
it generates [67].
It is evident from Table 2.5 that the detector of choice is clearly the p-i-n
photodiode, which even at high frequencies has high efficiency and a large impedance
under reverse bias, and hence ensures an appreciable transducer gain. Moreover, the
intrinsic region in a p-i-n can be made as wide as possible to allow satisfactory coupling
efficiency, so long as it does not result in a carrier lifetime longer than the minimum rise­
time necessary for communication over the desired bandwidth. A photosensitive region
with a diameter of 25 Jim, for instance, ensures a sufficiently short response time for links
up to 15 GHz and yet is large enough to permit efficient coupling to a single-mode optical
fiber with an 8 |im-diameter core. The models set forth in Chapter 3 are presented with the
semiconductor p-i-n in mind, although they apply for MSMs as well and could be rather
easily modified to account for avalanche multiplication (with its associated excess noise) in
an APD [39].
2.5.5
Optical Amplifiers
Optical amplifiers will undoubtedly be utilized in the optical beamforming networks
of many future phased arrays, where their gain may be needed to compensate for
cumulative optical insertion losses. It is important to clarify that, while many systems
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66
incorporating fiber-optic links may also employ optical amplifiers, the amplifiers are not
essential components in the fiber-optic links themselves. That is, the signal loss for which
an optical amplifier compensates is not loss in the optical transmitter or receiver which
together comprise a fiber-optic link, but rather losses in optical splitters, switches, timedelay devices, and other such components of optical beamforming networks. Therefore,
the modeling of optical amplifier performance is not included in the scope of this thesis.
This section of the literature review discusses two types of optical amplifiers which
are the most likely to be used in future optical signal processing systems—doped-fiber
amplifiers and semiconductor laser amplifiers. The discussion focuses on the relative
advantages and limitations of both types of devices in order to highlight the extent to which
they complement the performance of fiber-optic links.
Doped Fiber Amplifiers
Fiber amplifiers are created by doping a length of optical fiber with ions that radiate
at useful fiber-optic transmission wavelengths when they decay from high-energy to lowerenergy states. As in the case of a laser oscillator used as an optical source, energy must be
pumped into the optical amplifier to bias it so that there are more atoms in the higher of the
two energy bands that comprise the bandgap corresponding to the desired wavelength of
emission. In a doped-fiber amplifier, one or more semiconductor laser diodes usually
serve as the pump. Light from the pumping laser or lasers is absorbed by the dopant
atoms, exciting them to a high energy level. When an optical signal enters the core of the
doped fiber, the excited dopant atoms transfer their energy to the signal through the process
of stimulated emission [73].
The very high output level desired for an optical fiber amplifier often requires
pumping with two or more lasers, adding to the expense and complexity of the device.
This places a large premium on optimizing the efficiency of the doped fiber amplifier. For
an optical amplifier in a phased array signal distribution system, the goal, therefore, is to
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67
maximize the fraction of pump photons that are converted into excited dopant ion energies
and subsequently to photons having the same wavelength and phase as the optical input
signal. Pump photons are “lost” when they exit the amplifier without being absorbed by
the dopant ions, or when dopant ions excited to the high energy band by the pump
spontaneously decay to the lower energy and emit a photon (rather than emitting only when
stimulated by a signal photon). The former effect is reduced by improving the overlap
between the pump mode and the dopant ion distribution; the second effect can be reduced
by maximizing the overlap of the dopant ion distribution and the optical signal mode.
Optical fiber amplifier efficiency can also be enhanced for a given pump power by
increasing the fiber numerical aperture (NA) or by confining the dopant ion distribution to a
very tight region. For the pump powers between 25 and 100 mW that are typically
available using one or two diode lasers, the quantum conversion efficiency—and thereby
the signal output power—can be improved by up to 60% by increasing the fiber NA from
0.15 to 0.25; dopant confinement provides an additional enhancement of up to 20% [74].
The primary sources of noise in an optical amplifier are the frequency-dependent
relative intensity noise (RIN), the shot noise due to out-of-phase spontaneous emissions,
and beating—both between different spontaneous emission frequencies and between the
input optical signal and spontaneous emission frequencies. These beat noises usually
dominate over the RIN and shot noise components. The total noise output of the doped
fiber amplifier depends on the powers and wavelengths of both the pump and the input
optical signal; however, neither the fiber NA nor the dopant ion confinement have a
significant influence on the noise figure of the amplifier. This is because both the gain and
the spontaneous emission captured in the fiber are affected by the NA and the confinement
in the same way [74].
Most demonstrations of fiber amplifiers have employed erbium ion (Er3+) doping,
which has resulted in high efficiency at one useful wavelength for fiber-optic signal
transmission: 1.55 pm. Erbium-doped fiber amplifiers at 1.55 pm have many advantages,
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including broad optical bandwidth, low noise, high gain, low fiber-to-device coupling
losses, low pump power requirements, high saturation output power, high pump
efficiency, and insensitivity to polarization.
Pedersen et aL demonstrated an erbium-doped fiber amplifier with a numerical
aperture of 0.18 and a GaAs pump laser with a wavelength of 980 nm. They achieved a
high quantum conversion efficiency of 0.89 with 135 mW of launched pump power,
yielding a correspondingly large maximum signal output power of 18.9 dBm. Analytically
predicted noise figure was minimal (3-4 dB) for this same combination of device features
[75].
Way et a l demonstrated a three-stage erbium-doped fiber amplifier with a smallsignal gain of 49 dB and saturated output power of 12.9 dBm at a wavelength of 1.55 |im.
The noise figure of this device was 4 dB for input powers below -13 dBm, where the gain
of the first stage was high and the noise figure of the first stage dominated the overall noise
figure. However, this noise figure increased quickly with increasing input power [76].
Obviously, there is great interest in using optical amplifiers that are compatible with
the semiconductor laser diodes and external modulators developed to take advantage to the
minimum single-mode fiber dispersion at ^=1.30 pm. Neodymium (Nd3+) doping of
fluoride [77] and fluorozirconate fibers [78] has been demonstrated, but neodymium-doped
1.30 pm fiber amplifiers suffer from excess excited-state absorption and amplified
spontaneous emissions that limit the gain to about 10 dB [79].
Another promising fiber amplifier at 1.30 pm is the praseodymium (Pr) doped
fluoride fiber amplifier. A high gain of 38.2 dB has been demonstrated by Miyajima et al.
using such a device [80]. However, although the Pr3+-doped fiber amplifier meets
linearity, crosstalk, polarization sensitivity, and noise requirements of most systems [81],
the problem of low efficiency has yet to be solved in this type of fiber amplifier. The need
for an efficient optical gain block operating at the 1.30 pm wavelength is more completely
fulfilled by semiconductor laser amplifiers, as is discussed next
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Semiconductor Laser Amplifiers
Semiconductor laser amplifiers have the advantages of high total efficiency, high
gain, low noise, broad bandwidth, high saturation output power, availability at the 1.30
pm zero-dispersion wavelength, and compatibility with the other electronic components in
a typical system. One of the first proposals for the use of semiconductor laser amplifiers in
communication systems was presented in 1963 [82]. However, it was not until recent
years that high performance semiconductor diode structures have become available,
allowing practical amplifiers to be made.
The semiconductor laser amplifier uses the same basic construction as the
conventional buried-heterostructure Fabry-Perot semiconductor laser oscillator discussed in
2.5.2. A Fabry-Perot amplifier is operated at a bias current just below the lasing threshold
current. Under this condition, internal gains on the order of 25-30 dB are obtainable [83].
Using multimode rate equations (as is done when modeling semiconductor laser
oscillators as optical sources), Mukai et al. calculated both the gain characteristics and the
saturation output power of Fabry-Perot semiconductor laser amplifiers. The signal gain
G c for the Fabry-Perot amplifier is of the form [84]:
G - 1 (l-Y K IK J Gsf
c kl-R xK l-R aJG s
4VK7K7
. 2r2n(v-Vo)nL L]|~l
( 1 - R i ) ( 1 - R 2)
L
c
J| ’
(2-11)
where Gs, nL, and L are the single-pass gain, refractive index, and length of the active
medium, respectively, v is the incident signal optical frequency, and vo is the cavity
resonant mode frequency; Ri and R2 are the input and output mirror reflectivities.
Mukai et a l later extended the quantum mechanical multimode rate equations
originally derived by McCumber [85] to include an optical input signal term along with a
Langevin noise source. They also analyzed the SLA noise characteristics by using photon
statistics equations in the manner of Shimoda et al. [86]. Both analytical methods showed
that noise characteristics vary sharply with facet mirror reflectivities. Five different sources
of noise were represented as functions of the device’s physical parameters, the forward
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bias and the optical input power. These noise quantities were: amplified input shot noise;
spontaneous emission shot noise; beat noise between spontaneous emission and the input
signal; beat noise between different spontaneous emission components; and excess laser
noise at the signal frequency (as expressed in the RIN term) [87]. It was found that the
two beat noise powers predominate over the shot and excess noise terms by 30 to 40 dB,
depending on the signal frequency and its proximity to the laser’s relaxation oscillation
frequency, where the RIN is maximum. At input signal levels below -40 dBm, the most
significant term is the beating between the spontaneous emission components. Stronger
input signals produce beating with the spontaneous emission that dominates over the
spontaneous-spontaneous beating noise [87].
Noise characteristics for the Fabry-Perot cavity type semiconductor laser amplifier
can be improved by adding antireflective coatings to reduce the facet mirror reflectivities,
thus approaching an ideal traveling-wave type amplifier. In the ideal case, R i =R2=0, and
equation (2-11) reduces to
GC = G S .
(2-12)
Adding antireflection coatings to a Fabry-Perot semiconductor laser amplifier has
the effect of increasing its optical bandwidth and making the transmission characteristics
somewhat less dependent upon fluctuations in the bias current, temperature, and input
signal polarization [83].
In the limiting case, an amplifier with zero-reflectivity facets would be a traveling
wave amplifier with factor G s(R i R2)1/2 equal to zero. In practice, however, even with the
best antireflection coatings there is some residual facet reflectivity (the lowest reported
reflectivity is R=1 x 10-4 at 1.50 pm [88]) and the amplifier lies between traveling wave
and Fabry-Perot: the term near-traveling wave (NTW) has been used in this context to
denote amplifiers with Gs(Ri R2)1/2 ^ 0.2. The main advantages of the NTW amplifier are
wide bandwidth, low sensitivity to signal polarization, and an improved gain saturation
characteristic. Compared to Fabry-Perot amplifiers, NTW amplifier output power at
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71
saturation can be as much as 18 dB greater [84]. The principal disadvantages of NTW
amplifiers are an increased spontaneous noise component and an increased sensitivity to
reflections from external components such as fiber-to-device interfaces further down the
line [83].
The theoretical limit to the maximum available signal gain in NTW amplifiers is due
to spontaneous emission, which competes with the stimulated emission process responsible
for the desired optical gain. But the practical limitation to the maximum available gain is the
residual efficiency of the amplifier ends or the reflection from the other optical devices.
Provided that a 2 dB gain variation is permitted within the amplifier bandwidth, a maximum
signal gain of 20 dB and 30 dB is attainable for residual reflectivities of 0.1 and 0.01
percent, respectively. Compared to the gain saturation due to the amplified spontaneous
emission, residual reflectivity sets a lower limit on the maximum output power of NTW
semiconductor laser amplifiers [84].
2 .6
Existing Fiber-optic Link Performance Models
Because the fabrication of a photonic link consumes both time and money, the
ability to predict the performance of a designed link before fabrication has been sought by a
number of researchers. This section of the literature review chronicles some of the more
significant photonic link modeling efforts of the past few years.
Semiconductor Laser Diode Modeling
The most difficult device to model is the semiconductor laser diode that is both the
optical source and the modulator in a direct modulation fiber-optic link. The behavioral
model of a typical laser without modulation was given in section 2.2 [expression (2-4) and
Fig. 2.3]. This ideal model must be augmented to reflect the frequency-dependent
efficiency, noise, and linearity behavior of the device when modulated. To this end,
Harder and Katz derived a basic electrical equivalent circuit of the semiconductor laser
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72
diode, including a negative resistance to account for the noise effects of spontaneous
emission and self-pulsations [89]. They showed that the relative intensity noise (RIN) of a
semiconductor laser can be modeled by associating with each change in electron or photon
density a noise impulse of unit intensity, which appears as a Langevin noise source in the
laser equivalent circuit model [90].
To the Harder-Katz models, which impart the frequency-dependent efficiency and
noise characteristics of a directly modulated semiconductor laser, Tucker et al. have made
significant modifications in order to account for experimentally observed nonlinear largesignal effects [91]. These researchers have shown experimentally that in several types of
devices—ridge waveguide and etched mesa buried heterostructure Fabry-Perot (FP) lasers,
as well as distributed-feedback (DFB) structures—strong damping of the relaxation
oscillations occurs due to spatial and spectral hole burning. Performing measurements,
they found that each type of semiconductor laser generates approximately the same
distortion level for a given modulation depth and relaxation oscillation frequency. Slight
variations between laser noise spectra were considered to be due to differences in damping
characteristics, and were explained by gain compression. Therefore, the Tucker model
added a field-dependent optical gain compression factor to the modified single-mode rate
equations of Harder and Katz to account for the large-signal relaxation oscillation damping.
One phenomenon not predicted by the Tucker semiconductor laser model is the rise
in the RIN at low microwave frequencies (below about 2 GHz). Using multi-mode rate
equations (and thus disposing of the initial single-mode assumption of Harder and Katz),
Su et a l have shown that a laser will exhibit enhanced low-frequency noise unless the side­
mode suppression ratio is very high (greater than 30 dB). Even though this noise is at low
frequencies, it can be translated to the signal band by beating with the modulation signal,
thus adversely affecting high frequency performance. For a semiconductor laser with
optical power mostly in one mode but non-negligible power in a second mode, Su et al.
[92] calculate the relative intensity noise, RINsl. as follows:
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where they defined a normalized gain term, b, as
V
Ts
(2-14)
where r is the optical confinement in the laser active region, go is the differential gain (the
derivative of gain with respect to electron population density), Vol is the volume of the
active region, and Ts is the spontaneous emission lifetime. RSp is defined as the average
rate of spontaneous emission, and is proportional to the inverted electron population
density Ne and to P, the fraction of spontaneously emitted photons which couple into the
lasing modes:
R sp —
PNTse
'
(2-15)
Su et a l gave the frequency, damping rate, and photon density of the i^ cavity mode (CDn,
Ti, and Si, respectively) as follows:
^ 1 - ( § f + ’ i«»s* ) £ +b s) + ] i ^
^ =
( ^ + v8 E„ s 2) ( x + b s ) .
-
a -i6 )
(2i?)
^ - £ « . * S u +i + b S.
(2 . 18)
S = Si + S2 ,
(2-19)
and
where £o is the gain compression factor and vg is the group velocity of photons in the laser
active region. This analysis can be extended to account for a much larger number of cavity
modes, making Su’s model among the most physically rigorous of all available
semiconductor laser models. Predictions using this model, however, require a priori
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74
knowledge of many parameters not easily determined from measurements, which is a major
disadvantage.
For cases where secondary longitudinal modes are sufficiently suppressed (such as
in the lower-noise DFB lasers gaining pre-eminence in high-performance optical links),
Way at Bell Communications Research (Bellcore) proposed a simpler method of finding
unique solutions for all unknown laser parameters except the gain compression factor eo
and spontaneous emission coupling factor (3, which he assumed to have negligible effect on
the third-order intermodulation distortion. He obtained values for the laser chip and
bondwire parasitic elements by model-fitting to measured S-parameter data using a
microwave CAD tool such as SuperCompact [93], and calculated the remaining unknowns
in Tucker's model from measurements of the relaxation oscillation frequency and threshold
current. These remaining unknowns are the spontaneous emission lifetime (ts), the carrier
density when gain and loss in the active region are equal (No), and the product of the
optical confinement factor and the differential gain (rxgo). Way determined these three
unknowns from the following equations [94]:
(2-20)
(2-21)
and
(2-22)
In these expressions, Jth is the threshold current density of the active region material, d is
the active layer thickness, q is the electronic charge, and Tp is the photon lifetime in the
laser cavity.
To fully model the nonlinear behavior of a semiconductor laser using Way's
analytical expressions also requires knowledge of the damping ratio y and the relaxation
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75
oscillation frequency cop These terms may be determined at any bias current of interest by
curve fitting the data from modulation frequency response and relative intensity noise
spectrum measurements, respectively, to the following equations with which the noise
behavior of the laser is also modeled [95]:
|M |
" ( i + j_£!I_)2)(((Dr 2 - ( 1)2)2 + 72 £02) ’
V
Icorc/ I
(2-23)
and
a
-*
cd2 + y2
r i n s l = ^ a*ct----------- - J - ------%
+f(a2
(2-24)
where corc, the resonance frequency due to parasitic circuit effects, is related to the
forward-biased semiconductor laser junction resistance and substrate capacitance (Rjl and
Cs, respectively) as follows:
(oRC = 2 n fRc = i— -—
R
jl
C
s
'
(2-25)
In (2-24), SfsT is the Schawlow-Townes linewidth of the laser, given by:
h c2 In (
* -)
8 fsr = ------------------------------------
16 Tcn^XLTsTiL^L-Ith)
(2-26)
where X is the lasing wavelength, h is Planck’s constant, c is the speed of light in a
vacuum, and nL, L, R i, and R2 are, respectively, the refractive index, length, and facet
reflectivities of the laser active region.
For the purposes of predicting the large-signal performance of direct modulation
links, the new modeling method proposed in Chapter 3 uses a measurement of the laser
frequency response to determine both cor and y at each bias current of interest The
proposed model also presents a simplified version of expressions (2-20)-(2-22) of Way's
model to determine Ts, which is needed in order to further quantify the laser's nonlinear
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behavior. The proposed modeling technique also dispenses with Su's method of predicting
the laser RIN using (Of, y, and SfsT in favor of direct measurement of the laser noise.
External Modulator Modeling
Compared to the semiconductor laser analysis, modeling of electro-optic waveguide
modulators of the type used in external modulation links is a somewhat simpler matter.
After an equivalent circuit is determined for the modulator electrodes and microwave input
network, the optical power vs. electrode voltage given in expression (2-7) and Fig. 2.4 is
applied to model the device efficiency and nonlinearity. Thermal noise arises from all
resistances in this equivalent circuit, as is true for the directly modulated semiconductor
laser. Optical noise arises from the optical source and can be measured at all frequencies of
interest (again, just like the direct modulation link case). Not surprisingly, several
investigators have presented external modulator performance models [96-100]. These
models accurately predict external modulation link performance only over a very narrow
range of frequencies where certain assumptions are valid—indeed, some are valid at only a
single frequency. Moreover, most of these models fail to predict the effect of biasing the
modulator away from its most linear point—the quarterwave voltage defined in this work
as Vb=0.
Kolner and Bloom [97] did model the effects of biasing the modulator away from
its quarterwave voltage, and at a given input signal power they plotted the external
modulation link's output signal-to-noise ratio, S/N, and minimum detectable signal voltage
as a function of the DC modulator bias. They also predicted the limit to S/N imposed by
the modulator's nonlinearity (this limit defines CDReXt, the compression dynamic range),
but not the extent to which this nonlinearity creates harmonics resulting in intermodulation
distortion that also limits S/N (and defines SFDRext» the spurious-free dynamic range).
Bulmer and Bums [96] defined and thoroughly investigated intermodulation distortion and
spurious-free dynamic range for an external modulation link, but did not predict
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performance resulting from a non-quarterwave modulator bias voltage. Kolner and Dolfi
[99] later added the intermodulation distortion effect to the model in [97] and predicted
optimum modulator performance, including spurious-free dynamic range, at a bias level
away from the quarterwave switching voltage. Their quantitative predictions were only
accurate, however, at frequencies for which their modulator electrodes had a very specific
impedance (22+j 0 £2).
Presented in Chapter 3, Section 2, is a comprehensive microwave analysis of
external modulation link performance as a function of frequency, including the effect of
operating an electro-optic modulator away from its quarterwave bias point where most
results have been reported. This analysis is used in Chapter 4 to predict the optimum bias
voltage at which to operate a LiNb0 3 lumped-element Mach-Zehnder interferometric device
modulating the optical carrier supplied by a Nd:YAG (2. = 1.3 pm) laser in an L-band (870930 MHz) external modulation link.
Optical Detector Modeling
Modeling of the photodiode used in a direct or external modulation link has been
addressed by several investigators, and is generally not as complicated as the modeling of
other devices.
Photonic-to-electronic conversion efficiency is expressed by the
responsivity, T|d , of the detector at the optical wavelength of interest There is of course a
roll-off frequency, beyond which the transit time across the depletion region is too long for
the device to respond efficiently. The frequency dependent behavior IHdI2 of the
photodiode is expressed as follows:
|H D| 22 =
L
[_
G
L
1+
L2 Tt f3
f3dB
(2-27)
where f3dB is the 3 dB roll-off frequency of the detector when it is biased with a reverse DC
voltage Vd-
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Noise arises in the photodetector due to the statistical nature of the photogeneration
process. This statistical behavior is illustrated by the fact that, even when a watt of optical
power is incident on a photodetector, there is a finite probability that no carriers will be
generated. Such a phenomenon is known as shot noise, and has been shown to conform
with Poisson noise models. The photodetector shot noise current spectral density <d2shot>
is proportional to the average DC photocurrent Id (DC):
( 4 ot) = 2qlD(DC),
(2-28)
where q is the electronic charge.
Linearity of a photodetector is rarely a concern in a fiber-optic link, as detector DC
reverse bias voltage can usually be set sufficiently far from the nonlinear regions of its I-V
characteristic to ensure that saturation of the directly modulated laser or external modulator
will occur before the detector has the chance to cause significant AM compression.
Full Direct and External Modulation Link Modeling
Several investigators have endeavored, with varying degrees of thoroughness, to
render accurate performance models for complete fiber-optic links. Some [32,101] have
presented expressions which would be useful for calculating the gain and noise power
output of direct and external modulation links if certain terms were to be more clearly
defined. Stephens and Joseph, for instance, define three terms in their direct and external
modulation link models as simply "electrical matching losses at the output" of the laser,
modulator, and detector, and do not show how to quantify these and several other terms in
their expressions [32], Buckley's model [101], although it includes similarly vague
impedance definitions, renders a valid expression for the ratio of third-order
intermodulation product power to fundamental power in an external modulation link. This
expression is valid, however, at only one modulator bias point, and is not accompanied by
a linearity analysis. Moreover, Buckley’s model for the RIN of a semiconductor laserbased direct modulation link derives from the rate equations and requires a priori
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knowledge of the gain coefficient, spontaneous emission coupling coefficient, carrier
density at transparency, gain compression factor, optical confinement factor, photon
lifetime, and spontaneous emission lifetime in the laser [101].
More recently, some other modeling efforts have achieved broader ranges of
validity and applicability. Gulick et a l have given models for direct modulation link gain
that included detailed definitions of equivalent circuit components [98], and Cox et a l have
presented related models for an external modulation link biased at its quarterwave bias point
[100]. These models are valid, however, only at the single frequency at which their
highly-efficient reactive matching circuits are optimized.
In both the direct and external modulation link models presented in Chapter 3 of this
work, the effect of the semiconductor laser and modulator bias levels on link performance
is fully modeled. Furthermore, using the microwave scattering parameters of the laser,
modulator and detector circuits, which can be determined at any frequency from
straightforward manipulations of network analyzer measurements, the complete direct and
external modulation fiber-optic link equivalent circuit models presented in Chapter 3
achieve validity across the full range of frequencies at which device characterization
measurements are performed.
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80
CHAPTER 3
DEVELOPMENT OF ANALYTICAL MODELS
To facilitate a comparison of fiber-optic link architectures, this chapter presents
microwave models that allow the prediction of several fiber-optic link performance
parameters. Both the direct and external methods of modulating the power from an optical
source are considered. Theoretical analysis of a direct modulation link in section 3.1 is
based on the signal flow diagrams of the interface circuits to the semiconductor laser diode
and p-i-n photodiode. Similarly, in section 3.2, analysis of an external modulation link is
based on the signal flow diagram of the interface circuits to an electro-optic modulator and
p-i-n photodiode.
System parameters—gain, noise figure, and spurious-free and
compression-limited dynamic range—are expressed as a function of both frequency and the
operating point of the semiconductor laser diode (in the case of the direct modulation link)
and electro-optic modulator (in the external modulation case).
3.1
Direct Modulation Fiber-optic Link
A conceptual diagram of a semiconductor laser-based optical transmitter is given in
Fig. 3.1 (a), which shows an impedance matching circuit with the laser equivalent circuit
model. The microwave equivalent circuit shown for the semiconductor laser is that of any
forward-biased p-n junction. The junction provides one path for current flow (with
resistance R j l ) through the device. In parallel to the junction is a path through the
semiconductor laser substrate itself, which has both resistance Rs and capacitance Cs due
to the potential for charge storage on the device's electrodes. The bondwires, bond
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Detector
Cm
Rid
P«OX
Impedance*
:zo
Matching
Circuit
Z*D
Rid - i
(a)
(b)
b*x
Swn
• ,D
(c)
(d)
Figure 3.1
Analytical model of direct modulation fiber-optic link.
(a)
(b)
(c)
(d)
Equivalent circuit of semiconductor laser-based optical transmitter.
Equivalent circuit of p-i-n photodiode-based optical receiver.
Signal flow diagram of semiconductor laser-based optical transmitter.
Signal flow diagram of p-i-n photodiode-based optical receiver.
00
ribbons, via holes or other elements connecting the laser electrodes to the matching circuit
are modeled by the parasitic resistance R pl and inductance Lpl in series with the device.
The purpose of the impedance-matching circuit is to effectively transfer current
from the system input to the junction of the laser diode. That is, the matching circuit is
designed to maximize the magnitude of the current i'l passing through the junction
resistance Rjl at any given bandwidth of RF frequencies. Since Rjl is ordinarily less than
10 £2, the matching network is designed to effectively transform a 50 £2 impedance to
approximately 10 £2. As discussed in section 2.4.1, the minimum transmitter input
reflection coefficient attainable using reactive matching techniques is limited according to
Fano’s expression by the quality factor Qext of the laser and the percentage bandwidth over
which impedance-matching is performed.
Each resistance in the transmitter equivalent circuit generates thermal noise [102].
The Nyquist theorem [103] allows for straightforward calculation of the total noise due to
all uncorrelated sources of thermal noise in the transmitter. Therefore, Fig. 3.1 (a) also
shows a current source at the output of the optical transmitter circuit representing the total
thermal noise generated in the transmitter. This current source has a spectral density
<*2th,TX,dir>. which is used in section 3.1.2 to model the noise performance of the direct
modulation link. The term Ythi. in Fig. 3.1 (a), which is also used in the noise calculations
of 3.1.2, is the admittance of the transmitter circuit as seen from the semiconductor laser
junction. Finally, the term Tl , which is used in the gain calculations of section 3.1.1, is
the reflection coefficient of the laser junction resistance, defined by the simple expression:
P
_ Rjl- Z
L
q
R jl + Z o ’
(3-1)
where Zo is the system impedance (usually 50 £2).
A conceptual diagram of a p-i-n photodiode-based optical receiver is given in Fig.
3.1 (b), which shows the detector equivalent circuit model and reactive impedance
matching circuit. The detector’s microwave equivalent circuit is that of any reverse-biased
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83
p-n junction, except for the addition of an optical power-dependent source of current Id
across the junction. Again, the reactive matching circuit should effectively transform the
desired RF component of this photocunent to the output load impedance Zo. Ideally, an
impedance-matching network for the receiver would match the photodiode's high reversebiased junction resistance, R j d (typically on the order of 1 kQ to 1 Mfi), to the output load
impedance of the fiber-optic link (typically 50 £2). The quality factor of the photodiode is
extremely high if parasitics are neglected.
However, from the de-embedding and
equivalent circuit modeling of the detectors purchased from several different vendors, it has
been discovered that it is not generally possible to match to the high junction resistance of
the detector at many microwave frequencies because of the device’s parasitic series
resistance R p d - At most microwave frequencies this series resistance dictates a lower Qext
factor than the shunt R j d -C j d combination gives, and one cannot efficiently couple power
to or from a high-Qext element through an element having a lower Qext factor. Thus it is
the series resistance
R jd
that is transformed to the load impedance Zo in the detector’s
lossless impedance matching circuit.
Also shown in Fig. 3.1 (b) is a voltage source to represent the total thermal noise
introduced by the resistive elements in the receiver, as well as current sources representing
three sources of optical noise in the fiber-optic link. The term <v2th,RX> is the total output
voltage spectral density due to all thermal noise generated in the optical receiver, <i2RiN,dir>
is the noise current spectral density at the detector junction due to the directly modulated
semiconductor laser’s relative intensity noise ( R I N s l ) ;
< i2shot,dir>
represents the shot noise
of the photodiode due to incident optical power from a semiconductor laser, and < i2dark> is
the contribution from the photodiode's dark current
Ijark -
The term
Z th D .
which is also
used to calculate noise performance in 3.1.2, is the impedance of the optical receiver as
seen from its output Finally, I'd, which is used in the gain calculations of section 3.1.1,
is the reflection coefficient of the photodiode junction, defined by the expression:
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84
(3-2)
Rjd + Zo
For the semiconductor laser diode the relationship between the optical output power
Pout,op and the applied electrical current I I was shown in Fig. 2.3. At bias currents greater
than the threshold current Ith, the laser’s optical output power increases with increasing
current at a slope equal to the current-dependent DC external differential quantum efficiency
T|l(I)- That is,
Pout,op = T1l (D
(II ~ Ith)»
(3 -3 )
where t il (I) can be expressed in a Taylor series as follows:
t ] l ( I ) = t i l + t i l ( I I - Ith) + t T l ( I I - Ith)2 +
The ratio of detector photocurrent,
Id ,
to Pout,op is
i\'"l(II -
Ith)3 + ------
Kl f Lf Kf d
t |D>
where
(3-4)
Kl f
and K f d
are, respectively, the laser-to-fiber and fiber-to-detector optical coupling efficiencies, L f is
the total optical power loss due to attenuation in the fiber, and t | d is the DC photodetector
responsivity. This relationship is illustrated by the following expression:
I d = K l f L f K f d H d Pout,op •
(3-5)
Substituting expression (3-3) into (3-5) yields
I d = til Klf L f Kfd "Hd (II - Ith) •
(3-6)
In the model described here, the detector is assumed to operate at a DC reverse bias voltage
Vd which is large enough to ensure that it does not impose an upper limit on the RF power
handling capability of the link. That is, even at 100% modulation depth in the laser, the
detector is assumed to be operating within its linear region of operation.
3.1.1
Gain Analysis
The gain of a fiber-optic link can be calculated in terms of microwave scattering
parameters using the signal flow diagram (SFD) technique and Mason's gain equation
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85
[104]. In this subsection, the transducer gains of the semiconductor laser-based optical
transmitter and p-i-n photodiode-based optical receiver are derived separately and then
combined to yield the gain of a complete direct modulation link.
The SFD for the optical transmitter (an impedance-matched directly modulated
semiconductor laser diode) is shown in Fig. 3.1 (c). It is obtained by considering the
forward-bias junction resistance of the laser diode to be the port two termination T l of a
two-port network (represented by the scattering matrix [SijL]) consisting of the lossless
microwave impedance-matching circuit and the other device parameters of the laser.
Similarly, when a reverse-biased p-i-n photodiode is employed in the optical receiver, the
SFD is obtained by considering the junction resistance and capacitance of the diode in
series with the parasitic resistance to be the source termination
I 'd
of a lossless two-port
network (represented by the scattering matrix [SijD]) consisting of the other device
parameters of the photodetector and the microwave impedance-matching circuit Fig. 3.1
(d) shows the SFD for the optical receiver.
The output power of a fiber-optic link depends on the RF amplitude of
photocurrent, z'd (<o). generated in the detector, which is in turn proportional to the RF
current t'L(w). through the laser diode's active region. This RF current is expressed as
iL((0)
(3-7)
where ajL and biL are the square roots of the incident and reflected powers, respectively, at
the laser junction resistance. From the SFD and Mason's gain equation it is clear that ajL
and biL are related to the forward- and backward-traveling wave currents z‘l+ and z'l- as
follows:
= c m V 2 ? .—
---------- ,
1 -(S n L rgL+ S22LriiJ
and
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(3_g)
86
b«.=C«»)VZir =
hsLSmJju----1 - ( S u l rgL+ S 22L r1L/
(3-9)
where
bsL(l —S22L P il)
i-(snLrgL + s22Lr1L)
(3-io)
and where bsL is the normalized incident traveling wave intensity at the transmitter input
Because TgL=0 and TiL=r l ,
vZo i - s 22LrL
(3-ii)
The direct modulation link current transfer function, H<jir, is defined as the ratio of
detector current to RF current across the laser, and is given by
Hj* S 4 M =HLnLKu,LFKFDllDHD'
(3. 12)
where H l and Hd are defined as the frequency transfer characteristics of the laser and
photodetector, respectively, for a given set of device operating biases II and Vq .
Therefore,
km
iZo l- S 22LrL
(3-13)
The RF power at the output of the optical receiver is derived from its SFD [Fig. 3.1
(d)] as follows:
Pout,RX = |b R x | 2 .
( 3- 14)
where
^) r x _
aip(l - S n DrgD)
1 -(SnDPgD + S^ d Hd)
= aio (since H o = 0 ),
and
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(3 - 15)
87
ajD_ ______ bgp S21D______
1 - (S h d T gD + S 22Drid )
_
bgp S21D
l-S npF p
(3-16)
Substituting
bgp = iD((0) VZo
(3-17)
and (3-15) into (3-14) yields
|l —S22L.F1. 1 |l-Suprpl
(3-18)
Because Pin,TX,dir is equal to IbsiJ2. the transducer gain of the direct modulation link can be
expressed as follows:
Gdir = J >?-Ut,R^ ■= G xx.dirl H d ir|2 G r X »
(3 -1 9 )
lin.T X .dir
where we define
c-
_. _ iS2iLl2 l i - n l a
'J T X . d i r —
.
1 2 ’
11 - S22L r L I
(3-20)
and
Gv _ PoutRX _
P in,RX,dir
1S2iD 12
|
l - S 11Dr D| 2
(3-21)
The term IHdirl2 is the squared magnitude of the detector-to-laser current transfer function
calculated using (3-12):
I Hdir | 2 =
rp(co)
hM
= |H L|2 (riLKLFLFKFD'nD)2 |H D| 2 .
(3 22)
As was discussed in Chapter 2, the frequency transfer characteristics of the laser and
detector can be calculated as follows:
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88
(3-23)
and
(3-24)
where COis the RF modulation frequency f multiplied by 2%. The terms CDf and y in (3-23)
are the laser's relaxation oscillation frequency (multiplied by 2tz) and relaxation oscillation
damping rate, respectively. Both of these terms depend on the laser bias current II- The
f 3dB term in (3-24) is the frequency at which the detector's responsivity to incident RFmodulated optical power falls off by 3 dB relative to the DC responsivity t | d - This term is
a function of Vd, the DC reverse bias on the detector.
Note that when a perfect match is achieved in the reactive matching circuits in the
transmitter and receiver at some frequency, Grx,dir=Zo/RjL ^
G r x = 1 /( 4 c o 2C j d 2R p d Z o )
at that frequency if Rpd is very large [10]. Under these conditions, when f « f r and
f « f 3dB ,
the above expression for Gdjr reduces to the expression derived by Gulick et al.
[98] for a direct modulation link with perfect reactive matching of the input and output ports
at a single frequency.
3.1.2
Noise Analysis
As discussed in the introduction to section 3.1, the direct modulation link’s output
noise power N 0UtiR x ,d ir is the sum of the noise contributed by sources falling into three
categories: Nth,TX,dir. the thermal noise in the optical transmitter; Nth,RX. the thermal noise
in the optical receiver; and N o p ^ , noise which occurs because communication is via the
directly modulated optical carrier. Thus:
N 0ut.RX,dir = Nth.TX.dir + Nth.RX + Nop,dir •
(3-25)
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89
The portion of the total noise power at the output of the direct modulation link that
arises from thermal noise in the transmitter—defined here as Nth.Tx.dii— is calculated using
the Nyquist theorem, which states that the current spectral density at the output of the
optical transmitter due to all thermal noise sources (resistances) in the transmitter is:
(*th,TX,dir) = 4 kB T Re Y ,
(3-26)
where kg is Boltzmann's constant, T is the Kelvin temperature, and Y is the admittance
presented to the equivalent noise current source. It can be seen from Fig. 3.1 (a) that
(3-27,
Y = Y lb L + R jL '
where Yim is the admittance of the transmitter circuit as seen from the semiconductor laser
junction. Using the transfer function of the link from the transmitter output to the output of
the receiver, N^TX.dir is calculated from the portion of ith,TX,dirtkat flows through the
junction:
2
^ (itfa.TX.dir) B ~
Nth.TX.dir =
R jl
|H d ir|2 G R xZo
= 4 kB T ,? _(..1 + r JL Re X thL) I Hdir 12 G rx Zo,
RjLll+RjLYthLl2
(3-28)
where B is the resolution bandwidth of the receiver and Zo is the impedance of the output
termination.
Note that when a perfect match is achieved in the transmitter and receiver matching
circuits at some frequency, Ytht =1/R tt and G rx = 1/(4co2Cjl 2Rpd Zo) at that frequency if
Rjd is very large, so that at that same frequency Nlh,TX,dir=2 ke T B GoirThe portion of the total noise power at the output of the link that arises from thermal
noise in the optical receiver—defined here as Nth.RX—is calculated similarly. Fig. 3.1 (b),
the equivalent circuit of the p-i-n photodiode-based optical receiver, shows an equivalent
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90
thermal noise voltage source with spectral density <v2th ry > at the output of the optical
receiver. This spectral density can be calculated from the impedance Zfhr> as follows:
(3-29)
The total thermal noise arising in the optical receiver is therefore:
4 kfl T B-Re Zthp-Zp
IZthD + Zol2
(3-30)
Note that, if a perfect match is achieved in the receiver’s matching circuit at some
frequency, then Z>hn=Zn at that frequency, so that at that same frequency Nth,Rx=kB T B.
The individual sources of optical noise contributing to N0p,<jir can also be
represented as equivalent noise current spectral densities in the optical receiver. These
noise current sources are shown in Fig. 3.1(b). By multiplying the total of these noise
current spectral densities by the bandwidth, the impedance, and the transfer function of the
receiver, the output noise power due to these sources is obtained:
[(ijUN.dir)
(l"shot,dir)
(^dark)] ^RX B Z q
(3-31)
As expressed in (3-31), the optical noise arises from three sources: </2RiN,dir> is the noise
current spectral density at the receiver due to the directly modulated laser's relative intensity
noise (RINsl); <t2shot,dir> reflects the shot noise in the photodiode due to incident power
from a semiconductor laser; and ^ u a r ^ is tiie contribution from the photodiode's dark
current, 1 ^ .
Expressions for these optical noise current spectral densities are derived as follows.
The relative intensity noise of the semiconductor laser is defined as the ratio of its optical
noise power spectral density to its DC optical output power; the noise at the receiver due to
RINsl is therefore
(iRiN,dir) - Id r INsl »
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(3-32)
91
where Id is the DC photocurrent given by (3-6). Substituting (3-6) into (3-30) yields:
(*RiN ,dir) = [
K
lf
Lp K f d
"Hd
(II—Ith)]2 R IN sl -
(3-33)
Unlike the laser relative intensity noise, the shot noise and dark current noise arise due to
the statistical nature of the production and collection of photoelectrons when an optical
signal is incident on a photodetector, and are known to be Poisson processes [105] for
which the noise spectral density is twice the product of the DC current and the electronic
charge q. For the direct modulation link, the noise current spectral density due to shot
noise can therefore be calculated by substituting (3-6) into the following expression
(3-34)
to obtain
( ishot, dir ) = 2 Q tlL K l f L f K fd BD G l —^th) >
(3-35)
and the spectral density of the dark current noise is simply
(3-36)
Therefore, using equations (3-25), (3-28), (3-30), (3-31), (3-33), (3-35) and (3-36) to
arrive at the value of Nout,Rxidin ^ noise figure NFdir of the direct modulation fiber-optic
link, as defined in Chapter 1, is calculated as follows:
f.rc _ (S/N)ini(jir
Nrdir —/0/vr\
lir
3.1.3
(S/N)oUt,dir
—,
Nout.RX.dir
t* -d r*
k B T B Gdir
(3-37)
Intermodulation Distortion Analysis
The distortion characteristics in a direct modulation link are analyzed with respect to
the modulation index m<jir of the laser at frequency oii. The total optical power out of the
laser for a two tone (coi, 002) input signal was derived by Daryoush and Ni [106]:
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92
PoPt,dir(0 = I^
Io~ y ^Io(ai)Io(a2) + 2Io(a2) X IkteDcostkfoht + Oi)]
oo
+ 2 Io(ai) X
In(a2) COS [n (<o2t + 02)]
n= 1
+4 ( x
Ik(ai)cos[k(tOit + 0 i)]j | X In(a2)c o s [n(co2t + 02)]jJ ,
(3-38)
where In(aO and Ik(ai) are, respectively, the modified Bessel functions of the n * and k *
kind, and ai for i = 1, 2 can be obtained from the following equation for the modulation
index [107]:
“V (® - M 2+<o2t^
2
1PXS
+n2
I
(3-39)
In this equation tOf is the laser relaxation oscillation frequency (multiplied by 2rc); xp is the
photon lifetime in the cavity; and xs is the spontaneous emission lifetime. The term <J)(ai) is
defined as:
ai Io(ai)
(3-40)
The photon lifetime is calculated from the laser cavity length L, mirror reflectivities Ri and
R2, optical attenuation in the cavity ccl, and the semiconductor laser medium’s refractive
index nL as follows:
* ■ * -£ [ * * •* & “ ( * * ) ] •
(3-41)
where c is the speed of light in a vacuum. The spontaneous emission lifetime xs is
calculated from the following three equations, in which xs, No (carrier density at which the
active region has optical gain equal to loss), and the product of T (optical confinement
factor) and go (differential optical gain coefficient) are the three unknowns [94,106]:
N0 = ^ ;
qd
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(3-42)
93
it h = a m / _ L _ + N o \;
Ts
U pTgo
(3-43)
)
and
tp Ts
vith
I
(3-44)
where Jth, d, and Vol, are, respectively, the threshold currentdensity, thickness, and
volumeof the active region. Substitutingthe equation for No into theequations for o&r and
Ith, the spontaneous emission lifetime can be expressed as a function of known quantities
as follows:
T>
(IL-Ith)d
(0? Tp (In, d - Jth V ol)
(3-45)
where Tp is calculated from equation (3-41).
From the time-domain expression (3-38) the optical powers out of the laser at the
fundamental frequency and at the third-order intermodulation frequency can both be
obtained; these quantities are expressed here for clarity:
Popt,dir (COi) = 2
T IL
(IL - Ith)
lo w )
COS (OJtt).
(3-46)
and
Popt,dir (2fi>2 - G)i) = 2
til
( I I - Ith)
I 1? !1! cos (t2o>2 ~
lo w ) lo w )
•
(3-47)
The term IMD/C is defined as the ratio of optical signal powers at the third order
intermodulation product and fundamental frequencies. Thus, for small signals,
IMP _ Popt.dir (2 co2 - coi) _ I2(a2) _ a22
c
Popt,dir (g>i)
lo fo )
8
(3-48)
By definition, at the third order intercept point the IMD/C ratio is equal to 1; therefore,
using the value of z.%at the intercept, the value of the modulation index mjir at the third
order intercept can be defined as mjnt|(tir:
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94
m int,dir = m dir w h e n
a2 =
VS” ,
(3-49)
or [107]:
(3 -5 0 )
m int,dir
fcpXs
Therefore, for the direct modulation link the RF input power and output power at the
intercept point are calculated as follows:
m int.dir(IL - Ith)2 Zo
in.int.dir —'
G-IXdir
(3 -5 1 )
and
Pout,int,dir — Pin.int.dir * G dir •
3 .1 .4
(3 -5 2 )
Linearity Analysis
The ldB compression point is calculated in a fashion similar to the third-order
intermodulation distortion calculation. For small input RF powers, the output power at the
fundamental frequency increases linearly with the input power, since
r~
a2
'^ 2
r
l+
i<
+
Ii(ai) _ at
Io(ai) 2
1
11
64
=
2
for small ai .
J
(3 -5 3 )
Thus for small input RF powers the power at the fundamental frequency is
Popt,dir(0>l) = 2 7 lL (IL - I th) |^ C O s ( C 0 i t )
= ai t|L (II - Ith) cos(coit) for small a i .
(3 . 54 )
At larger input RF powers the fundamental begins to saturate. This response can be
obtained by considering more terms of the modified Bessel functions in the expression for
the fundamental, which gives
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95
r
a2
I + * H
COS (CDit)
a2 a4
J
1 + 4 64
a,4 + 24 a,2 +192
'Hl (II —Ith) cos (COit)
3
(af + 8) :
P opt,dir(0)l) = 2 T1l ( I I ~ Ith) TT-
(3-55)
The 1 dB compression point is then calculated at the RF input power where the output
power falls short of the linear (small-signal) gain by ldB. It is found using (3-53) that this
1 dB compression point occurs when ai = 1.010. From this value of ai the value of
mlCP,dir is obtained:
micp.dir = mdir when ai = 1.010
(3-56)
or [107]:
m 1Cp,dir
= 1.010 y
vcof
- 0.891 lj ^ + CO2 Tn /— -----+ l \ 2 /
la^CpTs
/
(3.57)
On substituting the value of mdir at the ldB compression point into the expression
for RF input power, the RF input power at the ldB compression point is obtained:
m lCP.dir ( I I ~ Ith
•in.ICP.dir —'
) 2 Zo
GlX.dir
(3-58)
in,lCP,dir G dir
1.259
(3-59)
and
Pout, 1CP,dir - '
3.1.5
Analog Link Performance: Dynamic Range Calculation
The spurious-free and compression-limited dynamic ranges of a two-port device or
network were defined in Chapter 1; for the direct modulation link, these figures of merit are
expressed as follows:
C P T tP
I
,2
— P out.int.dir)
^ " ( iW x .d ir )
_(
Pin.int.dir
~ \kB T B NFdir
(3-60)
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96
and
/irtn
— 1 -2 5 9 Pout.lCP.dir
C D R d i^
3.1.6
P in,lC P,dir
—-----------------------= -— rp p
Nout,RX,dir
htt?
kg T B NFdir
•
n
/:i\
(3 -6 1 )
Summary of the Direct Modulation Fiber-optic Link Model
In Tables 3.1 and 3.2, the equations which have been derived in the previous five
sections of this chapter have been reduced to their most compact forms and listed in a
logical order. Table 3.1 lists the 16 equations necessary for calculating the gain and noise
figure of a direct modulation link; Table 3.2 gives the 8 equations needed to calculate the
spurious-free and compression dynamic ranges.
In Chapter 4, the measured performance characteristics of three high-performance
direct modulation fiber-optic links are compared to the performance predicted by the above
model in order to assess the usefulness and accuracy of this modeling procedure.
3.2
External Modulation Fiber-optic Link
It is the goal of this section of the chapter to render a complete microwave model of
external modulation link performance as a function of frequency, including the effect of
operating a modulator away from its linear bias point where most results have been
reported.
Depending upon the design of the electrodes in an electro-optic modulator, the
device may or may not be modeled accurately by an equivalent circuit of lumped elements.
For external modulation of an optical carrier at millimeter-wave frequencies or across a very
broad band of microwave frequencies, a traveling-wave device is generally used. In either
case, modeling of the external modulation link gain, noise figure, and other figures of merit
depends on being able to determine I'm. the microwave reflection coefficient of the
modulator electrodes. One must also be able to express P0pt,ext. the optical output of the
modulator, as a function of the DC and microwave components of the electrode voltage.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Noise Figure
Small-Signal Insertion Gain
Gdir = GxX,dir | Hdir | 2 G rx
(3 -1 9 )
Noul.RX.dir
NFdir —
(3 -3 7 )
kB T B Gdir
where
where
^
J S --------2iL|2 | i - r L| 2
r=—
G rx, dir =
(3 -2 0 )
Nout.RX.dir = Nih.TX.dir + Nih.RX + Nop.dir
(3 -2 5 )
11 - s 22u r L12
Nui.TX.di, = 2 k flT B ( l + K jlR £ Y uil) | H jir l2G rx Z o
IV
. Rjl - Z q
R j l 1 1 + R j l Y u il|
(3 -1 )
(3 -2 8 )
R jl + Zo
_ 4 kB T B -Re ZihpZo
Nih.RX =
|Z ih D + Zoj"
(3 -2 1 )
(3 -3 0 )
| 1 - SiidFd|
r D = R jd - Zo
I Hdu | 2 = | H l | 2 ( t i l K l f L f K fd *1d ) 2 1H d | 2
|H
l
|2= ;
Nop.dir =
[(iR IN .dir) + (jo h o l.d ir)
(3 -2 2 )
(iR iN .dir) =
[ t i l K l f L f K fd
(3 -2 3 )
( J«h oi.
(3 -2 )
R j d + Zo
(Or
d ir
+ (fdork)] G r x B Zo
(3 -3 1 )
2 R IN s l
(3 -3 3 )
H d (Il-Iu i)]
) = 2 q T |l K l f L f K fd
tI d
(II
-
Iih )
(to? - co2f + y2 to2
(3 -3 5 )
and
and
(3 -2 4 )
(idaric) = 2 q Idirk
(3 -3 6 )
lH° ' 2‘ 7 u ± = P
\2 n fsdB/
Table 3.1 Summary of analytical model for small-signal gain and noise figure of a direct modulation link.
vO
Table 3.2
Summary of analytical model for spurious-free and compression dynamic range of a direct modulation link.
98
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99
Lumped-Element Modulator Model
The optical transmitter in an external modulation link employing a lumped-element
electro-optic modulator has the equivalent circuit model shown in Fig. 3.2 (a). The values
of the circuit elements are based on the physical parameters of the modulator. The
electrodes of the modulator are represented by capacitance Cm with parasitic series
resistance and inductance Rpm and Lpm» respectively. The impedance matching network
shown in the figure transforms the input RF voltage such that, for the desired bandwidth of
RF frequencies, maximum voltage Vm is obtained across the capacitor Cm- The lumped
series resistance Rpm. with typical values of less than 10 £2, forms the effective load
resistance. The limitation imposed on the impedance matching network is by the quality
factor of the external modulator determined by Cm and Rpm> as was given in Fano’s
expression (2-9). The term Tm in Fig. 3.2 (a), which is used in the gain calculation, is the
reflection coefficient of the modulator electrodes. For a lumped-element electro-optic
modulator this is given by the expression:
0-62)
n - t1 +t j S( D Cf mr Zl o f-
As has been shown by Alfemess [63], among others, for a lumped-element
interferometric electro-optic modulator the relationship between the optical output power
Popt,ext and the applied voltage Vm is
P o p « « = L m P s SL
•
(3. 63)
as was shown in Fig. 2.4, where P s s l is the unmodulated optical power—supplied in
most cases by a solid-state laser—Lm is the optical insertion loss of the modulator, and Vn
is the voltage required for 100 % on-off switching.
For the purpose of modeling the gain, noise figure, third-order intermodulation
distortion, and linearity of a lumped-element modulator-based external modulation link, Vm
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100
r-
“
' W ^ p~
l-j«SA
1+jmC^Z,
(a)
Z -L *
Characteristic impedance ■ Zq
Effective dielectric co n ittn t ■ Ceff
T o u l length o f N phase-reversed
s e c tio n s - L .
(b)
b*«
bsH
P«.TI
r.M- 0
21
S IS
*M
^ “ I'm
Figure 3.2
Analytical model of electro-optic modulator in external modulation fiber­
optic link
(a) Equivalent circuit diagram of lumped-element electro-optic modulatorbased optical transmitter
(b) Equivalent circuit diagram of traveling-wave electro-optic modulator-based
optical transmitter
(c) Signal flow diagram of lumped-element or traveling-wave electro-optic
modulator-based optical transmitter
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101
is generalized as a two-tone RF modulation voltage vM(sin ©it + sin ©2t) applied to a DC
bias voltage Vb:
Vm = Vb + vm (sin ©it + sin ©2t ) .
(3-64)
Substituting this expression for Vm into equation (3-63) yields expressions for the lumpedelement modulator's unmodulated optical output power Popt,ext(DC), as well as the
magnitude of P 0pt,ext at the modulation and third-order intermodulation frequencies:
PoPt,ext(DC) = LM P ssl cos2( f ^ - f ) :
P opt,ext(© 1)
= Lm P ssl
J i ( ^ )
(3-65)
cos ( ^ ) ;
(3-66)
and
Popt,ext(2©2—© I )
= Lm P ssl J i ( ^ )
cos ( £ X h j ,
(3-67)
where Jo, J i, and J2 denote the ordinary Bessel functions of order 0, 1, and 2 ,
respectively. The voltage Vb = 0 has been defined as the quarterwave bias point in order to
simplify the evaluation of the effects of non-quarterwave biasing.
Traveling-Wave Modulator Model
For a modulator having a traveling-wave structure (i.e., where electrode length is a
significant fraction of the intended microwave or millimeter-wave modulation wavelength),
a traveling electronic wave is realized on the transmission line formed by the electrodes by
terminating it with a load impedance Zt. Fig. 3.2 (b) shows a distributed circuit model for
a generalized coplanar electrode structure consisting of N periodic phase-reversed sections.
The impedance Zm looking toward the load Zt from a position z along the electrodes is
given by the transmission line equation [29]:
Zt + Zc tanh yez
Zc + Zt tanh yez
(3-68)
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102
where Z c is the characteristic impedance of the electrodes calculated using the same
grounded coplanar waveguide (GCPW) model [108] employed in the SuperCompact
microwave CAD software package [93]. The microwave propagation constant ye has both
real and imaginary parts, in general; that is:
Ye = 0Ce+jpe .
(3-69)
For ideal, lossless electrodes, IcteJ « IpeU and equation (3-68) is simplified. In general,
however, this is not an accurate assumption for many traveling-wave modulators operating
at microwave and millimeter-wave frequencies. Therefore, substituting (3-69) into
equation (3-68) yields the following cumbersome expression for Zm:
Z (z) = Zc Zt cosh 2 (Xez + Zt COS 2ftez + Zq sinh 2 a eZ+ j Zc sin 2fl ez
M
Zc cosh 2oteZ + Zc cos 2pez + Zt sinh 2 a ez + j Zt sin 2P ez ’
( 3 .7 0 )
Modeling of the traveling-wave modulator thus requires a method of determining Zc, Zt,
Oe, and pe. As was necessary for the lumped-element modulator, these parameters are
calculated from the equivalent circuit of the device, as obtained by selecting logical element
values for the model so that its one-port scattering parameter fits the one-port scattering
parameter de-embedded from a measurement of S 11 at the modulator input port.
The reflection coefficient of the traveling-wave modulator electrodes is obtained
using an expression analogous to the lumped-element expression (3-62):
( 3 - 7 1 >
where Le is the total length of the modulator transmission line and Zm (Lc) is evaluated by
substituting Le for z in expression (3-70). Note that the microwave impedance of the
electrodes is dictated only by their total length Le, and is independent of the phase-reversal
process (i.e., independent of zo,. . . zn). How the phase-reversed electrode structure
affects the modulator transfer function is through the relationship between the optical power
output and the voltage input.
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103
In traveling-wave Mach-Zehnder electro-optic modulators, just as in a lumpedelement one, the output power is amplitude-modulated by phase-modulating the coherent
wave in one path relative to that in another path before interferometrically combining them.
This frequency-dependent phase shift A|i-Le was defined by Alfemess [63] as a function
of the electric potential V m (co,z) encountered by the photons in the optical waveguides. If
the optical waveguide properties are affected by the traveling electronic wave on the
electrodes between the points zq and z n [see Fig. 3.2 (b)], then
(3-72)
where n 0 is the optical refractive index of the modulator electrodes, nj is the orientationdependent electro-optic tensor in the external modulator material (with units of m-V*1), Ge
is the inter-electrode gap, r eo is the overlap integral between the applied electric field and
the optical mode, and X is the optical wavelength. For a lumped-element electrode
structure, the microwave voltage is assumed to be constant along the electrodes; in a
traveling-wave device this is not the case and the integration in (3-72) must be carried out
The ’p' in the subtext of V m ( co, z) in equation (3-72) is meant to indicate that it is
the magnitude of microwave voltage with respect to a photon at position z that is important
when modeling the modulator performance. V m (g>,z ) is unaffected by the presence or lack
of a phase-reversal structure, and is calculated simply using voltage division:
where Zm(£0 ,z) is calculated using equation (3-70). The voltage Vm(G),z)p, on the other
hand, is affected by the phase-reversal electrode structure in that the orientation of the
electrical field with respect to the optical field is periodically forced to reverse direction,
resulting in a change in the sign (+ or - ) of Vm(g>,z)p. Additionally, the effect of the
velocity mismatch (or "walk-off') between the guided photonic and electronic waves in the
modulator is accounted for by normalizing the voltage Vm(<d,z) as follows [63]:
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104
VM(w,z)p = (- l)m V m ((0 ,z)
cos
(pe 8 z) ,
Zm < Z < Zm +1 ,
(3-74)
where m= 0,1 , . . . N -l, and the "walk-off" coefficient 8 is defined here:
8 = i - - B 2_ .
(3-75)
Vlar
The effective dielectric constant of the transmission line, seff, is also obtained from the
equivalent circuit model of the modulator. The frequency-dependent phase shift is
therefore:
AB -L _
x n^%rjj r eo
eo VYM ((0 ,L e )
2 Ge X
Zm(C0,Lc)
Z m (co,z) c o s ( p c8 z )
dz
As will become evident later in this chapter, it is useful for modeling purposes to
express the controlled phase change AP-Le at any frequency as simply the voltage
VM(to,Le) multiplied by the rate of change of phase with respect to Vm (co,Lc). Defining A
as this rate (which has units of rad/V),
(3-77)
AP -Le(C0) = A(t0>VM( 0J,Le),
where
Zm(g),z) cos (pe8 z) dz
(3-78)
and where Zm and 8 are calculated using equations (3-70) and (3-75), respectively. The
terms n0 and ry are known for the given modulator substrate; Ge, zm, and Zt are easily
measured; Zc, cte, and Pe are determined from the modulator’s equivalent circuit model.
An expression for P0pt,ext as a function of V m , which is needed for modeling of all
the external modulation link performance parameters, was derived for phase-reversed
traveling-wave interferometric modulators by Alfemess [69]:
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105
(3 -7 9 )
L m P ssl
Most commercially available modulators have either no phase reversal in their electrode
layout (N=l) or a two-section (N=2) phase reversal electrode layout In these two cases,
(3-75) can be approximated as follows:
f
*opt,ext _
M
v
cos2 ( ^ i ) , N = l
'
7t
i
\
jc
/
(3-80)
In both cases, the halfwave voltage occurs at Ap-Le=Jt2/4. Generalizing Vm as a two-tone
RF voltage VM(sin ©it + sin C02t) applied to a DC bias voltage Vb, equation (3-76) can be
expressed as follows:
Ap-Le(©) = A(DC) -V b + A(©i) -vm sin © it + A(©2) vm sin ©2t ,
(3-81)
where Vb=0 signifies the halfwave DC bias voltage. Substituting (3-81) into (3-80) yields:
l 2E t«L = C0S2 ( ^ C ) v b + ^ i l v M sin ©lt + ^ v Msin ©2t - ( - 1)N* ) .
L m P ssl
V jc
it m
jc
41 (3-82)
As for the lumped-element case, expressions for P 0pt,ext are needed both for the
unmodulated case (DC) and at the frequencies ©i (or ©2) and 2©2-© i (or 2©i-©2)- For
the unmodulated case,
PoPt.«t(D C ) = L M P ssl coS2 ( ^ W
b - (-1 )N | ) .
(3_g3)
Defining Vrt as the halfwave switching voltage (the voltage required for it radians of phase
shift), it is clear that
A(DC) =
,
V ,’
(3-84)
where V n is a measurable quantity for any modulator. This expression relating V K to the
DC value of A does not, in general, simplify the expression for A(©), because the DC bias
for a traveling-wave modulator with phase-reversed electrodes is generally applied on a
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106
separate set of electrodes. Therefore, the following expressions are used for the travelingwave modulator-based external modulation link modeling:
P o p iW D C ) = C0S2 ( ^ l L - ( , l ) N a . | ;
L m P ssl
l2 V ,
Popt,ext(fl>i) _ T ( 2 A(G>i) V m \
L m P ssl
’ M
S
(3-85)
4 1 ’
t
(2
A(<Mi) V m
l h\ ~
L
(ft
V b\ .
(3-86)
Jcosl- V ^ ) ’
and
Popt,ext(2t02-Q)i) _ . ( 2 A(2cd2~(0i) v m | j ( 2 A(2co2-tPi)
L m P ssl
'
ft
%
Lm
ssl
ft
'’ 2''
ft
vm
1
(ft
1'
v' Yu
V* >/
Vhi
(3-87)
where Jo, Ji, and J 2 denote the ordinary Bessel functions of the 0th, 1st, and 2nd order,
respectively.
With the above expressions, it is possible to proceed with the modeling of an
external modulation link using a traveling-wave modulator—with or without phase-reversal
electrodes—or a lumped-element Mach-Zehnder electro-optic modulator.
3.2.1
Gain Analysis
The small-signal gain of the external modulation fiber-optic link is derived using the
signal flow diagram (SFD) technique as was applied to direct modulation.
Fig. 3.2 (c) shows the SFD for the transmitter in an external modulation fiber-optic
link. This SFD is valid for both the lumped-element and traveling-wave type electrode
configurations. That is, whether a lumped-element or traveling-wave modulator is
employed, the optical transmitter SFD is obtained by considering the load I'm [calculated
using either (3-62) or (3-71), respectively] to be the port two termination for the network
represented by the two-port scattering network [SijMl- This network consists of the
microwave impedance-matching circuit and the parasitic device parameters in the equivalent
circuit of the modulator.
The output power of an external modulation fiber-optic link is calculated from the
optical receiver transfer function G rx as was derived in the direct modulation link case.
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107
Output power also depends on the amplitude of the detected RF photocurrent, /d(g>). which
is in turn proportional to the RF voltage v m
( co)
across the modulator electrodes. This RF
voltage is expressed as
vM(co) = VZo (aiM + biM) ,
(3-88)
where aiM and biM are the square roots of the incident andreflected powers at the
modulator electrodes and Zo is the characteristic impedance of the input system (50 Q).
From the SFD it is clear that
biM = aiMrim .
(3-89)
aiM =
(3-90)
and
- bgM S2^
r,
i - lS n M r gM + s 22Mr imJ
where
b s M ( l — S 22M f*lM )
1 -(SllM r gM + S22M Hm )
(3-91)
and where bSM is the normalized incident traveling wave intensity at the transmitter input
Because FgM=0.
VM
=
and IbsMl2 is equal to the incident transmitter power Pin,TX,ext.
V M (Le) = V P in ,T X ,e x t
Zo —
— (l + Tm) •
1 - S 22mFm
(3-92)
Lumped-Element Modulator Model
Equation (3-66) shows that the magnitude of the lumped-element modulator optical output
power at modulation frequency co is dependent upon the 0th* and l st-order Bessel
functions. For small arguments, these Bessel functions can be approximated as follows:
Jo(a) = l - Y + 6 4 ” -*= 1 forsmalla’
and
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( 3 _9 3 )
108
J , ( a ) = f ( l - f + t £ - . . . ) - f forsm alla,
^
and thus
P.pwx W = f ^
Lm P ssl co s ( ^ )
^
for small signals (i.e., small vm compared to V^).
The photocurrent detected by the optical receiver can be calculated using the
following expression:
iD(co) = L m L f K f d *1d | H d I P 0p t,e x t(w ),
(3 -9 6 )
where Lf, K fd, *1D» and IHdI are exactly as defined in the direct modulation link model.
Therefore, it is clear that
f_ | tc
K fd
tip
s s l f , , JjcVbj
IiD(co)12 _ |S 2 i M p | l + r M |2
7CLm
L mLp
L pK
fdT
ip pPSSL
| i -- Tr M
22m
Ml!22 '
m S
S22
1
2V*
lv ,t/
X |HdI2 Zo Pin.TX.ext .
(3-97)
Using the expression
Pout,RX = Iid®) 12 Zo Grx ,
(3 -9 8 )
where G r x was defined in the previous section on direct modulation link modeling, the
small-signal gain of the lumped-element modulator-based external modulation link operated
at the DC bias voltage Vb is obtained:
Gext = G jx .e x t I Hext 12 G rx ,
(3 -9 9 )
where
n._
_ IS 21M 12 11 + T m
'->TX,ext
|2
j------------------j-^—
1 1 ~ S 22mF m I
(3-100)
and
I H .H , j 2 =
p
l m L f K pp h d P s s l Zo j ^
j,H
p ,
,
(3 . 1 01)
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109
The cos 2 (itV \/V K) term in (3-101) indicates how the gain of the link employing the
lumped-element modulator varies as a function of the modulator DC bias voltage, which
will be discussed more thoroughly in section 4.2.4.
Traveling-Wave Modulator Model
In a fashion similar to the derivation of the lumped-element modulator-based link
gain, the following small-signal approximation is derived for the traveling-wave
modulator's optical output power at modulation frequency co:
P o p t,e x ^ ) = ^ - V M L m P s s l cos ( ^ ) ,
(3-102)
where the coefficient A is evaluated at the modulation frequency © using equation (3-78).
Except for the different calculation of Tm and the above derivation of the P0prvs.Vm characteristic, the small-signal gain of the external modulation link employing a
traveling-wave modulator is derived using the same SFD-based model as was used for the
lumped-element modulator link gain derivation. That is, when expression (3-102) is used
instead of the analogous equation for lumped-element modulators, the small-signal gain is
still calculated using equation (3-99), but with a different expression for IHextl2 that reflects
the different P0prvs.-VM characteristic:
|Hen| 2 =
Lm Lf
1,0PssL 1f r ) 2cos2 ( ^ ) IHD| 2,
(3-103)
where IHdI2 is calculated using equation (3-24).
3.2.2
Hoise-Analysis
The noise figure of an external modulation link is determined in the same fashion as
was used for the direct modulation noise figure calculation. That is,
v rc
(S /N )in ,ex t
Nout.RX.ext
NF“ = ( S T N W : - kfi T B Gext ■
ir\/i\
<3' 104)
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110
where Gext> the gain of the external modulation link, is calculated using the series of
expressions derived in the previous section, and depends upon whether a lumped-element
or traveling-wave electro-optic device is used as the modulator. N0UtJtX,ext. the total noise
at the output of the external modulation link, is the total of all noise falling into three
categories: Nth,TX,ext> the transmitter's thermal noise; Nthjtx, the receiver's thermal noise;
and Nop,ext. all noise which occurs due to the optical generation and detection of signals;
thus:
(3-105)
Nout,RX,ext = Nth.TX,ext + Nth,RX + N op,ext -
The thermal noise powers Nt^jx.ext and N^RX are calculated using the spectral densities
of the thermal noise voltage sources at the input to the optical transmitter and the output of
the optical receiver
(< v 2th,TX ,ext>
and
< v 2 th,R X > ,
equivalent circuit models of Fig. 3.2. The term
respectively), which are shown in the
N 0p>ext.
which is the noise contribution at
the link output due to the laser relative intensity noise at the modulation frequency
[RINssl(co)] and the shot noise and dark current noise at the detector, is calculated using
the spectral densities of these noise current sources (< i2RiN ,ext>. < '2shot,ext>. and < /2dark>.
respectively), which are also shown in Fig. 3.2.
The portion of the total noise power at the output of the external modulation link
that arises from thermal noise in the transmitter—defined here as Nthjx,ext—is calculated
using the Nyquist theorem, which states that the voltage spectral density at the output of the
optical transmitter due to all thermal noise sources (resistances) in the transmitter is:
(3-106)
where kjj is Boltzmann’s constant, T is the Kelvin temperature, and Z is the impedance
presented to the equivalent noise voltage source. It can be seen from Fig. 3.2 (a) that
Z - ZthM + Z o,
(3-107)
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I ll
where ZthM is the impedance of the transmitter circuit as seen from the input Using the
transfer function of the link, Nth,xx,ext is calculated from the portion of vth,TX,ext that is
applied to the input of the transmitter circuit
Nth.TX.ext =
^ ( vth,TX,ext)B ZthM 2 G-rx.extl Hext 12 G rx
ZthM + Zo
Zo
_ 4 k B T B | Z thMl2 (Zo + /te %im)
“
tiext»
—---------|Zum + Zo| 2 Zo
(3-108)
where B is the resolution bandwidth of the receiver and Zo is the impedance of the output
termination.
Note that when a perfect match is achieved in the transmitter and receiver matching
circuits at some frequency, ZthM=Zo at that frequency, so that at that same frequency,
Nth,TX,ext=2 kfi T B GextBecause the same optical receiver model applies for the external modulation link as
in the direct modulation case, Ntb,RX> the noise power at the link output contributed by the
thermal noise sources in the optical receiver, is calculated using equation (3-30) as in the
direct modulation link. Similarly, N0p(ext, the noise due to the optical signal conversion
process, is calculated using an expression very similar to (3-31):
Nop.ext = [(*RIN,ext)+ (4 o t .ex) + (&rk)] G rx B Z o .
(3-109)
Of the three summed current spectral densities in (3-109), <i2daik> is calculated exactly as it
was for direct modulation using equation (3-36), as is the optical receive module’s transfer
function G r x [expression (3-21)], whereas the noise current spectral densities <i2RiN,ext>
and <ti2shot,ext> are calculated as follows:
(iRiN.ex) = [ LF Kro tid Popt,ex«(DC)]2 RINSsl(g» ,
(3-110)
(l'shot,ex) = 2 q Lp Kfd “Hd Popt,ext(DC).
(3-1 11)
and
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112
Therefore, for the noise modeling in an external modulation link, the only parameter
that depends upon whether a lumped-element or traveling-wave external modulator is used
is Popt,ext(D C ).
the unmodulated optical power at the modulator output
Lumped-Element Modulator Model
For lumped-element modulators, equation (3-65) is used to calculate Popt,ext(DC),
and this result is substituted into equations (3-110) and (3-111) above in order to determine
N0p,ext for use in the external modulation link noise figure calculation.
Traveling-Wave Modulator Model
For traveling-wave modulators, equation (3-85) is used to calculate P0pt,ext(DC),
and this result is substituted into equations (3-110) and (3-111) above in order to determine
N0p,ext for use in the external modulation link noise figure calculation.
3.2.3
Intermodulation Distortion Analysis
In the derivation of external modulation link gain a small signal—i.e., small vm—
was assumed. As the input RF power is increased (and with it
vm
).
the sinusoidal
character of the modulator's P-V relationship eventually fails to approximate a linear
response, resulting in AM compression and the generation of harmonics and
intermodulation products. The distortion characteristics of the external modulation link are
analyzed in this section with respect to the modulation index mext. which, for an electrooptic modulator at a DC bias point Vb, is defined as:
=
(3-112)
For the third-order intermodulation products, which are usually the ones that limit
the spurious-free dynamic range, the intermodulation distortion to carrier ratio IMD/C is
given as follows:
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113
TMT~) _ Pppt.ext(2C02 ~ COp Of Pppt,ext(2Ct)i — (O2 )
C
Popt,ext(® l) Or Popt,ext(®2)
(3-113)
where the values of Popt,extat the various frequencies depend upon the type of modulator
used. The small-signal amplitudes of the fundamental and third-order intermodulation
product frequencies are extrapolated to determine mint
the modulation index at the third-
order intercept—i.e., where IMD/C = 1.
In Chapter 1 the spurious-free dynamic range of a fiber-optic link was defined as a
function of the third-order intercept input power Pin.int- Pin,int,ext is the external
modulation link input power at which the output powers at the fundamental and third-order
intermodulation frequencies are equal. This power depends on mjnt,ext> the modulation
index at the intercept power, as follows:
P in,int,ext—
G ix ,e x t Z o
4 G rx ,ex t Zo
(3-114)
Lumped-Element Modulator Model
The ratio of third-order intermodulation product output power to that of the
fundamental is calculated for a lumped-element modulator-based external modulation link
by dividing equation (3-67) into (3-66):
IMP _ Popt,ext(2 c02 - e>i) _ J2(a)
C
Popt,ext(Ol)
Jo(a)
(3-115)
where
—
a‘
7t vm
V* *
(3-116)
Given that the 2nd order Bessel function may be represented as follows:
(3-117)
it is found that for small signals
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114
M l - a2 _ 1 (n vM\2
C "8
8 I Vn I '
(3-118)
The small-signal behaviors of the fundamental and third-order intermodulation product are
extrapolated to determine the modulation index at the third-order intercept—i.e., where
IMD/C = 1:
mint,ext= mext w h e n a = - ^ L= V8 ‘ or vM = ^ V * .
(3 1 1 9 )
Therefore, using equations (3-112) and (3-114),
_
1Dt,eXt
YSIV*
^ ( V j t - 2 | Vb |) ’
(3_120)
and
■ "a< .« .(v « - 2 iv ,,i ) 2
r?
»
* in.int.ext----------- ITF*
4 GlX.ext Zo
_
8 V ,2
It2 Gxx,ext Zo
(3-121)
Traveling-Wave Modulator Model
The ratio of third-order intermodulation product output power to that of the
fundamental is calculated for a traveling-wave modulator-based external modulation link by
dividing equation (3-86) into (3-87):
IMP _ Popt,ext(2ft>2 - <Pl) _ J 2(a)
c
Popt,ext(®i)
Jo(a) ’
(3-122)
where in this case a is defined as follows:
. _ 2 A(co) vM
7t
’
(3-123)
Thus, for small signals,
IMP _ a 2 _ 1 (2 A(to) vm|2
C “ 8 8l
7C
(3-124)
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The small-signal behaviors of the fundamental and third-order intermodulation product are
extrapolated to determine the modulation index at the third-order intercept—i.e., where
IMD/C = 1:
m int,ext
=
m ext
When a = 2A (^
— = VS" or vM = j E j L ,
(3-125)
Therefore, using equations (3-112) and (3-114),
m in t,e x t =
4 V ?7t_____
Jt2 - 4 A(co) | Vb |
(3-126)
and
m int,ext U 2 - 4 A(OJ) | Vb | ) 2
*in,int,ext —
"
ZT~Z
“
16 [A(t0)]2 Gxx,ext Zo
2 ft2_____ _
[A(to)]2 Grx,cxt Zo
3.2.4
(3-127)
Linearity Analysis
The effect of AM compression is predicted similarly. The AM compression
characteristics of the external modulation link are analyzed in this section with respect to the
modulation index mext, which, for an electro-optic modulator at a DC bias point Vb, is
defined by equation (3-112).
In Chapter 1 the compression-limited dynamic range of a fiber-optic link was
defined as a function of the 1 dB compression input power Pin,iCP- Pin,lCP,ext is the
external modulation link input power at which the gain is compressed by 1 dB relative to
the small-signal gain. This power level depends on the modulation index at the 1 dB
compression input power, micp.ext* as follows:
ni i2Cp,ext ( l f - | V b | ) 2
* in .I C P .e x t
p
GTX,extZo
m fcp.ext ( V* - 2 1Vb | ) 2
a
p
rj
4UTX,ext4)
•
(3-128)
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116
Similar to the calculation of third-order intercept modulation index, the value of micp.ext
for an external modulation link is determined by examining the Popt.exrvs.-VM expression
appropriate to the type of modulator used; to model the AM compression, however, the
terms which become non-negligible at higher signal (vm) levels must be considered.
The power-dependent portion of the modulator's Popt.exrvs.-V M expression is the
factor Ji(a)-J 2 (a). For small input RF powers the output power at the fundamental
frequency increases linearly with the input power, since
J i(a) Jo(a>= 2 ( I* %- + i 92 - - * • ) ( l - ^ - + ^ - - - - ) = f forsmaUa.
(3 _129 )
At larger input RF powers the fundamental begins to saturate. This response is obtained by
considering more terms of the Bessel function. Compression of the fundamental output
power by 1 dB means that
a!
= 1.259,
aifl
4 V1
+
4
f (i _a! + _ai__
64
•"/I
192
8
" 'I
(3-130)
which corresponds to a = 0.5500. From this value of a, it is possible to obtain the value of
the modulation index mext at the point of 1 dB compression.
Lumped-Element Modulator Model
For an external modulation link using a lumped-element electro-optic modulator, the
modulation index at the 1 dB compression point is:
micp.ext = mext when a =
=
V ,t
0.5500 , or vM = 0 5500
2 x 0.5500 Vk
_ 7t(Vff- 2 | V b|) '
7t
(3-131)
Substituting this into the equation for input RF power in termsof modulation index mext,
the input power at the 1 dB compression point is therefore:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
117
in.iCP.ext
_ m lCP.ext ( 2
I
GlX.extZo
l) _ m fcp.ext ( ^ ~ 2 1Vb | ) 2
4 GrX.ext Zo
^ (0.550012 V j
It2 Gxx.ext Zo
(3-132)
Traveling-Wave Modulator Model
For an external modulation link using a traveling-wave electro-optic modulator, the
modulation index at the 1 dB compression point is:
micp,ext = mext when a = ?
VM = 0.5500 , or vM =
2 x 0.5500 jc
Jt2 - 4 A(©)jVb|
(3-133)
Substituting this into the equation for input RF power in terms of modulation index mext>
the input power at the 1 dB compression point is therefore:
m 2CPext ( jc2 - 4 A(co) 1Vb I ) 2
iD,1CP,eXt
16[A(©)]2 Gix,extZo
(0.2750)2 jc 2
[A(to)]2 Grx.ext Zo
3.2,5
(3-134)
Analog Link Performance: Dynamic Range Calculation
The spurious-free and compression dynamic ranges of the external modulation link
are defined exactly as they are for the direct modulation link, i.e.:
\2. 1 d. . it.e x t \2_|Pout,int,ext\o / Pin.int.ext
13
13
SFDRe" = l t W ^ ) ^ kB T B tN Fe*/13
(3-135)
and
— 1-259 Pput.lCP.ext _
ext"
Nout.RX.cxt
Pjn.lCP.ext
_ kB T B N F e x t ‘
(3-136)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
118
3.2.6
Summary of the External Modulation Fiber-optic Link Model
In Tables 3.3 and 3.4, the equations which have been derived in the previous five
sections of this chapter have been reduced to their most compact forms and listed in a
logical order. Table 3.3 (a) lists the 16 equations necessary for calculating the gain and
noise figure of an external modulation link using a lumped-element modulator; Table 3.3
(b) lists the 17 equations which are used when the modulator is of the traveling-wave
variety. Table 3.4 (a) gives the 6 equations needed to calculate the spurious-free and
compression dynamic ranges for a lumped-element modulator-based external modulation
link; Table 3.4 (b) gives the corresponding 8 equations for a link employing a travelingwave external modulator.
In Chapter 4, the measured performance characteristics of three high-performance
external modulation fiber-optic links are compared to the performance predicted by the
above model in order to assess the usefulness and accuracy of this modeling procedure.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Noise Figure
Small-Signal Insertion Gain
v,rN F eii
G « i = G-rx,e»t| H e«i| G rx
(3 -9 9 )
Nout.RX.exl
=------—
—
ku T
B Ge»t
(3 -1 0 4 )
where
where
~ __| s 2im| 2| i + r M12
G" '" - jr-tan.!*
r M= M “ ? m Zo
1 + j o) Cm Zo
(3 -1 0 0 )
Noul.RX.«»l= N|h,TX,eM+ Nih.RX + Nop.e»
(3 -1 0 5 )
kBTB|Zo,M| 2|Zo+/?e Zo,m| n
-----7---- ! - ■----------1 Gem
kI
4
Ntf,,TX.Ml =
|ZuiM+ Zo| Zo
(3 -6 2 )
(3 -1 0 8 )
x i _____ 4 kB T B -Re Z u ,d Z o
r . ___
**
| S21D| 2
| i - S u D r D| 2
r D= r ,d- Z o
(3 -2 )
R jd + Zo
1 H e ,,I 2 - ! ” ^
|ZthD+ Zo| 2
^
(3 -2 1 )
N o p .e iF [(fRIN.exJ + (f’ihol.ei} +
L f *gP!iPPssLfrj2cos2|ffVbj| H d | 7
(3 -1 0 1 )
( ir in .u ) = [
(iihoi.ex) =
and
IHdI2=—
r »— v»
1+
12 JTf3dB/
Lf Kfd t \ d
(3 -3 0 )
(ididi)] G r x B Zc
Popi.e»(DC)] 2RINssifco)
2 q Lp Kfd t)d Pop«,e»(DC)
(id.rft)= 2 q Ididc
(3 -1 0 9 )
(3 -1 1 0 )
(3 -1 1 1 )
(3 -3 6 )
(3-24)
and
PoP..e»(DC)
= Lm PsslcosfeVfe - S-\
\2 V* 4/
(3-65)
Table 3.3 (a) Summary of analytical model for small-signal gain and noise figure of an external modulation link employing a
lumped-element electro-optic modulator.
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Noise Figure
Small-Signal Insertion Gain
J..T1
(3-99)
G tx ,CXt | H u t | 2G rx
Noui.RX.eit
Nrut®------- ——
keTBGut
(3-104)
where
where
_ 1 S21 m | 21 1 + T m | '
Grx.ext =
(3-100)
I 1 - S22nT m | 2
r
Nout,RX.e*t= Nth.TX.ext + Nth.RX + Nop.ex
N u, tx
Z k{ U ) - Z o
| Z uiM + Z o | 2 Z o
kt ____4
= Zc Z| + 20
Zc + Zt tanh yez
Z m( z )
G rx =
r Di
_ 4 k B T B | ZthM|2 |Z o + R e ZthM| q ^
(3-71)
Z k< U ) + Z o
(3-68)
I S21D | ‘
(3-21)
(3-105)
kfl T B -Re Z u ,d Z o
|Z«,DtZ0p"
(3-108)
(3-30)
Nop,ext~ [((RIN.ex) + (ixhot.ex) + (idirii)] G rx B Z c
(3-109)
11 -SnD rD| 2
R) d - Z q
(3-2)
R jd + Zo
|Hui| 2= (A(o)) Lm
(iRIN.ex) = [ Lp K fd TId Popt.ex(DC)j] 2RlNsSl({l))
qp PsslZoj 2C0S2|nYbj | Ho | s
(fthot.ex) = 2 q Lp
(3-103)
and
K f d R d Popt.u(DC)
(idxrit) = 2 (J Idiric
1Ho | 2 = l+
(3-110)
(3-111)
(3-36)
and
\2 n fadB/
(3-24)
Popl.ex(PC) _ co;.2 |w Vb _ /_ |\N
Lm P s s l
*2 V r
41
(3-85)
Table 3.3 (b) Summary of analytical model for small-signal gain and noise figure of an external modulation link employing a
traveling-wave electro-optic modulator.
to
o
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Compression Dynamic Range
Spurious-Free Dynamic Range
2
SFDRe
Pin.ini.ot
(
j?
kuTBNFeJ
(3-135)
CDRcm = - —
(3-136)
kB T B NFe»i
where
where
_ mjn,.«»i ( Vk - 2 1 V b | ) 2
Pin,ini,cm =
4 G t x .cm Z o
P
(3-114)
irr
_ m ftp .eu ( V * - 2 1V b |) 2
* in ,l C P ,c » l----------------------—-----------—-------------4 G t x .m i Z o
(3-128)
and
and
mint,e*l =
V32 V k
n ( Vk—2 1Vb|)
Table 3.4 (a)
(3-120)
m iC P .e » i
_ 2 x 0.5500 V,
------------ j------rr
n ( V ,- 2 |V b |)
(3-131)
Summary of analytical model for spurious-free and compression dynamic range of an external modulation link
employing a lumped-element electro-optic modulator.
K»
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Compression Dynamic Range
Spurious-Free Dynamic Range
2
_ {
SFDRen =
Pin.im.cm
(3-135)
CDRe»t =
kB T B NFeni'
Pi",ICP,cl“
kB T B NFe*i
(3-136)
_ m&p,cm ( Vk - 2 1Vb 1) 3
(3-128)
where
where
_
( V* - 2 1Vb | ) 2
*in»int,exi “
(3-114)
Pin.lCP.eil
4 Gtx.ch Zo
(3-126)
and
m i C P ,e » l=
A/(0)S - n " ? r ij r ^ —
'
X
2 x 0.5500 n
it2 - 4 A (w )|V tJ
r l------r
2 Ge X Zw((0,Le)
N -l
Y H r I
.m=o
4 Gtx.bxi Zo
(3-133)
Zm(0),z) cos (pe8 z) dz , (3-78)
and
8 s 1-
nP
Table 3.4 (b)
(3-75)
Summary of analytical model for spurious-free and compression dynamic range o f an external modulation link
employing a traveling-wave electro-optic modulator.
to
to
123
CHAPTER 4
EXPERIM ENTAL VERIFICATION O F THE ANALYTICAL MODELS
In this chapter, the measured performance characteristics of six fiber-optic links are
described. These six links were designed such that together they exhibit a broad range of
characteristics—i.e.: both microwave and millimeter-wave frequency operation; both
narrowband and broadband operation; direct modulation of both Fabry-Perot (FP) and
distributed-feedback (DFB) semiconductor lasers, and; external modulation of both
lumped-element and traveling-wave external modulators. Section 4.1 describes the
measurements which were performed on each of the six links under a variety of bias
conditions.
Described in section 4.2 are the three experimental links in which a directlymodulated semiconductor laser diode was used in the optical transmitter. Section 4.3
describes the other three links, in which electro-optic external modulators were used to
impose the RF signal on an optical carrier supplied by a high-power solid-state laser.
For all six links, this chapter assesses the extent to which the link models set forth
in Chapter 3 accurately predict the measured performance.
4 .1
L ink Perform ance C haracterization Techniques
For each of the six links, the same four performance parameters—small-signal
insertion gain, noise figure, spurious-free dynamic range, and compression dynamic
range—were determined from three sets of microwave signal and noise power
measurements.
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124
4.1.1____ Small-Signal Gain Characterization
For each of the six links, the two-port insertion gain (Gdir or Gext as appropriate)
was measured using an automated microwave network analyzer. For the high-frequency
external modulation link described in section 4.3.3, a Wiltron 3600B 60 GHz analyzer was
used to reach frequencies above 26.5 GHz (the highest characterization frequency of the
HP8510 analyzer used to measure the insertion gain of the other five links). These
analyzers both measure the microwave power delivered to their port 2 input from the optical
receiver when a known (calibrated) microwave power is launched from their port 1 output
into the optical transmitter. The length of fiber used in each of the six links was on the
order of 2 meters, corresponding to about 10 nsec of delay between RF signal delivery to
port one and measurement at port 2. Delays on the order of 100 nsec or greater would have
required that the analyzer be calibrated to delay its power measurement at port 2 until
sufficiently long after the port 1 RF power launch.
Figure 4.1 shows the experimental set-up for measuring the link insertion gain.
For each link, calibration of the automated network analyzer was performed using a low
port 1 power—typically -10 dBm—to ensure that the small-signal and not the partiallycompressed link response was measured.
4.1.2____ Noise Figure Characterization
In cases where microwave small-signal gain is high (or at least no lower than -20
dB) and noise figure is expected to be less than 30 dB, the link noise figure NFdir or NFext
can be measured directly using an HP8970 noise figure meter. However, since only two
of the six links were expected to meet these criteria, an alternative noise figure
characterization technique was used. By using the power measurement mode of the noise
figure meter, the link's output noise power spectral density can be measured directly and is
expressed as a ratio (in dB) above the ambient thermal noise power spectral density kjjT.
Noise figure is then calculated from the measured noise output power spectral density
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
125
Automatic Network Analyzer
RF in
RFout
p- JTwo-Port NetworkJ
Q q (Hber-Optic Link) pj~~t
Under Test J
Figure 4.1 Experimental set-up for measuring the small-signal insertion gain of a
microwave fiber-optic link.
Signal
Generator
LO
Calibrated
Noise Source
JTwo-Port Network} RF
i (Fiber-Optic Link)i------J_ Under Test
J
_ _ _ j
Mixer
Noise Figure
Meter
Figure 4.2 Experimental set-up for measuring the output noise power from a
microwave fiber-optic link to determine its noise figure.
3 dB
20 dB
Coupler Isolator
50 f l [ J
Signal
Generator#!
J
[1
•-C H 20 dB
Isolator
Signal
Generator #2
JTwo-Port Network}
►i(Hber-Optic Link) t
1 Under Test J
h h
Spectrum
Analyzer
f l, f 2 ’
2fr f2’ 2f2- f l
Figure 4.3 Experimental set-up for measuring the two-tone intermodulation distortion
of a fiber-optic link to determine its dynamic range.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
N0uttRX,di/B or N0ut,RX,ext/B and from the measured small-signal gain G^ir or G ext using
Eq. (1-2).
Fig. 4.2 shows the experimental set-up for measuring a link's output noise power
spectral density. Since the HP8970 noise figure meter can only detect RF powers up to 1.6
GHz in frequency, higher-frequency RF inputs were down-converted using a highfrequency LO source and an external mixer, as the figure shows. The calibration of this
experimental set-up was performed with the noise source bypassing the link and connecting
directly to the mixer. Thus, the RF noise power generated by the mixer and IF signal
generator was automatically subtracted from the total measured noise out of this system
when the link was placed in the set-up as shown in Fig. 4.2.
4.1.3
Spurious-Free and Compression Dynamic Range Characterization
Determination of the links’ spurious-free dynamic ranges required that two-tone
intermodulation distortion (IMD) measurements be performed. Fig. 4.3 shows the set-up
that was used for this purpose.
As the figure shows, the microwave signal synthesizers were set at two different
frequencies (fi and f2) within the link band, their output powers were equalized, and their
outputs were combined and sent into the optical transmitter. The R F output was then
measured not only at fundamental frequencies fi and f2 but also at the third-order
intermodulation products 2fi-f2 and 2f2-fi, which also fall within the link band. This
measurement was repeated for many input power settings so that the third-order intercept
input power (Pin,int,dir or Pin,int,ext) could be determined. The input third-order intercept is
a fictitious fundamental frequency input power at which the link output power at the thirdorder intermodulation products would equal the output power at the fundamental
frequencies in the theoretical absence of AM compression. Spurious-free dynamic range
SFD R dir or SFDRext can then be calculated from the intercept input power and the
measured noise figure NFdir or NFext using Eq. (1-5).
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Another parameter determined from the same set of measurements was the 1 dB
compression input power Pin,1CP,dir or Pin,lCP,ext> which is the input power at which the
RF gain at the fundamental frequencies is compressed by 1 dB relative to the small-signal
gain.
Compression dynamic range CDRdir or CDRext is then calculated from the
compression input power and the measured noise figure NFdir or NFext using Eq. (1-4).
4 .2
Direct Modulation Fiber-optic Link
To assess the validity of the direct modulation link performance model rendered in
section 3.1, this section compares the measured performance of some direct modulation
links to the performance predicted by the model. Three cases are examined: 1) operation
within a small percentage bandwidth surrounding a low microwave frequency; 2) operation
within a small percentage bandwidth surrounding a higher microwave frequency, and; 3)
operation across a wide microwave bandwidth.
4.2.1____ Determination of Model Parameters
The direct modulation link model given in Chapter 3 was fully summarized by the
optical transmitter and receiver equivalent circuits and signal flow diagrams of Fig. 3.1,
and by the equations listed in Tables 3.1 and 3.2. All the equivalent circuit element values
and all the variables in the equations must obviously be determined in order to predict link
performance using this model. Table 4.1 lists all of these needed parameters, and briefly
describes how the parameter values may be determined. A more thorough description of
these methods is given in this section.
Table 4.1 indicates that the laser diode's forward-biased junction resistance Rjl and
all other laser equivalent circuit element values were de-embedded from the one-port
scattering parameter S n that had been measured for the device. The detector diode's
reverse-biased junction resistance Rjd and all other detector equivalent circuit element
values were determined in the same manner. These S-parameter measurement and de­
embedding methods were described in section 2.4.1 of the Review of Literature; in
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128
P arm eter
Rjl and all laser equivalent circuit element values
M ethod o f determ ination
de-embedded in Appendix A
from Si i measurements
[$ijlJ, YthL
calculated in Appendices D,
E, and F, from optical
transmitter equivalent circuit
using SuperCompact [93]
microwave CAD software
©r.Y
values which make Eq. (3-23)
fit laser frequency response
measured as in Fig. 4.4 (a)
and calculated in Appendix B
RIN sl
calculated in Appendix £ from
RF spectrum analyzer
measurement using detector
and amplifier with known
characteristics
nL, OCL» L, Ri, R2, d, Vol
quoted by laser manufacturer
TIL, Klf , Lp, Kpj), T]D, IL, Ith, idark
measured using DC ammeter
and/or optical power meter
Rjd and all detector equivalent circuit element values
de-embedded from detector
S ii measurements
[SijD], ZthD
calculated from optical
receiver equivalent circuit
using SuperCompact [93]
microwave CAD software
package
f3dB
value which makes Eq. (3-24)
fit detector frequency
response measured as in Fig.
4.4 (b)
Table 4.1
Methods for determining all parameters needed to predict direct modulation
link performance using model set forth in Chapter 3 (Fig. 3.1 and Tables
3.1 and 3.2)
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Appendix A, how these methods were used to determine the de-embedded one-port
scattering parameters of all the electro-optic devices in the experimental links is fully
documented.
Once the laser diode equivalent circuit was realized, the rest of the optical
transmitter was designed to efficiently couple power at the microwave frequencies of
interest from the 50 £2 input load to the laser’s junction resistance Rjl - This was
accomplished by inserting a combination of lumped and/or distributed circuit elements to
transform the microwave impedance of the laser diode’s equivalent circuit to 50 £2 across
the microwave band. The SuperCompact [93] microwave CAD software package was
used to facilitate the design of this circuit. Additionally, the CAD simulation allows easy
determination of the optical transmitter matching circuit’s two-port scattering parameters
[SyiJ and its output admittance YthT. Determination of the optical receiver’s equivalent
circuit parameters [Sip] and Z>hn was accomplished in the same way.
The laser’s relaxation oscillation frequency cor and damping rate y determine the
device’s frequency response. Therefore, as is stated in Table 4.1, measurement of the
device’s frequency response using a Hewlett Packard Lightwave Signal Analyzer enables
determination of these two parameters, which are also needed for accurate prediction of a
direct modulation link’s linearity and intermodulation distortion characteristics. Fig. 4.4 (a)
shows the set-up for performing this measurement, which yields the laser response IHlI2 as
a function of frequency as predicted by Eq. (3-23) in section 3.1.1 of the thesis. Fitting the
measured result for any bias current to this equation results in values of ©r and y for the
device under that bias condition. Equivalently, measurement of an optical detector’s
frequency response IHd I2 using the Lightwave Signal Analyzer set-up in Fig. 4.4 (b) and
fitting the measured data to Eq. (3-24) enables accurate determination of the device’s 3-dB
bandwidth f3dB- In Appendix B, the determination of the frequency responses of all the
electro-optic devices in the experimental links is fully documented.
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130
HP Lightwave Signal Analyzer
jSemiconduto{
Laser or
•Laser-Driven
i External
i Modulator
RF-modulated
optical out
L UnderTestj
(a)
HP Lightwave Signal Analyzer
RF-modulated
optical in
RFout
Optical
• Under Test •
i___________i
(b)
RIN
Optical
Under Test
Photodetected RIN
Wideband and shot noise
InGaAs
Photodiode
RF Amplifier
Spectrum
Analyzer
(c)
Figure 4.4 Experimental set-up for measuring the microwave frequency characteristics
of electro-optic devices for use in fiber-optic links.
(a) Set-up for measuring the frequency response of a directly-modulated
semiconductor laser or an external modulator with a CW optical source.
(b) Set-up for measuring the frequency response of an optical detector.
(c) Set-up for measuring the relative intensity noise of an optical source.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
131
To determine RIN s l . the relative intensity noise of the directly-modulated
semiconductor lasers, the test set-up shown in Fig. 4.4 (c) was used. Each semiconductor
laser was set to a bias current of interest and a broadband (0-40 GHz), resistively-matched
InGaAs Schottky photodiode with well-known characteristics was used to detect the optical
power. The RF output power of the detector consisted of the laser’s RINsl as well as the
detector shot noise and a negligible amount of thermal noise power. This RF output was
amplified using a low-noise amplifier with known gain and noise figure across the
frequencies of interest, and fed into an RF spectrum analyzer, as shown in the figure. A
simple calculation using the known detector responsivity, detector equivalent circuit,
detector DC photocurrent, and amplifier gain and noise figure yielded values of RINsl at
each frequency of interest under each of the desired laser bias conditions. Appendix C
shows how these measurements and calculations yielded the frequency-dependent RIN
values used for the optical sources in the six experimental links.
The following intrinsic parameters of the semiconductor laser diodes used in the
experimental direct modulation links were quoted by the device manufacturers: the
refractive index, length, thickness, and volume o f the active region (nL, L, d, and Vol,
respectively); the optical attenuation per unit length in the active region
( ocl) ,
and; the
reflectivities of the front and rear facets of the device (Ri and R2, respectively).
Finally, several parameters could be measured directly using a combination of DC
current sources and CW optical power sources with DC ammeters and optical power
meters. Using a DC current source and ammeter and measuring the semiconductor laser’s
optical output with an optical power meter at many bias levels yields a power vs. current
curve similar to the one given in Fig. 2.3. From this curve, the laser’s threshold current Ith
is determined along with the external differential quantum efficiency t i l at any value of
laser bias current II- Measuring the ratio of the laser’s output power at any value of I I
after and before fiber pigtailing yields an accurate value for the laser-to-fiber coupling
efficiency K l f - Similar optical power ratio measurements give values for the total loss in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the optical fiber and connectors (Lp) and the fiber-to-detector coupling efficiency (Kpo).
Photodetector responsivity tjd is measured by using a known optical power level to
illuminate a small portion of the detector’s photosensitive region and measuring the
resulting DC output current The detector’s dark current Idaik is measured using a DC picoammeter when incident light intensity is brought to zero.
4.2.2
Case 1: Small Percentage Bandwidth Surrounding a Low Microwave Frequency
This section describes a direct modulation L-band link which was developed for
high-performance operation centered at a frequency of 900 MHz. Table 4.2 at the end of
4.2.2 summarizes the measured performance of this link at f=900 MHz, and compares the
measured performance parameters at 900 MHz to the parameters predicted in Appendix D
by the direct modulation link model set forth in section 3.1 of the thesis.
Electro-optic Device Selection
The directly modulated optical source in this link was an InGaAsP Fabry-Perot
(FP) laser diode manufactured by BT&D, which emitted optical power at the 1.3 pm
wavelength and featured a large external differential quantum efficiency ( t | l = 0 - 2 7 mW/mA)
when biased above its measured threshold current of 1 8 mA. The detector used in the link
was an InGaAs p-i-n photodiode (also manufactured by BT&D), which also featured a
large responsivity ( t | d = 0 . 9 5 mA/mW) and appreciable 3-dB modulation bandwidth ( f 3 dB = 8
GHz) when reversed-biased with a DC voltage of 15 V. These device quantities, along
with the other important device parameters listed in Table 4.1, were determined using the
techniques described in section 4.2.1 and Appendices A, B, and C.
Electro-optic Device Characterization
The laser diode and photodetector were mounted in standard microwave test
fixtures to enable de-embedding of the device impedances out of the measured scattering
parameters of the devices in their test fixtures, as was described in section 2.4.1 and shown
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
133
by example in Appendix A. Two-port circuit parameters of the intermediary elements of
the test fixtures (bias tee, connector, and transmission line) were obtained using the ThruReflect-Line (TRL) technique [28]. For frequencies ranging from 100 MHz to 2.1 GHz,
both the measured scattering parameters of these devices in their test fixtures and their deembedded scattering parameters are given in Appendix A
Electro-optic Device Modeling
Equivalent circuit models of the semiconductor laser and detector in this link were
obtained by using the SuperCompact CAD program to fit values of L p l , R p l . R j l > and
C j l [for the semiconductor laser—see Fig. 3.1(a)] and C j d , R j d > R p d » and L p d [for the
photodetector—see Fig. 3.1 (b)] to the de-embedded scattering parameters of these
devices. The equivalent circuit models of the specific devices used in this link are also
rendered in Appendix A From these models the Q ext factor for each device was calculated.
The Qext factor is defined as the ratio of the imaginary part of the complex impedance at
some band center frequency to the real part of the impedance at that same frequency.
For the semiconductor laser diode used in the direct modulation link designed for
operation across a narrow band of low RF frequencies, a Qext factor of approximately 0.38
was calculated at the desired center frequency of 900 MHz.
Fano's theorem (see
expression (2-5) and [34]) predicts that, for a minimum return loss of 10 dB, a reactive
matching bandwidth of nearly 6.5 GHz can be achieved for a Qext=0-38 device if an
infinite number of reactive matching stages can be used (although a 6.5 GHz-wide
frequency band would obviously not be centered at 900 MHz).
At the same 900 MHz center frequency, the p-i-n photodiode used in this link has a
Q ext
of 32.
Fano’s theorem dictates a maximum -10 dB matching bandwidth of
approximately 77 MHz for the photodetector matched using an infinite number of lossless
reactive matching stages.
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134
Optical Transmitter and Receiver Fabrication
Optical transmitter and receiver modules were fabricated to incorporate the
semiconductor laser and p-i-n photodiode, respectively, with single-mode optical fiber
pigtails (on the order of 1 meter in length) and circuits consisting of reactive elements to
match the device impedances to 50 Q. These reactive matching circuits were designed and
simulated using SuperCompact [93]. A photograph of the optical transmitter and receiver
modules is shown in Fig. 4.5. The electrical input and outputs were 50 Q. microstrip
transitions to 7 mm microwave connectors. Measured 900 MHz return losses of 26 dB and
14 dB were obtained respectively for the laser and photodetector modules when the
inductances and capacitances that constitute the laser and detector matching circuits were
adjusted properly. Greater than 10 dB of return loss was obtained across a bandwidth of
220 MHz in the case of the optical transmitter, 30 MHz in the case of the optical receiver.
Optical power was coupled from the laser to the active region of the detector with a
measured efficiency (Klf Lf Kfd ) of 40% using a plano-convex gradient-index (GRIN)
lens with AR-coated facets to focus the diverging output beam of the semiconductor laser
into the 8 pm core of the single-mode fiber.
Optical Transmitter and Receiver Modeling
The equivalent circuit model of the optical transmitter and receiver modules
rendered in Fig. D .l of Appendix D was used to determine values of [SyL], Ythi. [Syo],
and Zthn at frequencies between 500 MHz and 1.5 GHz. The bias-dependent values of (Dr,
y, and RINsl were determined as described in section 4.2.1 and shown by example in
Appendices B and C, as were the rest of the parameters listed in Table 4.1. Table D .l (a)
in Appendix D lists the values determined for all of the frequency-independent model
parameters; Table D .l (b) gives all the frequency-dependent model parameters that were
calculated using the equations in Tables 3.1 and 3.2, including the link gain, noise figure,
spurious-free and compression dynamic range.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
135
F igure 4.5
Experimental L-band direct modulation link. The optical transmitter
module is shown on the upper right, and at the lower left is the optical
receiver module.
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136
Link Results
For one bias current
(Il = 2 7
mA), the insertion gain predicted by the direct
modulation link model is plotted in Fig. 4.6 alongside the insertion gain of the link as
measured using the set-up shown in Fig. 4.1. Both curves exhibit 3-dB bandwidths of
-100 MHz (11% bandwidth) and peak at 900 MHz, where the analytically predicted
insertion gain is 5.5 dB compared to the measured result of IS21I2 =3.7 dB. They also
seem to have the same basic shape. These curves show that the direct modulation model
predicts the performance of a narrowband link across a range of low RF frequencies much
broader than its 3-dB bandwidth.
Table 4.2 indicates that the measured dynamic range of this link was found to be
greater when the laser bias was increased to 44 mA, a bias for which the measured
insertion gain was 3.0 dB. Using the appropriate group of equations in Table 3.1, the
noise figure of the link was calculated at f=900 MHz for the same three bias levels at which
insertion gain was determined, and was predicted to be minimum under the 44 mA laser
bias condition. The noise figure of the link was experimentally determined using the set-up
in Fig. 4.2. The minimum noise figure of 30 dB was measured at the 44 mA laser bias, as
shown in Table 4.2, confirming the ability of the model to predict the effect of the laser bias
current setting on the direct modulation link’s noise figure.
Using the experimental set-up shown in Fig. 4.3, the two-tone intermodulation
distortion of the L-band direct modulation fiber-optic link was measured at two third-order
intermodulation products surrounding its center frequency of 900 MHz for each of the laser
bias currents at which gain and noise figure had been measured. Table 4.2 lists the
spurious-free and compression dynamic ranges determined from these measurements, as
well as the dynamic ranges predicted by the link model of section 3.1. The measured
compression dynamic range results compare very favorably with the compression dynamic
range predicted using the equations in Table 3.2. The measured spurious-free dynamic
range results do not compare as favorably with the analytical results, although the model
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137
0 .0 dB
tog MAG
1 0 . 0 43/
3 . 7 1 6 1 dB
MAF <ER 1
J 0 0 . ) Mf-z
STA RT
STO P
Calculated
Measured
0 .5 0 0 0 0 0 0 0 0
1 .5 0 0 0 0 0 0 0 0
GHz
GHz
Figure 4.6 Insertion loss of the L-band direct modulation fiber-optic link. The
measured result is shown along with the performance predicted in
Appendix D using the model rendered in section 3.1.
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138
L aser Bias C u rren t
20mA 27 mA 44 mA
G ain (dB)
Model
Measurement
0.7
-1.0
5.5
3.7
4.6
3.0
Model
Measurement
33.2
34.0
31.5
32.0
29.4
30.0
46.3
46.7
55.0
56.7
62.5
66.3
65.7
66.0
78.0
78.5
89.0
89.0
Noise Figure (dB)
Spurious-Free Dynamic Range (dB)
Model
Measurement
Com pression Dynamic Range (dB)
Model
Measurement
Table 4.2
Summary of the L-band direct modulation link performance at f=900 MHz.
Measured and modeled results are given at laser bias currents of 20 mA, 27
mA, and 44 mA. Spurious-free and compression dynamic ranges are
quoted for a resolution bandwidth of 1 MHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
139
did accurately predict the magnitude of the effect of laser bias current on dynamic range.
This anomaly is explained further in section 4.2.6.
4.2.3
Case 2: Small Percentage Bandwidth Surrounding a High Microwave Frequency
This section describes a direct modulation Ku-band link which was developed for
high-performance Ku-band operation centered at a frequency of 12 GHz. Table 4.3 at the
end of 4.2.3 summarizes the measured performance of this link at f=12 GHz and compares
the measured performance parameters at that frequency to the parameters predicted in
Appendix E by the direct modulation link model given in section 3.1 of the thesis.
Electro-optic Device Selection
The directly modulated optical source in this link was an InGaAsP distributedfeedback (DFB) laser diode manufactured by AT&T, which emitted optical power at the
1.3 |im wavelength and featured a large external differential quantum efficiency
(t i l = 0 . 2 6
mW/mA) when biased well above its measured threshold current of 13 mA. The detector
used in the link was an InGaAs p-i-n photodiode manufactured by GTE, which also
featured a large responsivity CnD=0-80 mA/mW) and 3-dB modulation bandwidth (f3dB=20
GHz) when reversed-biased with a DC voltage of 9 V. These device quantities, along with
the other important device parameters listed in Table 4.1, were determined using the
techniques described in section 4.2.1 and Appendices A, B, and C.
Electro-optic Device Characterization
The laser diode and photodetector were mounted in standard microwave test
fixtures to enable de-embedding of the device impedances out of the measured scattering
parameters of the devices in their test fixtures, as was described in section 2.4.1 and shown
by example in Appendix A. Two-port circuit parameters of the intermediary elements of
the test fixtures (bias tee, connector, and transmission line) were obtained using the ThruReflect-Line (TRL) technique [28]. For frequencies ranging from 11 to 13 GHz, both the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
140
measured scattering parameters of these devices in their test fixtures and their de-embedded
scattering parameters are given in Appendix A.
Electro-optic Device Modeling
Equivalent circuit models of the semiconductor laser and detector in this link were
obtained by using the SuperCompact CAD program to fit values of L pl , R p l >Rjl >and
C jl [for the semiconductor laser—see Fig. 3.1(a)] and C jd , Rjd *R pd . and L pd [for the
photodetector—see Fig. 3.1 (b)] to the de-embedded scattering parameters of these
devices. The equivalent circuit models of the specific devices used in this link are also
rendered in Appendix A. From these models the Qext factor for each device was calculated.
For the semiconductor laser diode used in this direct modulation link, a Qext factor
of approximately 0.56 was calculated at the desired center frequency of 12 GHz. Fano's
theorem (see expression (2-5) and [34]) predicts that, for a minimum return loss of 10 dB,
a reactive matching bandwidth of approximately 58.5 GHz can be achieved for a Qext=0-56
device if an infinite number of reactive matching stages can be used (although a 58.5 GHzwide frequency band would obviously not be centered at 12 GHz).
At the same 12 GHz center frequency, the p-i-n photodiode used in this link has a
Qext of 5.6.
Fano’s theorem dictates a maximum -10 dB matching bandwidth of
approximately 5.8 GHz for the photodetector matched using an infinite number of lossless
reactive matching stages.
Optical Transmitter and Receiver Fabrication
Optical transmitter and receiver modules were fabricated to incorporate the
semiconductor laser and p-i-n photodiode, respectively, with single-mode optical fiber
pigtails (on the order of 1 meter in length) and circuits consisting of reactive elements to
match the device impedances to 50 £2. These reactive matching circuits were designed and
simulated using SuperCompact [93]. The link appearance was similar to that of the L-band
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
141
direct modulation link described in section 4.2.2 and shown in Fig. 4.5. The electrical
input and outputs were 50 £2 microstrip transitions to 7 mm microwave connectors.
Measured 12 GHz return losses of 29 dB and 36 dB were obtained respectively for the
laser and photodetector modules when the inductances and capacitances that constitute the
laser and detector matching circuits were adjusted properly. Greater than 10 dB of return
loss was obtained across a bandwidth of 400 MHz in the case of the optical transmitter,
700 MHz in the case of the optical receiver.
Optical power was coupled from the laser to the active region of the detector with a
measured efficiency (K l f L f K f d ) of 40% using a plano-convex gradient-index (GRIN)
lens with AR-coated facets to focus the diverging output beam of the semiconductor laser
into the 8 |im core of the single-mode fiber.
Optical Transmitter and Receiver Modeling
The equivalent circuit model of the optical transmitter and receiver modules
rendered in Fig. E.1 of Appendix E was used to determine values of [SijiJ, Ytht, [SijDL
and ZthD at frequencies between 11 and 13 GHz in steps of 100 MHz. The bias-dependent
values of tor. Y> and R IN s l were determined as described in section 4.2.1 and shown by
example in Appendices B and C, as were the rest of the parameters listed in Table 4.1.
Table E.1 (a) in Appendix E lists the values determined for all of the frequency-independent
model parameters; Table E.1 (b) gives all the frequency-dependent model parameters that
were calculated using the equations in Tables 3.1 and 3.2, including the link gain, noise
figure, spurious-free and compression dynamic range.
Link Results
For one bias current (Il =60 mA), the insertion gain predicted by the direct
modulation link model is plotted in Fig. 4.7 alongside the insertion gain of the link as
measured using the set-up shown in Fig. 4.1. Both curves exhibit 3-dB bandwidths of
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
142
S2 1
lo g MAG
REF - 2 0 . 0 dB
k
S .0 d B /
V - 1 2 . 7 1 2 dB
KU-BAND =/Q LINK 07/25/B0
MAR <ER
1 1 . 9 !5 G1-z
START
STOP
Calculated
Measured
11.000000000 GHz
13.000000000 GHz
Figure 4.7 Insertion loss of the Ku-band direct modulation fiber-optic link. The
measured result is shown along with the performance predicted in
Appendix E using the model rendered in section 3.1.
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143
-800 MHz (6.7% bandwidth) and peak at 12 GHz, where the analytically predicted
insertion gain is -10.9 dB compared to the measured result of IS21I2 =-12.7 dB. This
small discrepancy is discussed in section 4.2.6. The curves also seem to have the same
basic shape. These curves show that the direct modulation model predicts the performance
of a narrowband link across a range of high microwave frequencies much broader than its
3-dB bandwidth.
Table 4.3 indicates that the measured dynamic range of this link was found to be
greater when the laser bias was increased to 70 mA, a bias for which the measured
insertion gain was -13.6 dB. Using the appropriate group of equations in Table 3.1, the
noise figure of the link was calculated at f=12 GHz for the same three bias levels at which
insertion gain was determined, and was predicted to be minimum under the 70 mA laser
bias condition. The noise figure of the link was experimentally determined using the set-up
in Fig. 4.2. The minimum noise figure of 45 dB was measured at the 70 mA laser bias, as
shown in Table 4.3, confirming the ability of the model to predict the effect of the laser bias
current setting on the direct modulation link’s noise figure.
Using the experimental set-up shown in Fig. 4.3, the two-tone intermodulation
distortion of the Ku-band direct modulation fiber-optic link was measured at two thirdorder intermodulation products surrounding its center frequency of 12 GHz for each of the
laser bias currents at which gain and noise figure had been measured. Table 4.3 lists the
spurious-free and compression dynamic ranges determined from these measurements, as
well as the dynamic ranges predicted by the link model of section 3.1. The measured
spurious-free and compression dynamic range results do not compare as favorably with the
analytical results as the measured gain and noise figure results did, although the model did
accurately predict the magnitude of the effect of laser bias current on dynamic range. This
also is discussed further in section 4.2.6.
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144
L aser Bias C u rren t
50 mA 60 mA 70 mA
G ain (dB)
Model
Measurement
-12.5
-14.0
-10.9
-12.7
-11.8
-13.6
Model
Measurement
45.2
46.3
46.7
47.8
44.0
45.0
56.0
55.5
54.1
55.8
54.9
58.6
73.2
77.2
71.8
75.0
76.0
79.4
Noise Figure (dB)
Spurious-Free Dynamic Range (dB)
Model
Measurement
C om pression Dynamic Range (dB)
Model
Measurement
T able 4.3
Summary of the Ku-band direct modulation link performance at f=12 GHz.
Measured and modeled results are given at laser bias currents of 50 mA, 60
mA, and 70 mA. Spurious-free and compression dynamic ranges are
quoted for a resolution bandwidth of 1 MHz.
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145
4.2.4
Case 3: Large Percentage Bandwidth
This section describes a direct modulation link which was developed for high-
performance operation across an octave frequency band (3-6 GHz). Table 4.4 at the end of
4.2.4 summarizes the measured performance of this link at three frequencies—3.0 GHz,
4.5 GHz, and 6.0 GHz—and compares the measured performance parameters at these
frequencies to the parameters predicted in Appendix F by the direct modulation link model
given in section 3.1 of the thesis.
Electro-optic Device Selection
The directly modulated optical source in this S/C-band link was the same type of
InGaAsP distributed-feedback laser diode used in the Ku-band direct modulation link,
which emitted optical power at the 1.3 [im wavelength and featured a measured external
differential quantum efficiency of t | l = 0 . 2 6 mW/mA when biased well above its measured
threshold current of 13 mA. The detector used in the link was a single-mode fiber-pigtailed
InGaAs (X=1.3 Jim) p-i-n photodiode manufactured by AT&T, which featured a
responsivity of T |d = 0 . 9 5 mA/mW and a measured 3-dB modulation bandwidth, f 3 d B , of 15
GHz. These device quantities, along with the other important device parameters listed in
Table 4.1, were determined using the techniques described in section 4.2.1 and Appendices
A, B, and C.
Electro-optic Device Characterization
The laser diode and photodetector were mounted in standard microwave test
fixtures to enable de-embedding of the device impedances out of the measured scattering
parameters of the devices in their test fixtures, as was described in section 2.4.1 and shown
by example in Appendix A. Two-port circuit parameters of the intermediary elements of
the test fixtures (bias tee, connector, and transmission line) were obtained using the ThruReflect-Line (TRL) technique [28]. For frequencies ranging from 2 to 7 GHz, both the
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
measured scattering parameters of these devices in their test fixtures and their de-embedded
scattering parameters are given in Appendix A.
Electro-optic Device Modeling
Equivalent circuit models of the semiconductor laser and detector in this link were
obtained by using the SuperCompact CAD program to fit values of L pl , R p l . R jl » and
C jl [for the semiconductor laser—see Fig. 3.1(a)] and C jd , Rjd . R pd . and L pd [for the
photodetector—see Fig. 3.1 (b)] to the de-embedded scattering parameters of these
devices. The equivalent circuit models of the specific devices used in this link are also
rendered in Appendix A. From these models the Qext factor for each device was calculated.
For the semiconductor laser diode used in this direct modulation link, a Qext factor
of approximately 0.16 was calculated at the desired center frequency of 4.5 GHz. Fano's
theorem (see expression (2-5) and [34]) predicts that, for a minimum return loss of 10 dB,
a reactive matching bandwidth of approximately 77.6 GHz can be achieved for a Qext=0.16
device if an infinite number of reactive matching stages can be used (although a 77.6 GHzwide frequency band would obviously not be centered at 4.5 GHz).
At the same 4.5 GHz center frequency, the p-i-n photodiode used in this link has a
Qext of 6.0.
Fano’s theorem dictates a maximum -10 dB matching bandwidth of
approximately 2.1 GHz for the photodetector matched using an infinite number of lossless
reactive matching stages.
Optical Transmitter and Receiver Fabrication
Fano’s theorem dictated a 2.1 GHz maximum limit to the theoretically achievable
-10 dB matching bandwidth for a purely reactive matching circuit centered at 4.5 GHz
designed to match this device to 50 Cl. Because it was desirable to achieve a 3 GHz
bandwidth, a pseudo-reactive matching approach was pursued for the detector circuit. This
approach was meant to achieve maximum gain at 6 GHz using mostly reactive elements,
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while introducing resistive components at the lower frequencies to counter-act the higher
Q ext (a n d
hence greater transducer gain) at low frequencies. The link equivalent circuit
given in Fig. F .l of Appendix F shows the detector’s pseudo-reactive matching circuit In
parallel with the detector is a 6.4 Q resistor in series with several lumped and distributed
inductive elements. Thus, the shunt resistor lowers the Qext of the detector-shunt element
combination to a greater extent at 3 GHz than at 6 GHz, in order to equalize the maximum
achievable insertion gain across this wide bandwidth.
The Qext of this device and shunt element together is 2.1 at the band center
frequency of 4.5 GHz. For a quality factor of 2.1, Fano’s theorem dictates a -10 dB
matching bandwidth of approximately 6.0 GHz. Therefore, perfect reactive matching to
this detector and shunt resistive element combination (i.e., pseudo-reactive matching to the
detector) could now easily yield the octave bandwidth desired.
Instead of fabricating separate transmitter and receiver modules, bi-directional
transceiver modules were fabricated to incorporate both the semiconductor laser and p-i-n
photodiode, with single-mode optical fiber pigtails (on the order of 1 meter in length),
coupling and isolating optics, and circuits consisting of reactive and resistive elements to
match the device impedances to 50 £2. These impedance matching circuits were designed
using SuperCompact [93]. The semiconductor laser and detector, single-mode fiber
pigtails and coupling optics were mounted onto a brass carrier measuring less than an inch
square, and an alumina motherboard was added to impedance-match the devices to the
microwave input and output cables (Zo=50 £2). This 3-6 GHz optoelectronic transceiver is
shown in Fig. 4.8. The 50 £2 input and output microstrip lines both include cut-outs for
future insertion of MMIC amplifier chips as necessary to counteract the anticipated insertion
loss of the bi-directional optical link formed by connecting the laser’s and detector’s fiber
pigtails of this transceiver to the detector and laser pigtails (respectively) of another identical
transceiver.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F igure 4.8
Experimental S/C-band (3-6 GHz) optoelectronic transceiver. The
microwave signal enters transceiver package at an SMA connector
(upper left of photo) and is fed through a reactive matching network to
semiconductor laser. The modulated optical signal is coupled through a
spherical lens, optical isolator, and GRIN lens to an optical fiber pigtail
(upper right). "Hie modulated optical signal enters transceiver package
through optical fiber pigtail at the lower right and is reflected onto the
photosensitive back-facet of the photodetector. The de-modulated
microwave signal is fed through a pseudo-reactive matching network to
the SMA connector at the transceiver output (lower left).
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149
Optical power was guided from the laser to the active region of the detector with a
measured efficiency (Klf L f Kfd ) of 15% using a combination of spherical (collimating)
and GRIN (focusing) lenses (both AR-coated) to couple the diverging output beam of the
semiconductor laser into the core of the single-mode fiber.
Optical Transmitter and Receiver Modeling
The equivalent circuit model of the optical transmitter and receiver modules
rendered in Fig. F .l of Appendix F was used to determine values of [SijL], YthT. [SijD],
and ZthD at frequencies between 2 and 7 GHz in steps of 250 MHz. The bias-dependent
values of cor, y, and R IN sl were determined as described in section 4.2.1 and shown by
example in Appendices B and C, as were the rest of the parameters listed in Table 4.1.
Table F.l (a) in Appendix F lists the values determined for all of the frequency-independent
model parameters; Table F .l (b) gives all the frequency-dependent model parameters that
were calculated using the equations in Tables 3.1 and 3.2, including the link gain, noise
figure, spurious-free and compression dynamic range.
Link Results
For one bias current
(Il = 3 0
mA), the insertion gain predicted by the direct
modulation link model is plotted in Fig. 4.9 alongside the insertion gain of the link as
measured using the set-up shown in Fig. 4.1. Both curves exhibit ±1.5-dB bandwidths of
~3 GHz (75% bandwidth) and peak at 3.75 GHz, where the analytically predicted insertion
gain is -17.9 dB compared to the measured result of IS21I2 =-18.0 dB. They also seem to
have the same basic shape. These curves show that the direct modulation model predicts
the performance of a broadband link across a very broad range of microwave frequencies.
Table 4.4 indicates that the measured dynamic range of this link was found to be
greater when the laser bias was increased to 70 mA, a bias for which the measured
insertion gain was -18.0 dB at the band center frequency of 4.5 GHz. Using the
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150
F 0.0 <B
10 0 <© /
-19.334 <B
3 . 5 Gl-
- - Calculated
— Measured
1r
START
STOP
2.000000000 GHz
7.000000000 GHz
Figure 4.9 Insertion loss of the S/C-band direct modulation fiber-optic link. The
measured result is shown along with the performance predicted in
Appendix F using the model rendered in section 3.1.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
151
appropriate group of equations in Table 3.1, the noise figure of the link was calculated at
frequencies of 3.0,4.5, and 6.0 GHz for the same three bias levels at which insertion gain
was determined, and was predicted to be minimum overall when the laser was biased at 70
mA. At this laser bias, the model predicts a noise figure of 41.2 dB for the link at f=4.5
GHz. The noise figure of the link was experimentally determined using the set-up in Fig.
4.2. The minimum 4.5 GHz noise figure of 38.5 dB was measured at the 70 mA laser
bias, as shown in Table 4.4, confirming the ability of the model to predict the effect of the
laser bias current setting on the direct modulation link’s noise figure. The discrepancy in
the magnitude of the measured vs. modeled noise figure is discussed in section 4.2.6.
Using the experimental set-up shown in Fig. 4.3, the two-tone intermodulation
distortion of the wideband direct modulation fiber-optic link was measured at two thirdorder intermodulation products surrounding microwave frequencies of 3.0, 4.5, and 6.0
GHz for each of the laser bias currents at which gain and noise figure had been measured.
Table 4.4 lists the spurious-free and compression dynamic ranges determined from these
measurements, as well as the dynamic ranges predicted by the link model of section 3.1.
The measured spurious-free and compression dynamic range results compare very
favorably with the dynamic range predicted using the equations in Table 3.2, showing that
the model accurately predicted the magnitude of the effect of laser bias current on dynamic
range.
Since the impedance of the reverse-biased p-i-n photodetector in this link is very
similar to the gate-to-source impedance of a HEMT or MESFET, a wider matching
bandwidth could probably have been achieved if these devices were reactively matched
directly to each other and the output (drain-to-source impedance) were reactively matched to
50 £2. Besides providing some amplification, the device would serve as an effective
wideband impedance transformer, thus increasing the passive gain/bandwidth product by
roughly a factor of ten. In the case of the 3-6 GHz link described above, the gainbandwidth trade-off of the detector matching circuit as governed by Fano’s rule [Eq. (2-5)]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
152
Laser Bias Current
30 mA SOmA 70 mA
Gain (dB)
f=3.0GHz
f=4.5GHz
f=6.0GHz
Model
Measurement
-19.6
-19.3
-19.4
-18.5
-19.6
-21.0
Model
Measurement
-18.3
-18.5
-17.6
-19.0
-18.0
-20.5
Model
Measurement
-20.9
-22.0
-19.0
-19.8
-19.6
-20.8
Model
Measurement
42.6
41.0
40.8
40.0
40.8
39.5
Model
Measurement
43.3
41.0
41.4
40.0
41.2
38.5
Model
Measurement
44.2
43.0
42.1
41.5
41.7
41.0
Model
Measurement
50.0
52.5
56.9
58.1
59.7
60.3
Model
Measurement
45.2
47.1
55.1
58.8
58.5
60.1
Model
Measurement
44.2
44.0
52.6
53.7
57.0
59.1
Model
Measurement
71.7
71.8
81.2
81.5
85.2
86.3
Model
Measurement
68.4
68.2
79.5
79.5
83.9
84.8
Model
Measurement
64.3
64.6
77.7
78.7
82.8
84.0
Noise Figure (dB)
f=3.0GHz
f=4.5GHz
f=6.0GHz
Spurious-Free Dynamic Range (dB)
f=3.0GHz
f=4.SGHz
f=6.0GHz
lie Range (dB)
f=3.0GHz
f=4.5GHz
f=6.0GHz
Table 4.4
Summary of the S/C-band direct modulation link performance at f=3.0,4.5,
and 6.0 GHz. Measured and modeled results are given at laser bias currents
of 30 mA, 50 mA, and 70 mA. Spurious-free and compression dynamic
ranges are quoted for a resolution bandwidth of 1 MHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
dictated that the external quality factor o f the circuit needed to be brought down by nearly a
factor of two to permit efficient wideband pseudo-reactive matching resulting in minimum
insertion loss. Since the link gain is proportional to the square of the detector quality
factor, this means that 6 dB of gain was sacrificed to achieve flatness. Active matching is
one area where future work should be directed, as evidenced by the payoff just illustrated.
4.2.5
Observation: Dependence of Performance Parameters Upon Laser Bias Current
Dependence o f Insertion Gain Upon Laser Bias
As can be seen in Tables 2.2, 2.3, and 2.4, there exists for each of the three
experimental direct modulation links a bias current at which the insertion gain Gdir is
maximum. Examination of the model shows why: three terms in the expressions for
calculating link insertion gain (see Table 3.1) are dependent on the laser bias current II.
These three terms are the external differential quantum efficiency, the relaxation oscillation
frequency, and the relaxation oscillation damping frequency of the semiconductor laser
(TIL. fr. and y, respectively).
At a laser current just above threshold,
t jl
usually has its highest value. This is
because at currents below Im, there are too few conduction-band electrons to sustain the
population inversion necessary for stimulated emission (amplification) to occur; and as
current is increased too far past I&, nonradiative emissions cause junction heating and thus
an increase in the current density necessary to sustain population inversion. Saturation of
the optical gain from stimulated emissions is also caused by spatial and spectral hole
burning effects (the inevitable depletion of conduction-band electrons in the highest-gain
portions of the active region and the energy spectrum, respectively). Optimum efficiency
therefore occurs at a bias just above Ifo.
However, the bias current dependence of til is usually mild compared to the effect
of relaxation oscillations. That is, when electron population density in the laser cavity is
changed, the photon population density oscillates around the steady-state response value at
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154
a frequency fr, which has been observed to increase as the square root of I I increases [see
Eq. (2-22)] [94]. These oscillations are damped due to the nonlinearity of the optical gain
as a function of photon and electron densities; the rate at which the relaxation oscillations
are damped, y, is also bias-dependent.
The dependence of Gdir on fr and on y is evident from the expression for the laser
frequency response IHl I2 [Eq. (3-23)]. In the Fabry-Perot semiconductor laser used in the
L-band link, and in the distributed-feedback laser used in the Ku-band and S/C-band links,
the laser response appeared to be underdamped (i.e., y was not large enough to minimize
the dependence of IHl I2 on fr). Therefore, input current signals at modulation frequencies
close to fr appeared to be amplified to a greater extent than those at frequencies far from fr,
and the bias currents at which fr fell in the reactive matching bands of the three links yielded
the largest gain in all three cases.
Consider the direct modulation link described in section 4.3.2, for instance. The
bias current resulting in the highest link insertion gain Gdir at f=12 GHz was Il =60 mA,
which is the same bias current at which the relaxation oscillation frequency fr was equal to
12 GHz. The 12 GHz noise figure of the link was also maximum at this bias current
because of the peak in RIN at f=fr.
Dependence o f Noise Figure Upon Laser Bias
A fiber-optic link’s noise figure is inversely proportional to its insertion gain, but
proportional to the total noise power at the output of the link, as expressed in Eq. (3-37).
The relative contributions of the different sources of noise in the link vary with the optical
power detected by the optical receiver, which is proportional to the laser bias current above
threshold. In Fig. 4.10 the contributions to the Ku-band direct modulation link’s output
noise floor at f=12 GHz have been calculated and plotted as a function of both the detected
optical power and the I I setting.
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155
-70
Output Noise Power
(dBm)(Bandwidth = 1 MHz)
-80
-90
Total noise power
RIN
-100
Shot noise
-110
Detector thermal noise
Laser thermal noise
-120
Dark current noise
-130
-140
-150
-160
-170
■5
0
-15
-10
Optical Power (dBm)
-20
I____________ i
i____________i
Ith
l-l lth
1-051*
5
i________ I__
1-5 Ith 21th
41*
II
Figure 4.10
Sources of noise contributing to the measured output noise floor (at f=12
GHz) of the experimental Ku-band direct modulation link, plotted as a
function of both the laser diode bias current above threshold and the
optical power detected in optical receiver.
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156
The effect o f laser bias current upon the laser module thermal noise contribution to
the link output noise yields the unusual shape shown for this curve in Fig. 4.10. This
curve has the same shape as the link gain dependence on II, which was shown previously
to be a complicated function peaking at the bias which causes fr to coincide with the link
modulation frequency. As Fig. 4.10 shows, for the Ku-band link this maximum occurred
at a bias current roughly 4.5 times greater than the threshold current. At this same bias
current, the laser’s RIN is also maximum, causing the RIN contribution to the total noise
power to also peak at this bias. And since the noise at the link output due to laser RIN is
the greatest contributor to total noise output for laser bias currents above 1.5 x Im, the total
noise output power peaks here as welL
The link output noise power due to laser RIN is for the most part proportional to
(IL-Ith)2, as predicted by Eq. (3-33), which would dictate a slope of two on the logarithmic
plot of Fig. 4.10. However, the variation of RIN itself with II yields the more complicated
curve shown in the plot, which has a slope greater than 2 at low II values, and which has a
negative slope above the maximum-RIN bias current as the relaxation oscillation frequency
moves further and further beyond the link measurement frequency.
Detector shot noise is proportional to the detected optical power, which is itself
proportional to lL-Ith> resulting in the slope of 1 for this curve in Fig. 4.10. Therefore,
shot noise is significant compared to RIN only at lower laser biases. There is a small range
of laser bias currents at which the Ku-band link noise output is mostly due to shot noise, as
shown in Fig. 4.10. At laser biases below that range, the link noise output is dominated by
thermal noise in the opdcal receiver.
Based on Fig. 4.10, it is possible to guess the laser bias current at which link noise
figure is minimum. Noise figure is proportional to the signal-to-noise ratio at the output of
the link, and the signal power depends on bias current in the same way that the laser
thermal noise contribution to total output noise does (see curve in Fig. 4.10). Of all the
bias currents considered, it is obvious from the figure that the highest bias current (about
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157
5.5 times Im) yields the best noise figure. That is, both gain and output noise power peak
at the bias where fo=fr (about 4.5 Ith). Slightly above this bias, however, the noise power
decreases with I I faster than gain decreases with II,
so
noise figure is minimum.
Dependence o f Dynamic Range Upon Laser Bias
It is obvious that the maximum input power for linear and spurious-free operation
increases with laser bias. This can be seen from Fig. 2.3, which shows how the threshold
characteristic of a semiconductor laser leads to a nonlinear and distorted response to input
RF powers high enough to swing the bias into the “knee” in this curve. Since it has also
been shown that noise figure is minimized at the highest bias current safe for the laser, it is
evident from Eq. (3-60) and Eq. (3-61) that the link’s spurious-free and compression
dynamic ranges, respectively, increase with increasing laser bias toward the maximum
permissible operating bias (beyond which the laser reliability is sacrificed).
4.2.6
Concluding Remarks
As shown in Figures 4.6,4.7, and 4.9, the measured insertion gain results for the
three experimental direct modulation links generally compare very favorably to those
predicted by the direct modulation link model set forth in section 1 of Chapter 3.
Differences in insertion gain (1-2 dB at most frequencies) may be accounted for by the
discrepancy between the scattering parameters of the simulated matching network and those
of the “tweaked” matching circuits.
As listed in Tables 4.2,4.3, and 4.4, the measured noise figure and dynamic range
results for the three experimental direct modulation links also compare favorably to the
analytically modeled link results. Differences in noise figure of 1-3 dB are most likely due
to some inaccuracies inherent in the measurement techniques available for measuring laser
RIN. Underestimations of the narrowband links’ spurious-free dynamic ranges by as
much as 2-4 dB may be due to their very narrow 3-dB bandwidths and one-pole matching
architectures, which cause output power to decrease rapidly as frequency is adjusted away
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158
from fo. Since different measuring equipment was used for characterizing the gain, noise
figure, and dynamic range of the links (see Figures 4.1,4.2, and 4.3, respectively), it is
likely that these results were actually measured at frequencies slightly offset from one
another, which has a large impact on narrowband link performance.
Discrepancies between the predicted and measured performance parameters may
also be exacerbated by a number of phenomena that are difficult to quantify—for instance,
the effect of finite optical reflections, such as from the input fiber end face back to the laser,
upon laser quantum efficiency, noise, and linearity (especially when the device is a DFB
laser, which is very sensitive to optical reflections). The fact that the model very accurately
predicted the measured performance of the 3-6 GHz link—which contained a DFB laser
with an optical isolator—but did not predict as accurately the performance of the 12 GHz
narrowband link—which contained a non-isolated DFB—is evidence to support this
hypothesis. Future work refining these modeling techniques may lead to methods of
quantifying such external optical feedback effects.
4 .3
External Modulation Fiber-optic Link
To assess the validity of the external modulation link performance model rendered
in section 3.2, this section compares the measured performance of some external
modulation links to the performance predicted by the model. Three cases are examined: 1)
operation within a small percentage bandwidth surrounding a low microwave frequency
using a lumped-element electro-optic modulator; 2) operation within a small percentage
bandwidth surrounding a higher microwave frequency using a traveling-wave electro-optic
modulator with a two-section phase reversal electrode layout, and: 3) operation across a
wide microwave bandwidth with a different two-section phase-reversal traveling-wave
electro-optic modulator.
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159
4.3.1
Determination of Model Parameters
The external modulation link model given in Chapter 3 was fully summarized by the
equivalent circuits and signal flow diagrams of the optical transmitter (see Fig. 3.2) and
optical receiver (see Fig. 3.1) and by the equations listed in Tables 3.3 and 3.4. All the
equivalent circuit element values and all the variables in the equations obviously must be
determined in order to predict link performance using this model. Table 4.5 lists all of
these needed parameters, and briefly describes methods by which the parameter values may
be determined. A more thorough description of these methods is given in this section.
Table 4.5 indicates that the lumped-element electro-optic modulator’s electrode
capacitance Cm and all other lumped-element modulator equivalent circuit element values
were de-embedded from the one-port scattering parameter S n that had been measured for
the device. The traveling-wave modulator’s electrode termination impedance, electrode
characteristic impedance, and complex microwave propagation constant (Zt, Zc, and Ye)
were all determined similarly by determining values that corresponded to the measured
input scattering parameter S n . Measurements of electrode dimensions Ge and zm under a
microscope facilitated this de-embedding process. The detector diode junction resistance
Rjd and all other detector equivalent circuit element values were determined in the same
manner. These S-parameter measurement and de-embedding methods were described in
section 2.4.1 of the Review of Literature; in Appendix A, how these methods were used to
determine the de-embedded one-port scattering parameters of all the electro-optic devices in
the experimental links is fully documented.
Once the modulator equivalent circuit was realized, the rest of the optical transmitter
was configured to efficiently couple power at the microwave frequencies of interest from
the 50 £2 input load to the electrodes. This was accomplished by inserting a combination of
lumped and/or distributed circuit elements to transform the microwave impedance of the
lumped-element or terminated traveling-wave electrodes’ equivalent circuit to 50 £2 across
the microwave band. The SuperCompact [93] microwave CAD software package was
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160
P arm eter
M ethod o f determ ination
Cm and all other lumped-element electro-optic modulator
equivalent circuit element values
de-embedded from device S n
measurements
Zt, Zc, Ye, and all other traveling-wave
electro-optic modulator equivalent circuit element values
de-embedded from device S n
measurements
[SijMl* ZthM
calculated from optical
transmitter equivalent circuit
using SuperCompact [93]
microwave CAD software
package
no, ry, Teo* A,
quoted by modulator and laser
manufacturers
Ge, zm
measured using microscope
RINssl
measured using detector and
amplifier with known
characteristics and RF
spectrum analyzer
Lm , Lp, K po, T|d , PSSL, VJt> Vb, Idark
measured using DC ammeter
and/or optical power meter
Rjd and all detector equivalent circuit element values
de-embedded from detector
S n measurements
[SijDJ, ZthD
calculated from optical
receiver equivalent circuit
using SuperCompact [93]
microwave CAD software
package
f3dB
value which makes Eq. (3-24)
fit detector frequency
response measured as in Fig.
4.4 (b)
Table 4.5
Methods for determining all parameters needed to predict external
modulation link performance using model set forth in Chapter 3 (Fig. 3.2
and Tables 3.3 and 3.4).
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used to facilitate the simulation of this circuit Additionally, the CAD simulation allows
easy determination of the optical transmitter matching circuit’s two-port scattering
parameters [SijM] and its input impedance ZthT. Determination of the optical receiver’s
equivalent circuit parameters [Sip] and ZthD was accomplished in the same way.
As was done for the direct modulation link modeling, measurement of the optical
detector’s frequency response IHd I2 using the Lightwave Signal Analyzer set-up in Fig. 4.4
(b) and fitting the measured data to Eq. (3-24) enabled accurate determination of the
device’s 3-dB bandwidth f3,jB- In Appendix B, the determination of the frequency
responses of all the electro-optic devices in the experimental links is fully documented.
To determine R IN s s l . the relative intensity noise of the solid-state laser used in an
external modulation link, the test set-up shown in Fig. 4.4 (c) was used. A broadband (040 GHz), resistively-matched InGaAs Schottky photodiode with well-known
characteristics was used to detect the optical power. The RF output power of the detector
consisted of the laser’s relative intensity noise as well as the detector shot noise and a
negligible amount of thermal noise power. This RF output was amplified using a lownoise amplifier with known gain and noise figure across the frequencies of interest, and fed
into an RF spectrum analyzer, as shown in the figure. A simple calculation using the
known detector responsivity, detector equivalent circuit, detector DC photocurrent, and
amplifier gain and noise figure yielded values of R IN s s l at each frequency of interest.
The following intrinsic parameters of the electro-optic modulators used in the
experimental external modulation links were quoted by the device manufacturers: the
refractive index no at the optical wavelength X; the magnitude of the electro-optic tensor ry
in the modulator substrate, and; Teo. the percentage overlap between the applied electric
field and the optical mode in the modulator’s integrated-optic waveguides.
Finally, several parameters could be measured directly using a combination of DC
voltage sources and CW optical power sources with DC ammeters and optical power
meters. Using a CW optical power source along with a DC voltage source and voltmeter,
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162
the electro-optic modulator’s optical output is measured with an optical power meter for
many modulator bias voltage settings to yield a power vs. voltage curve similar to the one
given in Fig. 2.4. From this measurement, the modulator’s halfwave switching voltage Vn
is determined along with its optical insertion loss Lm- Measuring the ratio of the modulator
output power at any value of modulator voltage Vb after and before the insertion of the
length of fiber and the connectors in the link yields a value for their total loss Lf- Similar
optical power ratio measurements give a value for the fiber-to-detector coupling efficiency
Kfd -
Photodetector responsivity t i d is measured using a known optical power level to
illuminate a small portion of the detector’s photosensitive region and subsequently
measuring the DC output current The detector’s dark current Ida* is measured using a DC
pico-ammeter when incident light intensity is brought to zero.
4.3.2
Case 1: Small Percentage Bandwidth Surrounding a Low Microwave.Frequencv
This section describes an external modulation L-band link which was developed for
high-performance operation centered at a frequency of 900 MHz. Table 4.6 at the end of
this section summarizes the measured performance of this link at f=900 MHz and compares
the measured performance parameters at that frequency to the parameters predicted in
Appendix G by the external modulation link model set forth in section 3.2 of the thesis.
Electro-optic Device Selection
A LiNbC>3 electro-optic interferometric device with a lumped-element electrode
structure was selected as the external modulator for the L-band link. The electrodes of this
modulator were approximately 0.5 cm long, which corresponds to less than one-tenth of a
wavelength in LiNbC>3 at 900 MHz. Thus it was deemed appropriate to model the
electrodes as a lumped element—i.e., a capacitor—at frequencies below the 3-dB
modulation bandwidth of 3 GHz quoted by the manufacturer (Crystal Technology). The
device exhibited a 23 dB extinction ratio when TE-polarized light at X=1.3 pm was
launched into its polarization-preserving input single-mode fiber pigtail. In addition, a
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halfwave switching voltage VK-S.3 V was measured using the method outlined in section
4.3.1. The detector used in the link was an InGaAs (X=1.3 |im) p-i-n photodiode
manufactured by BT&D, which featured a responsivity of
t id
= 0 .9 5
mA/mW and a
measured 3-dB modulation bandwidth, f3dB> of 18 GHz when reverse-biased with a DC
voltage of 15 V. These device quantities, along with the other important device parameters
listed in Table 4.5, were determined using the techniques described section 4.2.1 and
Appendices A, B, and C.
Electro-optic Device Characterization
The photodetector was mounted in a standard microwave test fixture to enable de­
embedding of the device impedance out of the measured scattering parameter of the device
in its test fixture, as was described in section 2.4.1 and shown by example in Appendix A.
The electro-optic modulator was purchased in a package that included an SMA connector to
receive the microwave input and a microstrip transmission line to carry it to the electrodes
on the LiNb0 3 integrated-optic substrate. The connector and microstrip line were modeled
similarly to those in the standard microwave test fixture so that de-embedding could be
accomplished in a similar fashion. Two-port circuit parameters of the intermediary
elements of the test fixtures (bias tee, connector, and transmission line) were obtained
using the Thru-Reflect-Line (TRL) technique [28]. For frequencies ranging from 100 MHz
to 2.1 GHz, both the measured scattering parameters of these devices in their test fixtures
and their de-embedded scattering parameters are given in Appendix A.
Electro-optic Device Modeling
Equivalent circuit models of the electro-optic modulator and detector in this link
were obtained by using the SuperCompact CAD program [93] to fit values of L p m .
Rpm>
and C m [for the lumped-element electro-optic modulator—see Fig. 3.2 (a)] and C j d ,
R jd .
R pd , and Lpo [for the photodetector—see Fig. 3.1 (b)] to the de-embedded scattering
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164
parameters of these devices. The equivalent circuit models of the specific devices used in
this link are also rendered in Appendix A. From these models the Q ext factor for each
device was calculated.
For the electro-optic lumped-element external modulator used in the external
modulation link designed for operation across a narrow band of low RF frequencies, a Q ext
factor of approximately 9.4 was calculated at the desired center frequency of 900 MHz.
Fano's theorem (see expression (2-5) and [34]) predicts that, for a minimum return loss of
10 dB, a reactive matching bandwidth of 260 MHz can be achieved for a Qextr=9.4 device if
an infinite number of reactive matching stages can be used.
At the same 900 MHz center frequency, the p-i-n photodiode used in this link had a
calculated Qext of 15. Fano’s theorem dictates a maximum -10 dB matching bandwidth of
approximately 160 MHz for the photodetector matched using an infinite number of lossless
reactive matching stages.
Optical Transmitter and Receiver Fabrication
Using the scattering parameters of the modulator and photodetector, de-embedded
from the measured S-parameters in the same manner as was used for the direct modulation
links, equivalent circuit models were developed. This made possible the design and
construction of single-stage reactive circuits to impedance-match the electro-optic devices to
50 f t at the link design frequency of 900 MHz. Figure G.l in Appendix G renders the
equivalent circuit models of the devices and reactive impedance matching networks.
Measured input and output 900 MHz return losses of 13 dB and 18 dB, respectively, were
achieved when matching circuits were constructed and properly tweaked, along with
measured 10 dB return loss bandwidths of 50 MHz for the modulator and 40 MHz for the
detector.
In order to maximize the gain and dynamic range of the external modulation link,
large optical pump power—40 mW at X=1.3 |im—was obtained from a single-mode fiber­
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pigtailed frequency-doubled Nd:YAG laser source manufactured by AMOCO. The solidstate laser and the optical receiver were optically coupled to the modulator’s input and
output fibers, respectively, and the input optical polarization was adjusted to maximize the
ratio of optical power measured at the “on” and “o ff’ state switch voltages. At the
modulator’s quarterwave bias point (Vb=0, which occurred at a bias voltage of -1.8 V), a
DC photodetected current Id = (LmLf Kfdt| d Pssl )/2=4.3 mA was measured.
A photograph of the external modulation fiber-optic link consisting of the solid-state
laser, polarization control device, and reactively matched modulator and photodetector
modules, is shown in Fig. 4.11.
Optical Transmitter and Receiver Modeling
The equivalent circuit model of the optical transmitter and receiver modules
rendered in Fig. G .l of Appendix G was used to determine values of Zt, [SijM]> ZthM.
[SijoL and Zthn at frequencies between 100 MHz and 1.5 GHz in steps of 100 MHz. The
frequency-dependent value of RINssl was determined as described in section 4.3.1, as
were the rest of the parameters listed in Table 4.5. Table G.l (a) in Appendix G lists the
values determined for all of the frequency-independent model parameters; Table G .l (b)
gives all the frequency-dependent model parameters that were calculated using the
equations in Tables 3.3 (a) and 3.4 (a), including the link gain, noise figure, spurious-free
and compression dynamic range.
Link Results
For the halfwave bias voltage (Vb=0), the insertion gain predicted by the lumpedelement modulator-based external modulation link model is plotted in Fig. 4.12 alongside
the insertion gain of the link as measured using the set-up shown in Fig. 4.1. Both curves
exhibit 3-dB bandwidths of ~50 MHz (5.5% bandwidth) and peak near 900 MHz, where
the analytically predicted gain is 1.8 dB compared to the measured result of IS2il2=-0.1
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F ig u re 4.11 Experimental L-band external modulation link. The optical transmitter
consisting of the solid-state laser, optical polarization controller, and
reactively matched lumped-element electro-optic modulator is shown on
the left, and at the upper right is the optical receiver module containing
the reactively matched, fiber-pigtailed, reverse-biased p-i-n photodiode.
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167
S2 1
le g MAG
REF 0 . 0 dB
k
1 0 .0 dB /
V - 0 . 0 6 9 4 - dB
hp
MAR <ER 1
c 0 0 . 3 Mh z
--------- Calculated
---------- Measured
i
V
r
V
\\
\
\ \
k
\
ii N
*In.
H A1 in n
START
STOP
Figure 4.12
0 .1 0 0 0 0 0 0 0 0 GHz
2.100000000 GHz
Insertion loss of the L-band external modulation fiber-optic link when
the modulator is biased at Vb =0. The measured result is shown along
with the performance predicted in Appendix G using the model rendered
in section 3.2.
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dB. They also share the same basic shape. These curves show that the lumped-element
modulator-based external modulation model predicts the performance of a narrowband link
across a broad range of microwave frequencies.
Table 4.6 shows that the measured spurious-free dynamic range of this link was
found to be maximum at a modulator bias voltage of -4.0 V (Vb=-0.34 V j^-2.8 V), a bias
for which the measured insertion gain was -3.6 dB at f=900 MHz. Using the appropriate
group of equations in Table 3.3 (a), the noise figure of the link was calculated at this same
frequency for the same eight modulator bias levels at which insertion gain was determined,
and was predicted to be minimum when the modulator was biased at -4.8 V (Vb=-0.43
Vjt=-3.6 V). Using the set-up in Fig. 4.2, the noise figure of the link was experimentally
determined as well. The minimum 900 MHz noise figure of 21.2 dB was measured at the
-4.0 V and -4.5 V modulator biases, as shown in Table 4.6. Thus the model has some
trouble predicting the link noise figure’s dependence upon modulator bias. This difficulty
is further discussed in section 4.3.6.
Using the experimental set-up shown in Fig. 4.3, the two-tone intermodulation
distortion of this fiber-optic link was measured at two third-order intermodulation products
surrounding its center frequency of 900 MHz for each of the modulator bias voltages at
which gain and noise figure had been measured. Table 4.6 lists the spurious-free and
compression dynamic ranges determined from these measurements, as well as the dynamic
ranges predicted by the link model of section 3.2. Again, the link dynamic range
dependence upon modulator bias predicted by the model does not perfectly match the
measurements. This is explained in section 4.3.6.
4.3.3
Case 2: Small Percentage Bandwidth Surrounding a High Microwave Frequency
This section describes an external modulation fiber-optic link which was intended
for high-performance operation across a high, narrow frequency band (32.0-32.5 GHz).
Table 4.7 at the end of this section summarizes the measured performance of this link at
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169
-1.5 V
-2.5 V
Modulator Bias Voltage (Absolute)
-3.0 V
-3.8 V
-4.0 V
-4.5 V
-4.8 V
-5.0 V
-3.6 V
-3.8 V
-1.8 V
-2.6 V
-2.8 V
-3.3 V
03 V
-13 V
(40.04 V ) (-0.16 V ) (-032 V ) (-0.31 V ) (-0.34 V ) (-0.39 V ) (-0.43 V ) (-0.46 V )
Gain (dB)
Model
Measurement
1.8
-
0.1
-
1.4
0.6
-
0.7
0.8
-
1.1
2.6
2.0
-3.6
-4.4
-
-
6.2
-6.4
-
-
8.2
8.8
-11.9
Noise Figure (dB)
Model
Measurement
24.2
24.3
22.6
22.8
21.9
22.2
21.2
21.4
21.1
20.9
21.2
21.2
20.8
21.5
20.9
22.C
73.8
75.7
74.2
76.0
74.6
76.5
74.7
77.0
74.9
75.7
74.9
74.9
74.9
74.3
96.4
100.1
97.0
99.6
97.7
99.3
97.9
99.1
98.1
97.7
98.1
97.9
98.1
95.9
Spurious-Free Dynamic Range (dB)
Model
Measurement
72.7
73.8
Compression Dynamic Range (dB)
Model
Measurement
Table 4.6
94.8
95.9
Summary of the L-band external modulation link performance at f=900
MHz. Measured and modeled results are given at modulator bias voltages
of -1.5 V, -2.5 V, -3.0 V, -3.8 V, -4.0 V, -4.5 V, -4.8 V, and -5.0 V.
Spurious-free and compression dynamic ranges are quoted for a resolution
bandwidth of 1 MHz.
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170
f=32.5 GHz and compares the measured performance parameters at that frequency to the
parameters predicted by the external modulation link model given in section 3.2 of the
thesis.
Electro-optic Device Selection
A LiNb0 3 electro-optic interferometric device manufactured by AT&T was selected
as the external modulator. This modulator achieved a bandpass response between about 32
GHz and 38 GHz by using a two-section phase-reversal traveling-wave electrode structure
as was discussed in section 3.2 of this thesis. The device exhibited a 26 dB extinction ratio
when TE-polarized light at A^1.3 pm was launched into its polarization-preserving input
single-mode fiber pigtail. In addition, the halfwave switching voltage (Vn) of 8.0 V and
the 3-dB modulation bandwidth of 32-38 GHz quoted by AT&T were verified using a
Wiltron 360 network analyzer with a low-efficiency, resistively matched InGaAs MSM
Schottky photodiode manufactured by NewFocus, which had a 3-dB roll-off frequency
greater than 40 GHz. These device quantities, along with the other important device
parameters listed in Table 4.5, were determined using the techniques described section
4.2.1 and Appendices A, B, and C.
A reverse-biased (-20 V) InGaAs p-i-n photodiode with a responsivity
t| d
= 0 .8
mA/mW at X= 1.3 pm and a measured frequency response bandwidth f3dB of 19 GHz was
employed in the optical receiver. This device was purchased in chip form from Epitaxx,
Inc., on a ceramic submount. As expressed by equation (3-12) of Table 3.2, the use of a
detector with a 3-dB bandwidth so far below the passband of the link caused a 5.9 dB
degradation of detector responsivity at 32.5 GHz and, thus, 11.8 dB lower insertion gain
than could be achieved if this same detector had a 3-dB modulation bandwidth greater than
35 GHz. This choice seemed preferable, however, to using a device with a higher roll-off
frequency such as the NewFocus InGaAs MSM Schottky photodiode, which had three
major disadvantages: 1) lower DC responsivity than the Epitaxx p-i-n photodiode (0.36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AAV compared to 0.8 AAV, corresponding to 7 dB lower insertion gain); 2) lower incident
optical power handling (1 mW for the MSM Schottky diode, compared to more than 6 mW
for the p-i-n, corresponding to more than 15 dB lower insertion gain), and; 3) greater cost,
because high-frequency MSM photodiodes are not sold in chip form.
Electro-optic Device Characterization
The InGaAs photodetector to be used in the link was mounted in a standard
microwave test fixture to enable de-embedding of the device impedance out of the measured
scattering parameter of the device in its test fixture, as was described in section 2.4.1 and
shown by example in Appendix A. The electro-optic modulator was purchased in a
package that included a Wiltron K connector to receive the microwave input and a
microstrip transmission line to carry it to the traveling-wave coplanar electrodes on the
LiNb 0 3 integrated-optic substrate. The connector and microstrip line were modeled
similarly to those in the standard microwave test fixture so that de-embedding could be
accomplished in a similar fashion. Two-port circuit parameters of the intermediary
elements of the test fixtures (bias tee, connector, and transmission line) were obtained
using the Thru-Reflect-Line (TRL) technique [28]. For frequencies ranging from 25 GHz
to 35 GHz, both the measured scattering parameters of these devices in their test fixtures
and their de-embedded scattering parameters are given in Appendix A.
Electro-optic Device Modeling
Equivalent circuit models of the electro-optic modulator and detector in this link
were obtained by using the SuperCompact CAD program [93] to fit values of L pm , R pm >
and Zt [for the traveling-wave electro-optic modulator—see Fig. 3.2 (b)] and Cjd »Rjd >
R pd , and L pd [for the photodetector—see Fig. 3.1 (b)] to the de-embedded scattering
parameters of these devices. The equivalent circuit models of the specific devices used in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
172
this link are also rendered in Appendix A. From these models the Qext factor for each
device was calculated.
For the electro-optic traveling-wave external modulator used in the external
modulation link designed for operation across a narrow band of high RF frequencies, a
Qext factor of approximately 3.0 was calculated at the desired center frequency of 32.5
GHz. Fano’s theorem (see expression (2-5) and [34]) predicts that, for a minimum return
loss o f 10 dB, a reactive matching bandwidth of nearly 30 GHz can be achieved for a
Qext=3-0 device if an infinite number of reactive matching stages can be used.
At the same 32.5 GHz center frequency, the p-i-n photodiode used in this link had a
calculated Qext of 4.0. Fano’s theorem dictates a maximum -10 dB matching bandwidth of
approximately 22 GHz for the photodetector matched using an infinite number of lossless
reactive matching stages.
Optical Transmitter and Receiver Fabrication
Using the scattering parameters of the modulator and photodetector, de-embedded
from the measured S-parameters in the same manner as was used for the previously
described links, equivalent circuit models were developed. This made possible the design
and construction of single-stage reactive circuits to impedance-match the electro-optic
devices to 50 Cl at the link design frequency band of 32.0-32.5 GHz. Figure H .l in
Appendix H renders the equivalent circuit models of the devices and reactive impedance
matching networks. As can be seen in the case of the modulator, the impedance Zm was
already so close to 50 £2 at all frequencies in the modulator passband (because the coplanar
traveling-wave electrodes were designed such that their width and spacing resulted in a
characteristic impedance of Zc=50 £2, and the electrodes were terminated in Zt=50 £2) that
only very minor impedance adjustment needed to be performed. Measured 32.5 GHz
return losses for the traveling-wave modulator and detector of 13 dB and 18 dB,
respectively, were achieved when matching circuits were constructed and properly
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tweaked, along with measured 10 dB return loss bandwidths of about 10 GHz for the
modulator and 3 GHz for the detector.
In order to maximize the gain and dynamic range of the external modulation link,
large optical pump power—40 mW at X=1.3 pm—was obtained from a single-mode fiber­
pigtailed Nd:YAG laser source manufactured by AMOCO. The solid-state laser and the
optical receiver were optically coupled to the modulator’s input and output fibers,
respectively, and the input optical polarization was adjusted to maximize the ratio of optical
power measured at the “on” and “o ff’ state switch voltages. At the modulator’s
quarterw ave
bias
point
(V b=0),
a
DC
photodetected
current
Id =
(LMLpKFDTlDPsSLy2=6.0 mA was measured.
The overall appearance of this high-frequency external modulation fiber-optic link is
indistinguishable from that of the L-band external modulation link depicted in Fig. 4.11.
Optical Transmitter and Receiver Modeling
The equivalent circuit model of the optical transmitter and receiver modules
rendered in Fig. H.1 of Appendix H was used to determine values of Zc, Zt, [SijM], ZthM>
[SijD], and Zrhn at frequencies between 25 GHz and 35 GHz in steps of 500 MHz. The
frequency-dependent value of RIN ssl was determined as described in section 4.3.1, as
were the rest of the parameters listed in Table 4.5. Table H.1 (a) in Appendix H lists the
values determined for all of the frequency-independent model parameters; Table H.1 (b)
gives all the frequency-dependent model parameters that were calculated using the
equations in Tables 3.3 (b) and 3.4 (b), including the link gain, noise figure, spurious-free
and compression dynamic range.
Link Results
For one bias voltage (Vb=0), the insertion gain predicted by the traveling-wave
modulator-based external modulation link model [see the equations in Table 3.3 (b)] is
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plotted in Fig. 4.13 alongside the insertion gain of the link as measured using the Wiltron
360 Automated Network Analyzer. Both curves exhibit 3-dB bandwidths of -6 GHz
centered at 28 GHz (21% bandwidth), and at the 32.5 GHz design frequency the
analytically predicted gain is -32.8 dB compared to the measured result of IS2il2=-34.6 dB.
The curves also share the same basic shape. This shows that the phase-reversal travelingwave modulator-based external modulation model serves to adequately predict the
performance of a narrowband link across a broad range of high microwave frequencies.
Using the appropriate group of equations in Table 3.3 (b), the noise figure of the
link was calculated at this same frequency for the same modulator bias level at which
insertion gain was determined (Vb=0). The noise figure of the link was also experimentally
measured using the set-up in Fig. 4.2. The noise figure measured for the Vb=0 case using
this set-up was 48 dB at f=32.5 GHz, as shown in Table 4.7. This approximates the
analytically determined 32.5 GHz noise figure result of 46.1 dB.
Using the experimental set-up shown in Fig. 4.3, the two-tone intermodulation
distortion of this fiber-optic link was measured at two third-order intermodulation products
surrounding its center frequency of 32.5 GHz. Table 4.7 lists the spurious-free and
compression dynamic ranges determined from these measurements, as well as the dynamic
ranges predicted by the link model of section 3.2. The tendency for the model to be
somewhat pessimistic in its signal-to-noise ratio predictions, as witnessed by Table 4.7, is
explained in section 4.3.6.
4.3.4
Case 3: Large Percentage Bandwidth
This section describes an external modulation fiber-optic link which was intended
for high-performance operation across a broad microwave frequency band (6-12 GHz).
Table 4.8 at the end of this section summarizes the performance of this link at three
frequencies—f=6.0 GHz, 9.0 GHz, and 12.0 GHz—and compares the measured
performance parameters at these frequencies to the parameters predicted by the external
modulation link model given in section 3.2 of the thesis.
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175
S 2 1 FORWARD TR A N S M IS S IO N
LOG MAG.
> R E F“ —2 0 . OOOdB
lO .O O O d B /D IV
Calculated
Measured
2 5 .0 0 0 0
GHz
3 5 .0 0 0 0
fig u re 4.13 Insertion loss of the millimeter-wave external modulation fiber-optic link
when the modulator is biased at Vb =0. The measured result is shown
along with the performance predicted in Appendix H using the model
rendered in section 3.2.
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176
Results a t the Halfwave M odulator Bias Voltage
G ain (dB)
Model
Measurement
-32.8
-34.6
Model
Measurement
46.1
48.0
Noise Figure (dB)
Spurious-Free Dynam ic R ange (dB)
Model
Measurement
66.3
69.0
Com pression Dynamic Range (dB)
Model
Measurement
Table 4.7
85.3
88.3
Summary of the millimeter-wave external modulation link performance at
f=32.5 GHz. Measured and modeled results are given at one modulator
bias voltage (-3.0 V). Spurious-free and compression dynamic ranges are
quoted for a resolution bandwidth of 1 MHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
177
Electro-optic Device Selection
A LiNbC>3 electro-optic interferometric device manufactured by United
Technologies Photonics was selected as the external modulator. This modulator achieved a
bandpass response between about 1 GHz and 19 GHz by using a two-section phasereversal traveling-wave electrode structure as was discussed in section 3.2 of this thesis.
The device exhibited a 29 dB extinction ratio when IE-polarized light at X=1.3 Jim was
launched into its polarization-preserving input single-mode fiber pigtail. In addition, a
halfwave switching voltage Vjt=4.4 V was measured using the method outlined in section
4.3.1. The detector used in the link was an InGaAs (X,=1.3 Jim) p-i-n photodiode
manufactured by Epitaxx, which featured a responsivity of
tjd =0.80
mA/mW and a
measured 3-dB modulation bandwidth, f3dB. of 9 GHz when reverse-biased with a DC
voltage of 20 V. These device quantities, along with the other important device parameters
listed in Table 4.5, were determined using the techniques described section 4.2.1 and
Appendices A, B, and C.
Electro-optic Device Characterization
The InGaAs photodetector to be used in the link had been mounted in a standard
microwave test fixture to enable de-embedding of the device impedance out of the measured
scattering parameter of the device in its test fixture, as was described in section 2.4.1 and
shown by example in Appendix A. The electro-optic modulator was purchased in a
package that included a Wiltron K connector to receive the microwave input and a
microstrip transmission line to carry it to the traveling-wave coplanar electrodes on the
LiNbC>3 integrated-optic substrate. The connector and microstrip line were modeled
similarly to those in the standard microwave test fixture so that de-embedding could be
accomplished in a similar fashion. Two-port circuit parameters of the intermediary
elements of the test fixtures (bias tee, connector, and transmission line) were obtained
using the Thru-Reflect-Line (TRL) technique [28]. For frequencies ranging from 5 GHz to
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
178
IS GHz, both the measured scattering parameters of these devices in their test fixtures and
their de-embedded scattering parameters are given in Appendix A.
Electro-optic Device Modeling
Equivalent circuit models of the electro-optic modulator and detector in this link
were obtained by using the SuperCompact CAD program [93] to fit values of Lpm, Rpm»
and Zt [for the traveling-wave electro-optic modulator—see Fig. 3.2 (b)] and Cjd, Rjd»
Rpd. and Lpd [for the photodetector—see Fig. 3.1 (b)] to the de-embedded scattering
parameters of these devices.
The equivalent circuit models of the specific devices used in
this link are also rendered in Appendix A. From these models the Qext factor for each
device was calculated.
For the electro-optic traveling-wave external modulator used in the external
modulation link designed for operation across a broad band of microwave frequencies, a
Qext factor of approximately 3.1 was calculated at the desired center frequency of 9 GHz.
Fano's theorem (see expression (2-5) and [34]) predicts that, for a minimum return loss of
10 dB, a reactive matching bandwidth of 7.9 GHz can be achieved for a Qext=3.1 device if
an infinite number of reactive matching stages can be used.
At the same 9 GHz center frequency, the p-i-n photodiode used in this link had a
calculated Qext of 7.0. Fano’s theorem dictates a maximum -10 dB matching bandwidth of
approximately 3.5 GHz for the photodetector matched using an infinite number of lossless
reactive matching stages.
Optical Transmitter and Receiver Fabrication
Using the scattering parameters of the modulator and photodetector, de-embedded
from the measured S-parameters in the same manner as was used for the previously
described links, equivalent circuit models were developed. This made it possible to
determine how the 50 Q microstrip transmission lines in the modulator and detector
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
packages could be altered to yield a link insertion loss characteristic that was as flat as
possible across the link design frequency band of 6.0-12.0 GHz. Figure 1.1 in Appendix I
renders the equivalent circuit models of the devices and reactive impedance matching
circuits. As can be seen in the case of the modulator, the impedance Zm was already so
close to 50 £2 at all frequencies in the modulator passband (by virtue of the carefully
selected termination impedance Zt for the traveling-wave electrodes) that no impedance
adjustment needed to be performed. Measured 12 GHz return losses for the traveling-wave
modulator and detector of 13.5 dB and 6.3 dB, respectively, were achieved when the
circuits were tweaked for optimum gain flatness.
In order to maximize the gain and dynamic range of the external modulation link,
large optical pump power—40 mW at X=1.3 pm—was obtained from a single-mode fiber­
pigtailed frequency-doubled NdzYAG laser source manufactured by AMOCO. The solidstate laser and the optical receiver were optically coupled to the modulator’s input and
output fibers, respectively, and the input optical polarization was adjusted to maximize the
ratio of optical power measured at the “on” and “o ff’ state switch voltages. At the
modulator’s quarterwave bias point ( V b = 0 ) , a DC photodetected current I d =
(LmLfKfdi1dPssl)/2=5.2 mA was measured.
The overall appearance of this broadband external modulation fiber-optic link is
indistinguishable from that of the L-band external modulation link depicted in Fig. 4.11.
Optical Transmitter and Receiver Modeling
The equivalent circuit model of the optical transmitter and receiver modules
rendered in Fig. 1.1 of Appendix I was used to determine values of Zc, Zt, [S^m L ZthM»
[SijD], and Zfhn at frequencies between 5 GHz and 15 GHz in steps of 500 MHz. The
frequency-dependent value of RIN ssl was determined as described in section 4.3.1, as
were the rest of the parameters listed in Table 4.5. Table 1.1 (a) in Appendix I lists the
values determined for all of the frequency-independent model parameters; Table 1.1 (b)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
gives all the frequency-dependent model parameters that were calculated using the
equations in Tables 3.3 (b) and 3.4 (b), including the link gain, noise figure, spurious-free
and compression dynamic range.
Link Results
For one bias voltage (Vb=0), the insertion gain predicted by the traveling-wave
modulator-based external modulation link model [see the equations in Table 3.3 (b)] is
plotted in Fig. 4.14 alongside the insertion gain of the link as measured using the
experimental set-up shown in Fig. 4.1. Both curves exhibit 3-dB roll-off frequencies at
about 12 GHz and peak at roughly 9 GHz. The curve shapes also track fairly well,
showing that the phase-reversal traveling-wave modulator-based external modulation model
serves to adequately predict the performance of a broadband microwave link.
Using the appropriate group of equations in Table 3.3 (b), the noise figure of the
link was calculated at frequencies of 6 GHz, 9 GHz, and 12 GHz for the same modulator
bias level at which insertion gain was determined (Vb=0). The noise figure of the link was
also experimentally measured using the set-up in Fig. 4.2. The noise figure measured for
the Vb=0 case using this set-up was 47.5 dB at f=9.0 GHz, as shown in Table 4.8. This
closely matches the analytically determined 9 GHz noise figure result of 45.7 dB.
Using the experimental set-up shown in Fig. 4.3, the two-tone intermodulation
distortion of this fiber-optic link was measured at two third-order intermodulation product
frequencies surrounding microwave frequencies of 6 GHz, 9 GHz, and 12 GHz under the
same modulator bias condition. Table 4.8 lists the spurious-free and compression dynamic
ranges determined from these measurements, as well as the dynamic ranges predicted by
the link model of section 3.2. The tendency for the model to be somewhat pessimistic in its
signal-to-noise ratio predictions, as witnessed by Table 4.8, is explained in section 4.3.6.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
181
C H I MEM1
lo g
MAG
5 dB/
REF - 4 0
Si —3 1 . S S I
dB
.0 0 0
dB
<100 OCO GHz
- 3 0 . S!9 4 dB
6.O 0C O GHZ
dBe
Sfflo
Calculated
Measured
START
S .000
0 0 0 0 0 0 GHz
STOP 1 5 . 0 0 0
000 000
GHz
Figure 4.14 Insertion loss of the wideband (6-12 GHz) external modulation fiber­
optic link when the modulator is biased at Vb =0. The measured result is
shown along with the performance predicted in Appendix I using the
model rendered in section 3.2.
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182
Results at the Halfwave Modulator Bias Voltage
Gain (dB)
f=6.0 GHz
f=90GHz
f=12.0GHz
Model
Measurement
-31.8
-31.0
Model
Measurement
-30.7
-313
Model
Measurement
-362
-35.5
Model
Measurement
44.8
46.0
Model
Measurement
45.7
47.5
Model
Measurement
48.0
50.0
Noise Figure (dB)
f=6.0GHz
f=9.0GHz
f=12.0GHz
Spurious-Free Dynamic Range (dB)
f=6.0 GHz
f=9.0 GHz
f=12.0GHz
Model
Measurement
65.4
66.7
Model
Measurement
64.8
66.9
Model
Measurement
63.4
65.5
Compression Dynamic Range (dB)
f=6.0 GHz
f-9.0 GHz
f=12.0GHz
Table 4.8
Model
Measurement
83.9
85.3
Model
Measurement
83.0
85.1
Model
Measurement
80.8
83.6
Summary of the broadband microwave external modulation link
performance at f=6, 9, and 12 GHz. Measured and modeled results are
given at one modulator bias voltage (-2 V). Spurious-free and compression
dynamic ranges are quoted for a resolution bandwidth of 1 MHz.
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183
4.3.5
Observation: Dependence of Performance Parameters Unon Modulator Bias Voltage
The gain, noise figure, and two-tone intermodulation distortion of each of the
external modulation links had been measured at a variety of modulator bias voltages. In
this section, the bias-dependent performance of the narrowband 900 MHz external
modulation link is examined, since it was for that link that the most accurate measurements
were obtained—due in part to its high insertion gain.
The measured 900 MHz gain and noise figure of the experimental L-band link are
plotted as a function of Vb in Fig. 4.15. Also plotted are the gain and noise figure at 900
MHz predicted by the 16 equations in Table 3.3 (a), using the 900 MHz values of [S p d ,
[SijoL ZthM. and ZthD taken from the link’s equivalent circuit model in Appendix G, along
with measured values of Lm, Lp,
Kfd ,
t id ,
P s s l . V ^ , f3dB, R I N s s l .
and I<iark-
The intermodulation distortion measurement was also repeated for each of the
modulator bias points at which the link gain and noise figure had been measured. At each
Vb setting the spurious-free and compression dynamic ranges at 900 MHz were determined
from the intermodulation distortion and output noise power measurements, and the results
are plotted in Fig. 4.16 as a function of Vb- On the same graph is a plot of the dynamic
ranges predicted by the six equations of Table 3.4 (a), which were also calculated using the
link parameters listed in Appendix G.
Dependence o f Insertion Gain Upon Modulator Bias
As Fig. 4.15 shows, an electro-optic modulator-based external modulation link’s
small-signal gain is optimum at the modulator's quarterwave bias point (Vb=0). This
occurs because the slope of the modulator's output vs. input characteristic is maximum at
this point, as could be seen from Fig. 2.4. This gain maximum at Vb=0 is predicted by the
model because o f the bias-dependent coefficient cos2 (itV yV jz) in equation (3-101) of
Table 3.3 (a) [and in equation (3-103) of Table 3.3 (b) in the case of a traveling-wave
rather than lumped-element modulator electrode structure].
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184
50
Gain (analytical)
/
a Gain (measured)
/
Noise Figure (analytical)
A Noise Figure (measured)
09 40
3
« 30
fa
•2P 20
b
•a
o 10
Z
0
*5
0-10
-20 4
-4
-3
V5 (Volts)
F ig u re 4.15 Gain and noise figure of the 900 MHz external modulation link at f=900
MHz as a function of the modulator bias voltage. Measured and analytically
determined values are shown.
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185
N
S3 100
S
w*
II
£ 90
Compression Dynamic Range
' — (Analytical)
a (Measured)
80
CO
S
»ex> 70
B
a
/
OS
o
60
sa
Spurious-Free Dynamic Range
— (Analytical)
A (Measured)
B
>>
Q 501 i i i i i i i i i i i
- 4 - 3 - 2 - 1 0
1 2
Vb(Volts)
i
i
i
3
i
i
4
Figure 4.16 Compression and spurious-free dynamic range of the experimental external
modulation link at f =900 MHz as a function of the modulator bias voltage.
Measured and analytically determined values are shown.
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186
Dependence o f Noise Figure Upon Modulator Bias
The modulator bias voltage affects the noise figure in a more complicated manner
than how it influences the small-signal gain. The noise figure curve in Fig. 4.15 clearly
indicates the presence of a minimum-NF bias point Equation (3-104) of Tables 3.3 (a)
and (b) indicates that this optimum bias point must lie somewhere between Vb=0, where
gain is maximum, and a point near the halfwave voltage Vb=-V,j/2, where NoutRX,ext is
its minimum value.
To further illustrate this external modulation link noise figure dependence on
modulator bias, in Fig. 4.17 are the calculated contributions to the measured output noise
power of the experimental link at f=900 MHz, plotted as a function of the detected optical
power as well as the Vb setting. The relative contributions of the different sources of noise
in the external modulation link vary with the optical power detected in the receiver, which is
a sinusoidal function of the modulator DC bias voltage. In Fig. 4.17 it is evident that shot
noise increases linearly with the DC optical power impinging on the photodetector, whereas
noise in the receiver due to RINssl increases as the square of optical power. Modulator
thermal noise is proportional to the microwave-modulated optical power, and the remaining
noise contributions (detector dark current and thermal noise) are independent of the optical
power.
Dependence o f Dynamic Range Upon Modulator Bias
Note from Fig. 4.16 that the maximum dynamic range did not occur at the linear
bias point Vb=0, where gain was maximum. Optimum dynamic range was obtained by
biasing the modulator where its noise figure was minimum, since equations (3-135) and (3136) of Table 3.4 (a) show that dynamic range is inversely proportional to noise figure,
and where equations (3-114) and (3-128) of the table illustrate that the third-order intercept
and 1 dB compression input powers are independent of Vb- When the equations in Table
3.4 (a) and (b) are examined, it can be seen that the AM compression and third-order
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
187
Output Noise Power (dBm)
(Bandwidth = 1 MHz)
-80 r
Total noise power
Shot noise
Receiver noise from R IN ^ ^
Modulator thermal noise
Dade current noise
Detector thermal noise
Optical Power (dBm)
Figure 4.17 Sources of noise contributing to the measured output noise floor (at
f=900 MHz) of the experimental L-band external modulation link,
plotted as a function of both the modulator bias voltage and the optical
power detected in the optical receiver.
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188
intennodulation distortion effects increase as cos2 (rcV\/V K)—the same rate at which the
fundamental signal gain decreases—resulting in no net change in Pin,int,ext or Pin,lCP,ext
with changing Vb. Thus the spurious-free and compression dynamic ranges are maximum
at the modulator bias where the noise figure is minimum, as has been verified
experimentally (in Figures 4.15 and 4.16).
The exact value of this optimum modulator bias voltage depends upon all the
variables listed in Table 4.5. The model allows the equations of Tables 3.3 and 3.4 to be
used to determine how the optimum Vb changes with any of these variables. As an
example, in this section of the thesis the effect of the available solid-state laser power P s s l
is investigated.
Provided that the optical source is a solid-state laser with low RIN, Fig. 4.17
showed that the shot noise in the external modulation link is always more significant than
the noise due to R IN s s l - A s P s s l is increased by using higher-power optical sources,
modulator thermal noise eventually overtakes the shot noise due to the increased link gain,
and biasing the modulator even closer to the halfwave voltage is necessary to reduce the
output noise floor to its minimum value. Thus the bias point at which maximum dynamic
range is achieved approaches -Vn/2 asymptotically as larger optical source power is made
available. An important trade-off enters the picture here, since gain is always greatest at the
linear bias point Vb=0.
The equations of Tables 3.3 (a) and 3.4 (a) were used to calculate the experimental
L-band link's 900 MHz spurious-free dynamic range for several assumed levels of
available optical power Pssl- In Fig- 4.18 these predictions are plotted as a function of the
modulator bias Vb. As the plot shows, between the halfwave and quarterwave modulator
bias points the dynamic range varies less with larger optical source powers. For larger
optical source powers there is thus a less severe trade-off between gain and noise figure—
i.e., at the quarterwave bias point both are excellent
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189
0
ex)
s
es
X
<y
90
uop = 1 W
100 mV
80
10 mW
70
lm W
Q X
« 2 60
«U C•O
h1 ’O
CO w 50
100
10
S
JO
•a
s
a
co
40
l*iW
30
-2
-1
0
1
2
3
Vb (Volts)
F igure 4.18 Calculated spurious-free dynamic range of the experimental L-band external
modulation link as a function of the modulator bias voltage, plotted for
several assumed levels of available optical power.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
190
If a high-power, Iow-RIN solid-state laser can be used without damaging the
modulator or detector, and if the detector has very low dark current, then near the lumpedelement electro-optic modulator's halfwave voltage (-Vjj/2) equations (3-108) and (3-104)
of Table 3.3 (a) reduce as follows for the case of perfect reactive matching of the modulator
electrode and system impedances (ZthM and Zo, respectively):
Nout.RX.ext - Nth.TX.ext
= 2 ks T B Gext»
(4-1)
and thus
NFe*t = 2 .
(4-2)
The lowest possible noise figure for an optimally reactive-matched external
modulation link is therefore 3 dB, as has been claimed in the literature [17]. Since at high
optical source powers the external modulation link noise figure varies only slightly with Vb
between 0 and -Vjt/2, even at the quarterwave bias voltage the noise figure approaches 3
dB, and the spurious-free and compression dynamic ranges, as expressed by equations (3135) and (3-136) of Table 3.4 (a) approach their theoretical limits, i.e.:
2
SFDRext
4 v £ | i - s 22MrM|2
U 2 kBT B Zo IS21M12 | l + r M 12/
(4-3)
and
CDRext ->
O-1513^ ! 1 - ^ ^ ! 2
Jt2 kBT B Zo | S21M12 11 + r M| 2
(4-4)
The absolute upper limits to the spurious-free and compression dynamic ranges of the 900
MHz experimental external modulation link are therefore 86.8 dB»MHz2/3 (126.8
dB^Hz2^3) and 176.0 dB*MHz (106.0 dB»Hz), respectively.
Equations (4-3) and (4-4) illustrate that conversely to the link gain—which is
optimum when the modulator capacitance, resistance, and halfwave switching voltage are
minimized—the dynamic range upper limit can only be increased by increasing these same
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parameters. The optimum dynamic range is approached, however, only when gain is
maximized. Therefore, the gain/dynamic range trade-off and how it may be controlled by
varying the modulator bias voltage must be understood when attempting to design an
external modulation fiber-optic link to meet stringent performance specifications.
4.3.6
Concluding Remarks
For each of the three external modulation links described in this section the
spurious-free dynamic range calculated from predicted intercept and noise powers
consistently fell 1-3 dB short of the SFDR calculated from the intermodulation distortion
and noise floor measurements. This discrepancy was worse for the narrowband links, and
may have been due to the links’ very narrow 3-dB bandwidths. Since different measuring
equipment was used for characterizing the gain, noise figure, and dynamic range of the
links (see Figures 4.1, 4.2, and 4.3, respectively), it is likely that these results were
actually measured at frequencies slightly offset from one another, which has a large impact
on narrowband link performance.
In the case of the high-frequency external modulation link, the larger discrepancies
between the measured and modeled performance are very likely due to the difficulty with
which electrical parasitic effects are included in the equivalent circuit model. At high
microwave frequencies, inductance errors of less than 0.1 nH and dimension errors of less
than 0.1 mm are sufficient to cause significant discrepancies between a physical device or
circuit and its equivalent circuit model
Inaccuracies may also have resulted from the fact that the intermodulation distortion
and AM compression predictions were based on a modulator with an optical output power
that varies sinusoidally with bias voltage Vb as shown in Fig. 3.2 (c). It was observed in
measurements that the P-V characteristic of the modulators used in the three experimental
links deviated 5-10% from perfectly sinusoidal behavior. Most especially, it appeared that
the AT&T LiNbC>3 traveling-wave electro-optic modulator that was used in the millimeterwave link had been designed to give a highly linear P-V characteristic between about -V^/8
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192
and Vjj/8, which would account for the measured dynamic range being greater than that
which was predicted based on a sinusoidal P-V assumption.
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193
CHAPTER 5
COM PARISON O F A RCH ITECTU RES
Chapter 4 illustrated how the direct and external modulation fiber-optic link models
set forth in Chapter 3 were used to accurately predict the performance of current state-ofthe-art links. This chapter shows how the model also facilitates an estimation of future
direct and external modulation fiber-optic link performance. Probable values for each of
the parameters in the device models can be assumed by examining current trends and
predicting likely future developments. Speculations about direct and external modulation
link component developments are given in sections 5.1 and 5.2 of this chapter,
respectively.
To provide a benchmark for selecting the optimum fiber-optic link architecture to
meet any given set of system specifications, this chapter also compares the link
architectures and modulation methods described in sections 2.1 and 2.2. In section 5.3.1
the direct and external modulation methods are compared using the known characteristics of
currently available electro-optic devices in conjunction with the models set forth in Chapter
3. Substituting into the model the assumed characteristics of future devices (as predicted in
sections 5.1 and 5.2), section 5.3.2 repeats the direct vs. external modulation performance
comparison.
In section 5.4 the performance o f two different architectures—CPU-level data
mixing and T/R-level data mixing—is predicted across the same microwave-to-millimeterwave spectrum of frequencies using the known characteristics of currently available electro­
optic devices (in section 5.4.1) and then the predicted performance of future devices (in
section 5.4.2).
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5,1
Characteristics of Electro-optic Devices Used in Future Direct
Modulation Fiber-optic Links
The sixteen equations in Table 3.1 and the eight equations in Table 3.2 were used to
fully model direct modulation links for which the semiconductor laser and detector diodes
were available for measurement of all the parameters required for modeling. A different set
of equations and assumptions is needed to predict direct modulation link performance when
the devices to be used aren’t available for characterization, as is the case when attempting to
predict the improved performance of future direct modulation links.
In this section some trends in semiconductor laser and detector developments over
the past few years are examined, and some additional assumptions that facilitate the
present-day modeling of a future direct modulation link comprised of advanced (theoretical)
devices are outlined.
5.1.1.
Semiconductor Laser Development Trends
Current knowledge about semiconductor laser development trends is sufficient to
support speculations about the characteristics of a typical future device. Present-day
modeling of future direct modulation links can be accomplished if a number of reasonable
assumptions are made. Table 5.1 at the end of section 5.1 gives equations for modeling
future direct modulation links, as derived from the assumptions discussed in this section
and section 5.1.2. Of the assumptions made in this section regarding a typical future
semiconductor laser diode, those which affect the prediction of the performance of the link
are also shown in the table. The assumptions that have been listed in Table 5.1 appear in
the text in boldface.
The extrapolation of current semiconductor laser development trends into
assumptions about future device parameters is summarized in the flowchart of Fig. 5.1.
The breakdown of this section of the chapter follows the arrows in the flowchart.
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195
Enabling Technology
Advances
Monolithic integration reduces
circuit parasitics
Quantum-well Fabry-Perot lasers'
longitudinal mode profiles
approach those of DFB devices
Quantum-well active regions are
achieved simultaneously with
short cavity lengths
Present
Improved gain-bandwidth
product
Effect on. present model
(Af, CDboth in GHz)
GxX,dir = 11-9 ('1 - e“^ f)
Nth,TX,dir=
Strong suppression of all but Y = ^ E-+Vg£0 S + f - + b S
a single cavity mode
Very small active region
volume
Constructive interference in
Very large photon density,
quantum well increases
prob. of stimulated emission
probability of stimulated emission
Minimum steady-state
electron density
Y = % L + v g e0 S +
t f ^ f ^ +&V g E o S
v s
Y = v g eoS
£Dr2= Vg £0 S / X ,
S = Tn
m
c
—
Near-perfect backfacet reflective
coatings are achieved
Maximum in-cavity photon
lifetime
Likely device parameters
Improved modeling enables
tailoring of relaxation oscillation
damping
Critical damping of
relaxation oscillations
tp
p
-* •
.q (Vol)
N«
Ts.
^
q~ dA
m
col
d = 50 nm 10 Vol = 5 x 10_1° ra"3
It = 50 mA
S = 7 .1 8 x l0 2 3 m‘3
vg = 1.07 x 108 m/s
£a = 3 x 10*^^
Y= 231 GHz
(Dr = 164 GHz
*
1.39X10-11 Hz-1
SL~* [ t f + U s i ) 2 ]
Minimum threshold current
VCSELs and monolithic
integration enable coupling
efficiency advances
2 kn T B Ga;r
“
1 —e at
Ith = 4 mA
til
Maximum laser-to-fiber
coupling efficiency
= 0.96 raW/mA
Kl f = 1
Future
Figure 5.1 Projected improvements in the state of the art of future semiconductor lasers.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
196
Improved gain-bandwidth product (Fano’s limit achieved)
The first assumptions listed in Table 5.1(a) and the first milestone in the
extrapolated technology flowchart of Fig. 5.1 concern the extent to which future
semiconductor lasers will be successfully impedance-matched to the input of the optical
transmit module to maximize the link insertion gain. The maximum insertion gain that can
be achieved in a reactively-matched semiconductor laser-based optical transmitter—i.e.,
maximum Grx,dir—is achieved if and only if the matching circuit is a lossless reciprocal
network (so that IS2 il2= l-IS nl2) and a perfect match is achieved at every frequency in the
desired band at both the input and output (so that S n = 0 and S22=Fl*)- These conditions
cause the equation for Grx,dir [equation (3-20)] to become greatly simplified:
(5-1)
From the definition of I I [equation (3-1)], it is easily seen that
(5-2)
Maximum Gxx dir — >
R jl
Note that this assumes that a perfect match can be achieved at every frequency, which
violates Fano’s rule as discussed in Chapter 2. Therefore, from the lossless reciprocal
condition assumed above, substitution of Fano’s rule [expression (2-9)] into expression (51) yields:
(5-3)
This is where some reasonable speculations will be made in order to illustrate an example
of how the model enables predictions about the likely performance of links using devices to
be developed in the next 5-10 years. One important assumption is that fiber-optic links for
microwave and millimeter-wave signal transmission will continue to operate in conjunction
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with other system components having 50 Q characteristic impedances: Zo—>50 Q . The
semiconductor laser and p-i-n photodetector in a high-performance direct modulation link
therefore need to be reactively matched over the link band to a 50 Q, system impedance.
Equations (5-2) and (5-3) show how advantageous it is to use a semiconductor
laser having a minimum junction resistance Rjl - There have been few published efforts to
reduce this resistance, but values as low as 4.2 £2 have been reported [11]. With so many
more pressing design concerns, it does not seem reasonable to assume that semiconductor
laser manufacturers will achieve smaller values of Rjl in the near future.
The quality factor Q in equation (5-3) is defined as the ratio of the imaginary and
real parts of the impedance of the load—in this case the semiconductor laser. If the
parasitic inductance of the device lead is minimized via monolithic or other advanced
packaging schemes, then the laser is essentially a parallel R-C circuit, for which
Q = to R jl C jl .
(5-4)
Obviously, minimum junction capacitance is also desirable; however, the smallest devices
typically have capacitances on the order of 1 pF or more. Assuming that 1 pF will remain
achievable in future devices, equation (5-3) now reduces to
GTX.dir -»11.9 (l - <T^) (Af in GHz).
(5-5)
Under these matching conditions, the expression for the thermal noise generated in the
optical transmitter is similarly simplified; i.e.,
Nth.TX.dir -> 2 kB T B238Gdlr (Af in GHz).
1-e-f-
(5-6)
Strong suppression o f all but a single cavity mode
The introduction of the quantum size effect into laser active media by many
researchers [16, 46-51, 95] has led to differential gain factors several times larger than
those of ordinary buried-heterojunction devices, which also improves the extent to which a
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198
single longitudinal mode (wavelength) is favored over the others. Indeed, the ratio of the
optical power in the dominant longitudinal mode to that of the second most prominent has
been measured and found to be as high in some multiquantum-well devices as it is in the
most wavelength selective distributed-feedback lasers—as high as 40 dB [109].
As shown in Fig. 5.1, many of the predicted advances in the state of semiconductor
laser technology stem from expectations of better-performing quantum-well devices. Thus
it is prudent at this point to discuss the quantum size effect and why it is beneficial to a
laser's performance.
Some of the fastest lasers ever demonstrated have been short-cavity-length strainedlayer devices having multiple quantum wells 50 A or less in thickness to which the gain
phenomenon is restricted [16]. When restricted by potential barriers to dimensions of this
order, photons and electrons begin behaving more like waves than particles because there is
only a single allowable energy level that is less than the potential barrier height. This
results in the highest possible degree of phase coherence between particles. That is,
because the photons and electrons in quantum wells must have the same energy level, they
retain phase coherence over far greater distances than in macroscopic active regions.
Optimal constructive interference effects are thus attained, resulting in maximum probability
that stimulated emissions will occur.
Strong suppression in a quantum-well laser's gain spectrum of all but a single
cavity mode reduces the number of factors that determine the device performance. This is
because if there is a second cavity mode substantially amplified in the gain spectrum, then a
second relaxation oscillation occurs in the laser cavity at its own frequency (co^) and with
its own photon density (S2) and damping factor (72). Su et al. [92] expressed these second­
mode effects as follows:
S = Si + S 2 ,
Yi,2 =
S 1.2
+ vg £0 S i ,2 +
(5-7 )
+b S,
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(5-8)
199
a* 2 = f tSi? +T«e»Si)
K
‘/ \ £
t s +bS)I + * ^ Vol
a il
(5-9)
and
w‘H
! f +v* E» Sj) ( i +bs)'
(5-10)
where
t,
Rsp =
PTN,Xs2- ’
(5-11)
(5-!2)
and
e 12 = gQl±PjEpl^£lZ^l
1 +[Xp(C0ri-C0r2)]2
(5_13)
The terms b, go, Ne, RSp, S, vg, Vol, P, eo, T, t s, and xp in the above expressions were all
defined in Chapter 2. The term gi is the optical gain in the dominant longitudinal mode of
the active region; £12 is the term in the laser's nonlinear gain matrix which indicates the
level of mixing between the first- and second-order longitudinal modes, and; p is the ratio
of real and imaginary refractive index change in the active region associated with the
nonlinear gain.
Strong suppression of all but the dominant mode in future semiconductor lasers will
mean that: S2-»0; Si-*S; Y2-»°o; Yi-»Y. ^2 -^°°; tOri->Q)r, and; £i2->0. The equations for
Yand cpr are also simplified as follows:
Y88
o
+Vg£0 S+-^- + b S ,
T$
(5-14)
and
* - ( ¥ - . * s) £ +bS)* s!& i -
(5-15)
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200
Very small active region volume
Better laser performance at higher microwave frequencies will result from the
continuing trend toward short cavity lengths (on the order of 100 Jim) together with the
effect of extremely narrow (quantum-dimension) active layer thickness as already
discussed. The combined effect is a dramatic reduction in the volume of the active region.
As this happens, the 'b' term in Su’s model [expression (5-11)] approaches zero; therefore:
y«
(5-16)
and
(5-17)
Very large photon density and probability o f stimulated emission
It is also logical to assume from an extrapolation of the above discussions that in a
quantum-well laser the photon density S will be very large, and that stimulated emission
will be favored over spontaneous emission to a correspondingly large degree so that
VgeoS»Rsp/S and vge o S » l / t s. This assumption simplifies expressions (5-16) and (517) to a further degree, so that
Y « v g e0 S ,
(5-18)
and
(5-19)
Estimation of the active region's steady-state photon density S is accomplished using the
rate equations, which account for all changes in the active region electron and photon
densities; Su et a l give these rate equations as follows [92]:
(5-20)
and
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201
75T = [ go( Ne - N0) - vg Eo S] T S
*
+
tp
T*
(5-21)
The speculation that has already been made concerning the high probability of stimulated
emissions due to the high photon density and phase coherency in a quantum well is
consistent with the further assumption that (3, the ratio of spontaneously-emitted to
stimulation-emitted photons, will remain small. Even currently available devices have |3
factors as small as l(k3.
It can also be assumed that strong confinement of both electrons and photons to the
quantum-well active region, as has already been described, is likely to maximize the
overlap integral (T—>1). Applying the small (5 and maximum T conditions to the steadystate @/9t—>0) solutions to (5-20) and (5-21) yields:
(5-22)
Therefore,
ii.
Tp Lq(Vol)
(Itl - Po)W
N et '1
~
*C«
r
_
f II.
TP .q (Vol)
..-1
Nel
Ts .
(5-23)
Minimum steady-state conduction-band electron density
Manufacturing the fastest possible laser requires that electrons not be allowed to
linger in the conduction band too long before being stimulated to emit a photon. The
speculations that have already been made about the maximizing of coherency, photon
density, and stimulated emission probability in a quantum-well laser active region are
consistent with the further assumption that in future semiconductor lasers the steady-state
inverted population density Ne is likely to be only slightly above the minimum necessary to
achieve threshold [as expressed in (3-42)]:
- M_ - Jth T.S
Ne =
N0 =
qd '
(5-24)
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202
Maximum in-cavity photon lifetime
It is evident from the direct modulation link dynamic range equations of Table 3.2
that long cavity photon lifetime Tp is advantageous to link performance, which is one
reason why it is such a good idea to coat the laser's back-facet with as highly-reflective a
mirror as possible. From the expression for photon lifetime set forth in Chapter 3 [(3-41)],
the maximum achievable value of Tp is:
(5-25)
or tp -» 12.5 psec for InGaAsP (nL=3.675, ai=981.5 n r 1). This assumption along with
the minimum steady-state conduction-band electron density assumption simplifies the
expression for steady-state photon density:
(5-26)
Likely device parameters
To calculate the steady-state photon density using (5-26) and subsequently
determine y and ©t from equations (5-18) and (5-19), it is necessary to speculate about the
likely active region dimensions of a future semiconductor laser.
It can be assumed that the smallest cavity length will continue to be on the order of
100 Jim due to manufacturing yield limits [110]. Additionally, to guide a A.=1300 nm
optical wave, the cavity width w must exceed 650 nm, and an undesired second transverse
mode is possible if this dimension exceeds 1300 nm. It is therefore reasonable to assume
an optical confinement cross-section on the order of 1 pm square.
It would be advantageous to bury as many gain-guiding quantum layers (of
approximately 50 A thickness) as possible in this 1 pm-thick region. Approximately 5% of
the thickness can be filled in this way [110] (for instance, ten InGaAs 50 A layers separated
by 500 A undoped barrier layers). To summarize, the electron-photon interactions in a
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203
future semiconductor laser have been assumed to take place in a region with approximately
the following dimensions: L—>100 pm; w—>1 pm, d->50 nm; Vol—>5xl0*18 m3.
It is also necessary to assume a bias current I I when using expression (5-26) to
calculate the photon density S. To maximize cor, y, and the saturation input RF signal
power, it will still be necessary to operate future semiconductor lasers at reasonably high
bias; but for the purpose of minimizing the power consumption and maximizing poweradded efficiency, it seems prudent to set a limit of about 50 mA: I I —>50 mA. Therefore,
continuing to use a value of 4xl02 A/m2 for Jth in InGaAsP, it is seen that the steady-state
photon density S approaches 7.18X1023 n r 3.
The laser active region dimensions also dictate a value for the single guided mode's
group velocity vg. Given that the single optical mode has been assumed to be very tightly
confined to the active region, its group velocity can be approximated by that of a wave in a
metallic waveguide as follows [111]:
v
£
(5-27)
or Vg=1.07xl08 m/s for X=1300 nm in InGaAsP. If it is also assumed that in future
devices it will be possible to tailor the gain compression factor so to an order of magnitude
smaller than its value in currently available devices (Su et al. give the value for a typical
device as 3x1 O'20 m2 [92]), then from (5-18) it can be approximated that y->231 GHz.
Critical damping o f relaxation oscillations
For the ideal balance between high-frequency efficiency and linearity, it is desired
that the laser’s relaxation oscillations be critically damped. Underdamping causes extreme
nonlinearity and hence poor dynamic range; overdamping precludes efficient highfrequency modulation. Continually improving the state of the art in device modeling is
likely to enable future device designers to tailor the damping rate and frequency of the
relaxation oscillations to correspond to critical damping. Given y=231 GHz, critical
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204
damping occurs when ts-»8.65 nsec. This value of spontaneous emission lifetime is a
factor of 5-10 larger than that of many currently available devices, which corresponds to
the previously mentioned assumption that spontaneous emissions will occur less frequently
in future quantum-well devices. Equation (5-19) can now be used to predict that cor—>164
GHz (fr—>26 GHz).
The relative intensity noise of the semiconductor laser, RIN s l . can also be
calculated by substituting the results of the above assumptions, as well as expressions (512), (5-16), (5-17), and (5-20) into the general multi-mode expression for RINsl(<d) [92]:
RINsl(g>) = ^
.
S2
“2 +( t +bSF]
■+p ;
(© rl2 - (02f + ©2 Yl2
s2
(5-28)
(©r22 “ G)2)2 + CO2 Y22.
resulting in the following equation:
2 P Jth
R I N s l ( co) =
q d S [ © 2 + ( v g e o S ) 2]
(5-29)
or
R IN sl(co) -> r -L3- X 10 -1—t H z"1 (co in GHz).
[ CD2 + (231 ) 2 ]
(5-30)
For most useful microwave frequencies, equation (5-30) predicts a relative intensity noise
of about -155 dB/Hz.
In section 5.1.2, regarding expected future photodetector
developments, this impact of this predicted value of RIN sl upon link noise figure is
compared to the expected impact of other sources of noise expected from a future link.
Minimum threshold current
Minimizing a semiconductor laser’s threshold current maximizes the output optical
power from the device at a given DC bias current setting. Thus the external differential
quantum efficiency of the device, til, is maximized by minimizing Ith, and efforts to
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205
minimi7f» 1^ are likely to continue. The minimum achievable value of Ith is limited by the
material and dimensions of the active region as follows [94]:
Minimum !& = Jth L w ,
(5-31)
or Ith-^ 4 mA. The external differential quantum efficiency is defined as the ratio of
optical power output to the current input above threshold:
out.op
(5-32)
Substituting expressions (5-25) and (5-26) into (5-32) yields the expected result:
(5-33)
or til—>0.96 mW/mA (at X=1300 nm).
Maximum laser-to-fiber coupling efficiency
Currently, efforts to improve Klf> the optical coupling efficiency between a
semiconductor laser and its fiber pigtail, are focused on improved lensing and optical
mode-matching techniques. In Chapter 2 some recent efforts to improve the optical
coupling efficiency were described, and the best results to date were shown to be about
K lf=
60% between an edge-emitting laser and a single-mode optical fiber.
Improvements in laser-to-fiber coupling are likely to stem from two developments:
1) vertical cavity surface-emitting lasers (VCSELs) with circular optical mode profiles, and;
2) monolithic integration of edge-emitting semiconductor lasers with optimally tapered
integrated-optical waveguides. Especially with the latter technique, optical reflections can
be avoided and the numerical apertures of the laser active region and optical waveguiding
region can be matched by gradually tapering both the dimension and refractive index profile
of the integrated-optic waveguide between the device and standard waveguide sections of
the substrate. The best-possible culmination of such efforts would result in
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206
S. 1.2.
Photodetector Development Trends
Current knowledge about photodetector development trends is sufficient to support
speculations about the characteristics of a typical future device. Such speculation is
necessary if the performance of future direct-detection links is to be estimated. Of the
assumptions made in this section regarding a typical photodetector, those which affect the
prediction of the performance of a direct modulation link are also shown in Table 5.1. The
assumptions that have been listed in Table 5.1 appear in the text in boldface.
It is assumed that future direct and external modulation links for RF signal
applications will both continue to employ the straightforward direct detection technique as
discussed in Chapter 2. The extra componentry required for interferometric detection
techniques dictates an increased cost for fiber-optic links employing these architectures.
Furthermore, the success of these techniques depends on maintaining a very high degree of
temperature stability throughout the fiber-optic links. Because the current trend in fiber­
optic link development is a focus on the reduction of cost without loss of performance, a
future link is almost certain to employ direct (intensity) detection using a p-i-n photodiode.
The heterojunction p-i-n was compared to other types of photodetectors in Table
2.5 of Chapter 2. It is preferred over the APD and MSM Schottky devices because of its
large bandwidth compared to that of an APD, its high efficiency compared to that of an
MSM device, and its large junction resistance Rjd under reverse bias. Moreover, its
intrinsic region can be tailored to permit the best trade-off between optical fiber-to-detector
coupling efficiency (KfdX intrinsic quantum efficiency (t|iD, the percentage of incident
photons that generate electron-hole pairs), junction capacitance (C jd ). 3-dB roll-off
frequency (f3dB)> and power handling.
The extrapolation of current p-i-n photodiode development trends into assumptions
about future device parameters is summarized in the flowchart of Fig. 5.2. The breakdown
of the remainder of this section of the chapter follows the arrows in the flowchart.
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207
Enabling Technology
Advances
Present
Effect on present model
(Af in GHz)
Monolithic integration reduces
circuit parasitics
1r
Improved gain-bandwidth
product
G rx = 500 (l - e~5A?)
Nthjix = -kB" ~
1 —e'jAf
New device architecture has long
light collection path for high
efficiency, short current collection
path for high frequency response
1
Very fast, efficient travelingwave photodetectors
^3dB =
GHz
TliD = 1
r|j} =1.05 mA/mW
Index matching and monolithic
integration enable coupling
efficiency advances
1r
Maximum fiber-to-detector
coupling efficiency
Increasingly defect-free materials
processing
KFD = 1
<z'2RIN,dir>
= 5.51 x 10'19 A2/H z
<i2shot,dir>
= 1.47 x IQ’20 A2/H z
1
Minimum dark current
^ “dark5, _ ®
t
Future
Figure 5.2 Projected improvements in the state of the art of future p-i-n photodiodes.
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208
Improved gain-bandwidth product (Fano’s limit achieved)
As is the case in the optical transmitter, the maximum insertion gain that can be
achieved in a reactively-matched p-i-n photodetector-based optical receiver—i.e., maximum
G rx —is achieved if and only if the matching circuit is a lossless reciprocal network (so
that IS21IM -IS 11I2) and a perfect match is achieved at every frequency in the desired band
at both the input and output (so that S22=0 and Sh=Fd*). These conditions cause the
equation for G rx [equation (3-21)] to become greatly simplified:
(5-34)
|i - s „ DrD|2~*i-|rDr '
The assumption that the network of equivalent circuit elements is lossless dictates that all
parasitic resistance in the detector must be included in the load represented by T d - A s was
shown in Chapter 4, the equivalent circuit models of the detectors in the experimental links
all included a junction capacitance C j d in parallel with the very large junction resistance
R jd, and a parasitic contact resistance Rpd in series with this combination. It can be
assumed with confidence that the trend toward monolithic integration of photodetectors
with other circuit elements will reduce the parasitic resistance so that in future optical
receivers it is the diode junction resistance that is reactively matched to the output.
Therefore, substituting the expression for Td [equation (3-2)] into (5-34) yields:
(5-35)
Maximum Grx —>
Note that this assumes that a perfect match can be achieved so that S22=0 at every
frequency, which violates Fano’s rule as discussed in Chapter 2. To correct this, Fano’s
rule [expression (2-9)] is used in conjunction with expression (5-34) so that:
G RX= t i - i ^ 2 j m a x )
2 nfol
- e AfQ>1AR7jd
(5-36)
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209
Equations (5-2) and (5-3) show why it is advantageous to continue using p-i-n
photodiodes with large
( R j d —>100
kQ) reverse-biased junction resistance. Therefore, if
the parasitic inductance of the device lead is minimized via monolithic or other advanced
packaging schemes, then the detector is essentially a parallel R-C circuit, for which
Q = © R jd C jd .
(5-37)
For high insertion gain, minimum junction capacitance is desirable; however, few
publications have described efforts to achieve these goals. One investigator did report a
very encouraging junction capacitance of 0.05 pF [68]. This capacitance value was
achieved by constructing a device with the smallest possible active area that still permitted
high photon coupling and absorption efficiency. Assuming that this level of capacitance is
maintained in future devices (i.e., Cjd —>0.05 pF), then:
G rx ->500 (l - e “ 5 A?)(Af in GHz).
(5-38)
Under these ideal matching conditions, the expression for the thermal noise generated in the
optical receiver is greatly simplified; Le.,
N«h.RX >kp ™ (Af in GHz) .
1 —e~s AT
(5-39)
Very fast and efficient traveling-wave photodetectors
The major limitations to the speed of conventional heterojunction p-i-n
photodetectors are: 1) the time it takes a carrier to drift across the depletion region; 2) the
time it takes carriers to diffuse out of undepleted regions; 3) the time it takes to charge and
discharge the inherent capacitance of the diode plus any parasitic capacitance, and; 4)
charge trapping at heterojunctions [112]. These transit time considerations suggest that
very thin intrinsic layers are needed to achieve high-speed responses in conventional
photodiodes. However, in a p-i-n photodiode there is a direct trade-off between speed (as
limited by the 3-dB modulation bandwidth f3dB) and efficiency T|iD. To achieve a high
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210
quantum efficiency, the depletion layer must be thick enough to permit a large fraction of
the incident light to be absorbed.
This trade-off can be circumvented to a large degree by collecting light parallel to
the junction plane in a traveling-wave device rather than perpendicular to it as in
conventional back-illuminated p-i-n diodes. Illuminating the junction from its edge enables
a long light-collection path and a short current-collection path to exist in the same device,
resulting in both high efficiency and large bandwidth. The electron transit-time limit to the
device response is about 150 GHz for devices with useful waveguide dimensions.
Unfortunately, the corresponding intrinsic quantum efficiency T|jD is normally only about
50% [112] due to the velocity mismatch between the microwave transmission line contacts
and the optical waveguide.
Recently, however, a device architecture has been proposed using discrete p-n
junctions placed periodically along the optical waveguide. Between the individual
photodiodes the transmission line is diverted away from the optical waveguide enough to
achieve a broadband velocity match so that the photodetector contributions add up in phase.
With sufficiently many photodetectors in this series chain, nearly 100% of the guided
photons are detected [113]. It is logical to assume that this structure will be successfully
demonstrated in the next few years. Therefore, the same traveling-wave device that has a
bandwidth of f 3dB—>150 GHz will also feature a quantum efficiency of T|iD—>1The responsivity t| d of a future photodetector can be estimated from the intrinsic
quantum efficiency using the following expression [39]:
TlD= TliD j^-,
(5-40)
which yields T|d—>1.05 mA/mW (for X,=1300 nm).
Maxinuan fiber-to-detector coupling efficiency
The manufacturers of p-i-n photodiodes have had increased success at minimizing
optical reflections at the aperture in recent years. Reducing reflections at the fiber-detector
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211
interface is especially important when the optical source in a link is not protected by an
optical isolator. Some manufacturers have even packaged their photodiodes in conjunction
with an integrated-optic waveguide port; this can effectively eliminate reflections at the
photodiode. Fiber-to-waveguide reflections are easily minimized using index-matching
epoxy. These index-matching trends are likely to enable direct modulation links in which
nearly every photon emitted from the semiconductor laser’s active region reaches the
junction of the photodetector, i.e., K l f L f K fd - >1Minimum dark current
The noise power in the optical receiver due to the detector’s dark current is
proportional to the DC dark current, as was explained in Chapter 3. Detector dark currents
as low as 0.04 pA have been reported recently [68], with order of magnitude reductions
occurring every few years. Increasingly defect-free materials processing is likely to ensure
that photosensitive devices will become increasingly immune to the thermal and vibrational
perturbances that presently result in undesired electron-hole pair generations. Dark current
is thus likely to have an increasingly negligible effect upon link noise figure in the future;
therefore it makes sense to assume I<iark->0 and consequently <i2dark>—>0.
At this point there is sufficient information to determine the dominant source of the
microwave noise at the output of a theoretical future direct modulation link. The sources of
noise are the thermal noises arising from lossy elements in the optical transmitter
(Nth,xx,dir) and optical receiver (N ^ rx ), and the noise arising from the optical generation
and detection processes (Nop,dir)- With dark current assumed to be negligible, the
contributions to Nop.dir are from the laser’s relative intensity noise and the statistical (shot)
noise. Straightforward calculation of the noise spectral densities in the optical receiver of
the direct modulation link arising from these two optical noise sources is possible using the
speculations outlined above in conjunction with expressions (3-33) and (3-35) from
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Chapter 3; i.e., <«‘2RiN,dir>—>5.51 x 1O'19 A2/H z a t most microwave frequencies and
<*2shot,dir>->l-47xlO‘20 A2/Hz. Both of these terms are much greater than the total
spectral density of the thermal noise in the optical receiver. Thus it appears likely that even
in future direct modulation links, the laser’s relative intensity noise will remain the
dominant source of noise.
All the assumptions needed to predict the performance of future direct modulation
links have been presented. Table 5.1 (a) summarizes the equations with which a future
direct modulation link’s insertion gain is predicted in section 5.3.2 and section 5.4.2 of this
chapter. The noise figure and dynamic range of such a link are calculated using the
equations in Table 5.1 (b) and (c), respectively.
5 .2
C h arac te ristic s o f E lectro-optic Devices Used in F u tu re E x tern al
M odulation Fiber-optic Links
The equations in Tables 3.3 and 3.4 were used to fully model external modulation
links for which the electro-optic modulator and p-i-n photodetector diodes were available
for measurement of all the parameters required for modeling. A different set of equations
and assumptions is needed to predict external modulation link performance when the
devices to be used aren’t available for characterization, such as is the case when attempting
to predict the improved performance of future external modulation links.
In this section some trends in electro-optic external modulator developments over
the past few years are examined, and some additional assumptions that facilitate the
present-day modeling of a future direct modulation link comprised of advanced (theoretical)
devices are outlined.
The modulators showing the greatest promise in terms of high efficiency out to the
highest frequencies have been electro-optic traveling-wave devices manufactured in Tidoped LiNb0 3 . Modulators fabricated in GaAs have one advantage over LiNb0 3 devices
in that they can be monolithically integrated with other devices; however GaAs has a much
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Relevant Assumptions (from section 5.1)
Small-Signal Insertion Gain
G d ir
= ClTX,dir| Hdir | 2
G rx
(3-19)
G n c ,d ir -> U .9 (l-C
m) (Af in GHz)
->500 (l -
(Af in Gllz)
G rx
where
| IIdir|2 = | H l | 2 ( tI l K l f L f K f d TId ) 2 I H d | 2
(3-22)
nL-»0.96mW/mA
Kjj:LpKpD->l
T1D->105 mA/mW
|H l|2 = ---------^ --------
(3-23)
tor->164 GIIz
((Of - to2j2 + y2 w2
Y ->231 G H z
and
| Hd|2 = ------- 1------ r
(3-24)
f3dB->150GHz
'2 1t fjdB I
Table 5.1 (a) Summary of analytical model for predicting small-signal insertion gain of a future direct modulation link.
to
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Relevant Assumptions (from section 5.1)
Noise Figure
N oul.R X .dir
N F d ir =
(3-37)
kn T D Gdir
where
N oul.R X .dir = N ih.T X .dir + N ih.R X + N o p .d ir
(3-25)
Nih.TX.dir ->2
(Af in GHz)
1- e 4,
N o i.rx
—> knTP- (Af in GHz)
l-e'TTf
Nop.dir - [(iRIN.dir) + (/shot,dir) + (/dark)] GRX B Z o
(3-31)
<i2shot,dir>-» 1.47x10-2° A2/Hz
<i2dark>-»0
and
(iRIN.dir) = [ T|L K l F L f K fD HD (iL-Ith)] 2 R IN sl
(3-33)
Il-»50 mA
Ith—>4 mA
RINsl((0) ->
^ 9 x l0~»‘ Hz-i (winGHz)
[ to2 + ( 231 )* ]
Table 5.1 (b) Summary of analytical model for predicting noise figure of a future direct modulation link.
214
Table 5.1 (c)
Relevant Assumptions (from
Section 5.1)
Summary of analytical model for predicting dynamic range of a future direct modulation link.
Spurious-Free Dynamic Range
-215
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216
smaller electro-optic figure of merit (n03xry) than LiNbC>3. In GaAs, n03xr4i=58xlO*12
m/V compared to no3xr33=320xl(H 2 m/V in LiNb 0 3 [114]. Because of this large
difference in the strength of the electro-optic effect, the best-performing external
modulation links are likely to include LiNb0 3 electro-optic modulators in the near future.
Current knowledge about electro-optic external modulator trends is sufficient to
support speculations about the characteristics of a typical future device. Present-day
modeling of future direct modulation links can be accomplished if a number of reasonable
assumptions are made. Table 5.2 at the end of section 5.2 gives equations for modeling
future external modulation links, as derived from the assumptions discussed in this section
and section 5.1.2 (future p-i-n photodetectors). Of the assumptions made in this section
regarding a typical future modulator, those which affect the prediction of the performance
of the link are also shown in the table. The assumptions that have been listed in Table 5.2
appear in the text in boldface.
The extrapolation of current electro-optic external modulator development trends
into assumptions about future device parameters is summarized in the flowchart of Fig.
5.3. The breakdown of this section of the chapter follows the arrows in the flowchart
Improvedgain-bandwidthproduct (Fano’s limit achieved)
As in the semiconductor laser-based direct modulation optical transmitter, the
maximum insertion gain that can be achieved in a reactively-matched electro-optic external
modulator-based optical transmitter—i.e., maximum Gxx,ext —is achieved if and only if
the matching circuit is a lossless reciprocal network (so that IS2 il2= l-IS n l2) and a perfect
match is achieved at every frequency in the desired band at both the input and output (so
that S n= 0 and S22=Fm*)- For broadband performance, the traveling-wave electrodes of
the external modulator need to be terminated in an impedance Zt equal to the electrode
characteristic impedance Zc so that equation (3-68) reduces to ZM(Le)=Zt regardless of
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217
Enabling Technology
Advances
Present
Effect on present model
(Af in GHz)
Monolithic integration reduces
circuit parasitics
Improved gain-bandwidth
product
Grx.ext = 2 ( l
2 kR T B G«t
Nth.TX.ext = —f
^
1- e " ^
Improved buffer layer
optimization
Perfect velocity matching
8= 0
Optimum waveguide and
electrode geometry maximizes
overlap integral
Maximum voltage-length
_______ product_______
Ge = 10 nm
V x L = 0.125 V m
Suitable gain vs. dynamic
range compromise
A = 0.97 V
Efficient coupling to
integrated laser diode
LMPSSL = 30mW
popt,ext= ^
•2
shot,ext>
= 4.61 x 10-21 A2/H z
Future
Figure 5 3 Projected improvements in the state of the art of future electro-optic external
modulators.
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218
frequency. These conditions cause the equation for G r x ,e x t [equation (3-100)] to become
greatly simplified:
Gt x « , * |S 21w|2! ■—
.
Ii-s^ F m P
(5-41)
i - | r M|2
Substituting the expression for Tm [equation (3-71)] into (5-41) yields:
Maximum Grx ext —
>7 7 - Zo
(5-42)
Note that this assumes that a perfect match can be achieved at every frequency, which
violates Fano’s rule as discussed in Chapter 2. Therefore, from the lossless reciprocal
condition assumed above, substitution of Fano’s rule [expression (2-9)] into expression (541) yields:
Cl
'JTX.ext
_(i-lSnL£j|i + r M|2
-------------- :
rz
i - | r M|
= (1 . 10- ^ ) | = ( , - e- ^ ) | .
(M 3 )
Equations (5-42) and (5-43) show how advantageous it is to maximize the
traveling-wave electrode characteristic impedance and terminate them in the same
impedance Z i=Zq . There have been few published efforts to maximize Zq . With the
advent of velocity-matched devices with buffer layers tailored specifically with the goal of
achieving a certain microwave group velocity, it seems feasible to also design these layers
with the resulting characteristic impedance in mind. With other more pressing design
concerns, it is probably unreasonable to assume that electro-optic modulator manufacturers
will achieve electrode impedances greater than Zt—>100 Q. in the near future.
The quality factor Q in equation (5-43) is that of the modulator electrodes with any
parasitic inductance associated with connecting it to a lossless reactive matching network.
Because the matching circuit is likely to be on another substrate, this connection will
probably be a bond wire or ribbon with a minimum inductance on the order of Lpm —>0.1
nH. Therefore,
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219
q
= “ L el
Zt
0.628 f0 (f0 in GHz).
(5-44)
Equation (5-43) now reduces to
G jx.ext -» 2 (l - e -iJzr) (Af In G Hz).
(5-45)
Under these matching conditions, the expression for the thermal noise generated in the
optical transmitter is similarly simplified; i.e.,
Nth.TX.ext ~>2 kB T ^ CXt <A f in GHZ)
1 —e~ at
(5-46)
Perfect velocity matching
It is possible to increase the high-frequency modulation capability of electro-optic
Mach-Zehnder modulators by using a periodic phase-reversed traveling-wave electrode
structure to counter-act velocity mismatch, as has been demonstrated by Korotky and
Veselka [115] as well as many others. However, the broadest-band performance will be
achieved when the optical and RF waves are forced to travel along the device at the same
velocity. Noguchi etal. [116] have developed a Ti:LiNb0 3 optical intensity modulator
with a coplanar waveguide having a shielding plane (i.e., a buffer layer) for opticalelectrical velocity matching and a confined waveguide for lowering the drive voltage. This
modulator’s electrical bandwidth was only verified to 20 GHz, but a minimal switching
voltage—only 5.2 V—was achieved and the effective microwave index was successfully
reduced from its usual unshielded value of 4.3 to nearly 2.2 (the optical refractive index).
Continuing efforts along the same lines will ultimately result in velocity matching that for
all practical purposes can be considered perfect; i.e. 5—>0.
Maximum voltage-length product
Calculation of external modulation link performance also requires knowledge of the
electro-optic modulator's halfwave switching voltage Vn and the parameter defined as A in
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220
Chapter 3. Assumptions about these characteristics can only be made for a typical future
modulator if its coplanar electrode gap Ge and overall interaction length Le are both known.
The most important figure of merit for any electro-optic modulator is its voltagelength product VnXLe. If this is minimized, then the electrodes don’t have to be very long
in order for high-efficiency (i.e., small Vjt) performance to be attained. This figure of
merit is defined as follows [59]:
V n U = - - Ge- - ,
n? r,j
r eo
( 5 -4 7 )
where no is the optical refractive index, ry is the electro-optic tensor (with units of m/V),
and Teo is the electrical and optical field overlap percentage. The LiNbC>3 material has a
large electro-optic tensor r 33 of about 3 x l0 ‘n m/V, and an index of n0=2.2 for X=1.3 pm.
Current devices feature coplanar electrode gaps on the order of 10 pm, which cannot be
made smaller without also reducing the overlap integral because of the size of the optical
waveguide. This overlap integral has been getting closer and closer to unity in recent
devices. It is therefore reasonable to assume that Ge—>10 pm and r eo->l in future devices,
resulting in a voltage-length product of VnxLe->0.125 V*m.
Suitable compromise between gain and dynamic range
At this point some design choices come into play. Small V n improves an external
modulation link’s insertion gain, but adversely affects its dynamic range. Therefore, Vrc
should be chosen with more regard for the result on modulator size; a suitable compromise
which satisfies the above assumptions is: Vjt—>5 V and L e—>2.5 cm. From expression
(3-78) in Chapter 3, these assumptions also result in a value of A(co)->0.97 V*1.
At this point it is also necessary to evoke one of the assumptions set forth in section
4.2.4. That is, it was proven that maximum dynamic range occurs near the modulator's
halfwave voltage (Vb=-Vn/2), but only at the expense of much lower insertion gain.
However, if a very high-power, low-RIN solid-state laser can be procured, as has already
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221
been assumed, then even at the quarterwave bias voltage the noise figure approaches its
minimum value, and the dynamic range approaches its theoretical lim it Thus, for
prediction of future external modulation link noise figure and dynamic range, one additional
assumption is made: Vb—>0.
Efficient coupling to integrated semiconductor laser diode
The optical power at the output of the modulator (the product of Lm and P ssl ) is
limited only by the maximum optical power the modulator or detector can withstand
without incurring damage. For currently available electro-optic modulators this power is
on the order of 100 mW [117]. It is reasonable to expect that this could be improved by an
order of magnitude with the addition of advanced materials to preserve the index profile and
thus the mode confinement of the optical waveguide in the substrate. However, it is
unlikely that this high an optical power will be desired in systems with low optical loss,
since this places a severe demand upon optical source and detector performance.
The optical transmitter in a future external modulation link is likely to incorporate a
semiconductor or other solid-state laser in the modulator package. It was already assumed
in section 5.1 of this chapter that future semiconductor lasers would feature high output
power with low relative intensity noise. The future semiconductor laser's output power
PSSL can be calculated from the assumptions made about t |l . II. and Ith in section 5.1.
These were assumed to be 0.96 mW/mA, 50 mA, and 4 mA, respectively, for a future
device, resulting in Pssl - >44 mW. Coupling this optical output power directly into the
optical waveguides of a IiNbC >3 modulator, which has an optical insertion loss Lm, will
result in about 30 mW out of the modulator. Thus, using the same semiconductor laser
described in section 5.1 to provide the optical carrier in a future external modulation link
results in LmPssL- >30 mW and relative intensity noise dictated by equation (5-28). At
the quarterwave bias voltage Vb=0, P0pt,ext therefore approaches (Lm P ss l )/2, or
Popt,exf"> 15 m W .
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Finally, many assumptions about future p-i-n photodetectors made in section 5.1 to
predict future direct modulation link performance are invoked again in Table 5.2 to enable
future external modulation link performance predictions. Using equation (3-111), the noise
spectral density in the external modulation link’s optical receiver arising from shot noise is
calculated: <t2shot,ext>-»4. 61 x 10_21 A2/H z.
5 .3
D irect vs. E xtern al M odulation: C rossover Frequency fo r a Given
Percentage B andw idth
The direct and external modulation methods are compared in this section. The
comparison is valid for links that use the conventional CPU-level data mixing architecture.
In this architecture, the fiber-optic link must relay signals at the RF frequency at which
remote signal distribution is desired.
Comparisons are made assuming three different percentage bandwidths—0%,
10%, and 70%. The meaning of percentage bandwidth is the percent of the frequency at
the center of the RF band. For example, given a CPU-level data mixing link with an RF
band centerfrequency o f 6 GHv
(a) 0% Bandwidth denotes a link for which performance at only the single
(6 GHz) frequency is of interest;
(b) 10% Bandw idth denotes a link for which performance across a 600
MHz-wide band centered at 6 GHz (5.7-6.3 GHz) is of interest;
(c) 70% Bandwidth denotes a link for which performance across a 4 GHzwide band centered at 6 GHz is of interest (4-8 GHz). This case always
denotes an octave band.
5.3.1
Predictions Made Using Characteristics of Currently Available Electro-optic
Devices
In this subsection direct and external modulation links are compared using the
known characteristics of currently available electro-optic devices in conjunction with the
models set forth in Chapter 3.
Figure 5.4 shows the result of the analysis. A spreadsheet program was used to
calculate the result of every equation in Table 3.1 (for the direct modulation link) and Table
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Relevant Assumptions (from section 5.2)
Small-Signal Insertion Gain
(3-99)
G « t = (rrx.em 11Icai | 2 G rx
Grx,e»i —>2 (1
(AfinGHz)
G rx - » 5 0 0 ( l -
(A fin G H z )
where
| H.„ | 2= (A(0>) Lm Lf
- SSLg i)2cos2 j l ^ J | hd I2
(3-103)
A({o)-»0.97 V 1
Lmp SSL~»30 mW
LpKpo-»l
tid- >1*05 mA/mW
vb->o
(3-24)
f3dB->150GHz
Table 5.2 (a) Summary of analytical model for predicting small-signal insertion gain of a future external modulation link.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Relevant Assumptions (from section 5.2)
Noise Figure
KIT,
N oul.R X .eil
N l'e x l = ----------------------
ko T D Gext
(3 -1 0 4 )
where
Nout.RX.exl = Nth.TX.exl + Nth.RX + Nop,ext
(3 -1 0 5 )
N
t h
. T
X
. e
1-e
x
t
(AfinGHz)
4f
Nut.RX -» KB-T-B- (AfinGHz)
1
Nop,ext = [(<RlN,exl) + (fxhot.ext) + ((dark)] G rx B Zo
(3 -1 0 9 )
<»2s h o t,e x t> - » 4 .6 1 x l0 - 21 A 2/ H z
<»2dark > —
and
(iRIN.ext) = [ L f
Kfd IfD Popl,ext(DC)] 2 RINssiX© )
(3 -1 1 0 )
P o p t.e x l^ lS m W
RINsl(w) ->
1;39 * 1Q ‘‘ . Hz-* (to in GHz)
[to2 +(231 )2 ]
Table 5.2 (b) Summary of analytical model for predicting noise figure of a future external modulation link.
224
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Relevant Assumptions (from Section 5.2)
Spurious-Free Dynamic Range
S F D R ext =
Pjn.int.ext
p
(3-135)
kuT B N Fext
where
n
_ mint,ext ( V h — 2 1 V b | )
I in.inl.exl-------------------------------------------
(3-114)
Vft—>5 V
4 Grx.ext Zo
and
4Y?n____
n2 - 4 A(©) | Vb |
niint.cjit —
(3 -1 2 6 )
Compression Dynamic Range
Pin.lCP,ext
C D R ex, — ■
kfl T B N Fext
(3 -1 3 6 )
where
m (fcp,ext ( V ie — 2 1 V b | ) 2
Pin.lCP.exl = --------------- 1--------------1--------- —
(3 -1 2 8 )
4 Grx.ext Zo
and
m ic p ,e x t =
2 x 0.5500 n
n2 - A A(co)|VtJ
(3 -1 3 3 )
Table 5.2 (c) Summary of analytical model for predicting dynamic range of a future external modulation link.
to
to
u
3.2 (for external modulation) at band center frequencies ranging from 100 MHz to 50 GHz.
Three different percentage bandwidths are plotted: (a) 0%—the single-frequency case; (b)
10%, and; (c) 70%—the octave-bandwidth case. The highest frequency in the band (equal
to the center frequency plus half of the bandwidth) was always used in the frequencydependent equations to give worst-case results. The parameter values used were those
measured or quoted by vendors for the most recently-manufactured devices used in the
experimental links of Chapter 4— for instance: the high-speed DFB-BH laser diode used in
the 3-6 GHz and 11.5-12.5 GHz direct modulation links; the broadband electro-optic
modulator and high-speed p-i-n photodiode used in the 32-33 GHz external modulation
link.
Note from the three versions of the figure [(a), (b), and (c)] that the optimum gain
worsens at any center frequency as the percentage bandwidth is increased; the spurious-free
dynamic range, however, is independent of percentage bandwidth. This result was
anticipated in the link models by the fact that gain and signal-to-noise ratio are both
proportional to both G t x and G r x (the impedance-transformation gains in the optical
transmit and receive modules, which depend on the percentage bandwidth in accordance
with Fano’s rule), while the dynamic range equations are only sensitive to the electro-optic
device parameters (which are not a function of percentage bandwidth) and G t x - Fano's
rule showed that it was possible to reactively match to semiconductor lasers and travelingwave electro-optic modulator electrodes across very wide bands because of the low Q
factors for these devices. Thus the spurious-free dynamic range did not depend on the
percentage bandwidth.
Similar trends in the direct vs. external modulation link comparison are evident in
all three percentage bandwidth settings plotted in Fig. 5.4. For instance, the dynamic range
of direct modulation links is poor for center frequencies right at the relaxation oscillation
frequency of the semiconductor laser, where nonlinearity and intermodulation products are
strongest At frequencies much greater than the laser relaxation oscillation frequency and
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
€
€
’O
-a
G
a
«
£
s
rH
CJ
c
•m
&
§
Pi
u
e
•a
o
c
o
s0)
-10
Direct M odulation Link
External M odulation Link
s
-20
Ia>
-30
£
3
o
-40
G<
Cfl
-50
0.1
10
Link Center Frequency (GHz)
1
Figure 5.4 (a) Predicted insertion gain and spurious-free and compression dynamic range of fiber-optic links as a function of the
center frequency in the link band, assuming the use of the conventional CPU-level data mixing architecture and
devices consistent with the current state of the art. Performance is shown for both direct and external modulation
links, as calculated using the expressions in Tables 3.1 and 3.2, respectively, and assuming link design optimization at
a single frequency (Bandwidth=0% of center frequency).
to
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100
50
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Figure 5.4 (b) Predicted insertion gain and spurious-free and compression dynamic range of fiber-optic links as a function of the
center frequency in the link band, assuming the use of the conventional CPU-level data mixing architecture and
devices consistent with the current state of the art. Performance is shown for both direct and external modulation
links, as calculated using the expressions in Tables 3.1 and 3.2, respectively, and assuming a 10% link bandwidth
(Bandwidth=10% of link center frequency).
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Figure 5.4 (c) Predicted insertion gain and spurious-free and compression dynamic range of fiber-optic links as a function of the
center frequency in the link band, assuming the use of the conventional CPU-level data mixing architecture and
devices consistent with the current state of the art. Performance is shown for both direct and external modulation
links, as calculated using the expressions in Tables 3.1 and 3.2, respectively, and assuming an octave link bandwidth
(Bandwidth=70% of link center frequency).
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detector 3-dB modulation bandwidth, direct modulation link dynamic range decreases
because of the quickly decreasing gain and worsening noise figure.
Similarly, at
frequencies much greater than the detector 3-dB modulation bandwidth, external
modulation link dynamic range decreases.
Figure 5.4 shows that, using present state-of-the-art devices in a CPU-level data
mixing architecture, external modulation links can always be designed to have better
dynamic range than the best direct modulation links. This holds true regardless of the
center frequency or bandwidth. However, in systems where cost is a more important
criterion than dynamic range, direct modulation is likely to be chosen as the baseline
architecture. All three iterations of Fig. 5.4 show that direct modulation links exhibit
roughly the same insertion gain as external modulation links up to a very high frequency,
beyond which external modulation gives higher gain. This departure frequency is roughly
10 GHz for all three percentage bandwidths considered.
The approximate equivalency of direct and external modulation link insertion gains
at lower microwave frequencies is supported by experimental data. In Chapter 4, two
experimental demonstration links—one a direct-modulation link and the other an extemalmodulation link—with the same center frequency (900 MHz) and percentage bandwidth
(about 10%) were shown to exhibit roughly the same maximum insertion gain (about 0 dB
and 3 dB, respectively).
5.3.2
Predictions Made Using Characteristics of Future Electro-optic Devices, with
Expected Improvements Based on Analysis of Physical Models
In this section direct and external modulation links are compared using the
characteristics of future devices, as presupposed in sections 5.1 and 5.2 (especially Tables
5.1 and 5.2), respectively. Figure 5.5 shows the result of the analysis. The parameter
values used were those derived in sections 5.1 (for direct modulation links) and 5.2 (for
external modulation links).
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Figure 5.5 (a) Predicted insertion gain and spurious-free dynamic range of fiber-optic links as a function of the center frequency in
the link band, assuming the use of the conventional CPU-level data mixing architecture with future state-of-the-art
devices. Performance is shown for both direct and external modulation links, as calculated using the model and
assumptions summarized in Tables 5.1 and 5.2, respectively, and assuming link performance optimization at a single
frequency (Bandwidth=0% of link center frequency).
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Figure 5.5 (b) Predicted insertion gain and spurious-free dynamic range of fiber-optic links as a function of the center frequency in
the link band, assuming the use of the conventional CPU-level data mixing architecture with future state-of-the-art
devices. Performance is shown for both direct and external modulation links, as calculated using the model and
assumptions summarized in Tables 5.1 and 5.2, respectively, and assuming link performance optimization across a
10% bandwidth (Bandwidth=10% of link center frequency).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Direct Modulation Link
External Modulation Link
Link Center Frequency (GHz)
Figure 5.5 (c) Predicted insertion gain and spurious-free dynamic range of fiber-optic links as a function of the center frequency in
the link band, assuming the use of the conventional CPU-level data mixing architecture with future state-of-the-art
devices. Performance is shown for both direct and external modulation links, as calculated using the model and
assumptions summarized in Tables 5.1 and 5.2, respectively, and assuming link performance optimization across an
octave bandwidth (Bandwidth=70% of link center frequency).
Note from Fig. 5.5 that the optimum gain worsens at any center frequency as the
percentage bandwidth is increased (as they did in the case of currently available devices),
and the dynamic range is independent of percentage bandwidth and is fairly independent of
center frequency up to about 30 GHz. This result is explained by the fact that the laser
relaxation oscillation frequency, modulator walk-off frequency, and photodetector 3-dB
bandwidth have all been credibly assumed to be much greater for future ultrahigh-speed
devices, and that the laser relaxation oscillations have been assumed to be critically
damped, resulting in a fairly constant signal-to-noise ratio across the lower microwave
frequencies.
Figure 5.5 also shows that, using future state-of-the-art devices in a CPU-level data
mixing architecture, direct modulation links can always be designed to have better insertion
gain than most external modulation links up to fairly high microwave frequencies, beyond
which external modulation links have better insertion gain. The crossover frequencies, as
determined from Fig. 5.5 (a), (b), and (c), respectively, are roughly 60 GHz for the 0%
bandwidth case, 50 GHz for 10% bandwidth, and 40 GHz for the octave (70%) bandwidth
link. This turnabout in future link trends can be anticipated by the fact that future external
modulators were not assumed (in section 5.2) to be designed for the smallest-possible
switching voltage (V ^. Very small Vn would have yielded better insertion gain at the cost
of reduced linear input RF power handling and thus smaller dynamic range. By contrast,
all the speculations about future semiconductor lasers in section 3.1 were ones that tended
to improve both efficiency (gain) and frequency response, with no detriment to their RF
power handling capabilities.
5 .4
CPU-level vs. T/R-level d a ta mixing
In this section, the CPU-level and T/R-level data mixing architectures are briefly
compared. In the T/R-level data mixing architecture, the total system performance is
limited only by the performance of the IF fiber-optic link (assuming here that RF-IF mixing
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235
technology will continue to lead fiber-optic link technology in terms of performance [3]).
The performance advantage of T/R-level data mixing is therefore obvious: it effectively
increases the system performance to the same performance that could be achieved using the
CPU-level data mixing architecture at a much lower (IF) frequency than the RF.
5.4.1
Predictions Using Characteristics of Currently Available Electro-ontic Devices
In this section, the performance of a present-state-of-the-art fiber-optic link using
the T/R-level data mixing architecture discussed in Chapter 2 is compared to the
performance of a link using the straightforward CPU-level mixing approach. The
comparison is performed using the known characteristics of currently available electro-optic
devices, namely the devices used in an external modulation link demonstrated in Chapter 4.
Figure 5.6 illustrates how the architectures compare with regard to the analytically
determined spurious-free dynamic range of an external modulation link. The solid line in
the graph of SFDRext vs. frequency represents the performance that can be achieved using
currently available devices—specifically, the AMOCO Nd:YAG laser, the UTP LiNb03
Mach-Zehnder traveling-wave modulator, and the Epitaxx InGaAs p-i-n photodiode used in
the wideband (6-12 GHz) experimental link described in section 4.3.4. This line is
different in magnitude from the spurious-free dynamic range plotted in Fig. 5.4 because of
the different modulator and laser parameters used for that analysis. The measured dynamic
range of the link described in section 4.3.4 is also included along the solid line in the
graph.
Following through an example of how to optimally design a link using T/R-level
data mixing will best illustrate the degree of flexibility it affords a link designer. The
example that is outlined in Fig. 5.6 is a present-state-of-the-art external modulation link
with a center frequency of 55 GHz and roughly 10% bandwidth (52-58 GHz). This
frequency band was selected for the example because of its usefulness in space-based
antennas being deployed to monitor the earth’s ozone layer thickness. The extent to which
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75 r
6-12 GHz Link Result
(section 4.3.4)
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Example of how, using the T/R-level data mixing architecture with suitable choice of LO frequency, the anticipated
performance of future straightforward (CPU-level mixing) external modulation links can be approached currently.
237
a spot in the atmosphere absorbs these RF frequencies is an indication of the ozone layer
thickness at that spot
Figure 5.6 illustrates the extent to which performance is sacrificed when the CPUlevel mixing approach is used, due to the fact that this architecture requires an external
modulator to function at RF frequencies beyond the walk-off frequencies of most currently
available devices (arising from the microwave-optical wave velocity mismatch).
The flexibility imparted from the choice of the T/R-level data mixing approach is
that the 6 GHz RF bandwidth around a center frequency of 55 GHz can be achieved using
any combination of narrowband LO and broadband IF fiber-optic links whose frequencies
add up to the desired RF frequencies. For example, Fig. 5.6 shows the 6-12 GHz link
described in section 4.3.4 of this thesis being used as the IF link in conjunction with a
narrowband 46 GHz LO link. RF-IF mixer technology has progressed to the point where
it can be assumed that the range of the resulting RF output powers from the mixed outputs
of the IF and LO links will be essentially that of the IF link. Thus, the T/R-level data
mixing architecture enables 52-58 GHz link performance to approach that of present-day 612 GHz links.
It should be mentioned also that the 46 GHz LO link used in this example might just
as well be realized using the narrowband 11.5-12.5 GHz direct modulation link described
in section 4.2.4 in conjunction with an RF-IF mixer that operates using the fourth harmonic
of the input LO.
It is apparent how much flexibility this architecture imparts to a system designer.
However, there are definitely optimal methods for choosing appropriate and viable LO and
IF bands to result in the desired RF signal feed. For instance, to achieve the 52-58 GHz
RF band for the example application, note from Fig. 5.6 that an IF link band of 6-12 GHz
was chosen to mix with a 46 GHz LO. Realizing the RF band using this LO-IF band
combination is more advantageous than using a 1-7 GHz IF link with a 51 GHz LO, a 2-8
GHz IF link with a 50 GHz LO, a 12-18 GHz IF link with a 40 GHz LO, etc. This is
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because accomplishing efficient impedance matching to the electro-optic devices is much
harder across bands like 1-7 and 2-8 GHz (which correspond to 150% and 100%
bandwidths, respectively); conversely, higher bands were not chosen because of their
proximity to or intersection with the modulator’s and/or detector’s roll-off frequencies.
The advantage of the T/R-level data mixing architecture is that it reduces the problem of RF
link performance optimization to the simpler challenge of optimizing of a band of lower IF
frequencies, for which it is easier and less expensive to obtain high-performance electrooptic devices. Therefore it makes little sense to choose IF-LO link frequency combinations
that require IF link optimization across bands as high as 12-18 GHz, for instance.
In short, the choice of the optimal band over which to design the IF link is dictated
by the device limitations, which is why it is interesting to again apply the speculations
about future devices set forth in earlier sections of this chapter.
5.4.2
Predictions Made Using Estimated Characteristics of Future Electro-optic
Devices
Also plotted as a function of frequency in Fig. 5.6 is the expected spurious-free
dynamic range of an external modulation CPU-level data-mixing link comprised of the
future multiquantum-well semiconductor laser, velocity-matched LiNb0 3 modulator, and
traveling-wave p-i-n photodetector postulated in sections 5.1 and 5.2. Note that at the high
center frequency selected for the example in section 5.4.1 the expected dynamic range of a
future link using straightforward CPU-level mixing is not much lower than it is at more
moderate microwave frequencies.
From this observation two important conclusions can be drawn: first, that future
device developments are likely to increase the crossover frequency above which simple
CPU-level data mixing is abandoned for the better-performing but more complicated T/Rlevel mixing approach, and; second, that present-day use of the T/R-level data mixing can
impart fiber-optic link performance on the scale of what will otherwise be achieved after the
introduction of next-generation electro-optic devices.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 5.6 suggests that T/R-level data mixing currently serves as a means of
achieving optimum external modulation fiber-optic link performance at RF frequencies
above 20 GHz or so. In the future, however, it appears that the incremental performance
improvement will not warrant the use of this more complicated architecture unless the
highest RF frequency is at least 60 GHz or so. This architecture may still benefit the
designers of missile guidance systems, for example, at frequencies like 94 GHz. In such a
case, the same concerns and trade-offs discussed in the previous section will apply when
choosing the frequency band over which to design the IF link.
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240
CHAPTER 6
SUMMARY AND CONCLUSIONS
Fiber-optics will improve the performance of present and future phased arrays
operating at microwave and millimeter wave frequencies. This thesis has identified
microwave/millimeter-wave fiber-optic link development as the crucial first step toward that
goal, has outlined the procedures for predicting and optimizing link performance, and has
reported the measured performance of several links designed using these procedures. The
measured performance of the experimental links closely matched the performance that had
been predicted using the analytical model set forth in the thesis, and thus verified the
model’s usefulness.
Given the characteristics of current state-of-the-art electro-optic devices, the models
enable a link designer to select the optimum architecture with which performance
specifications can be met. The effects of projected improvements in electro-optic device
technology upon link performance have been calculated to show how they can result in
revised conclusions regarding the relative merits of the various architectures. A specific
example was addressed to illustrate this turnabout
Throughout this thesis, opportunities for future work promising the largest payoffs
have been identified. The most beneficial work that could be performed to round out the
link model would probably also entail the greatest amount of theoretical rigor: enhancing
the model to include the effect of optical reflections upon the performance of devices such
as semiconductor lasers and electro-optic modulators.
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Another desired enhancement to this work would be to perform active matching in a
wideband p-i-n photodiode-based optical receiver, as outlined in Chapter 2, in order to
improve the device’s gain-bandwidth product
As optical amplifiers and other active optical components that increase the
functionality of fiber-optic links continue to be developed, the model should also be
expanded to accommodate their use.
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LIST OF REFERENCES
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242
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APPENDICES
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251
APPENDIX A
DETERMINATION O F ELECTRO -O PTIC DEVICE
EQUIVALENT C IR CU IT MODELS
This appendix contains the details of how the equivalent circuit models for the
electro-optic devices used in the six experimental links were derived. Shown in Fig. A.1 is
a schematic diagram of the technique for measuring the one-port scattering parameter S n '
of an electro-optic device in a microwave test fixture. The two-port circuit parameters of
the microstrip line, microstrip-to-connector transition, and connector are embedded within
the measured one-port S-parameter S n ’ of the device in the fixture. The two-port circuit
parameters of each of these elements must therefore be determined and subsequently de­
embedded from the measured scattering parameter values in order to recover S n , the true
scattering parameter of the device.
To attain an accurate model of the connector and microstrip line requires two
additional measurements. These are shown schematically in Fig. A.2. Connectors are
placed at both ends of a 50 Cl microstrip line of "through" length 1=1t and the two-port Sparameters [Syj] are measured. Then connectors A and B are placed at the ends of a
second line of "delay" length 1= 1d , and the S-parameters [SijD] are measured. Connectors
A and B are represented by their two-port scattering matrices [Ay] and [By], respectively.
Here is where some reasonable assumptions help a great deal in simplifying the
determination of the connector parameters. First, the microstrip lines are assumed to be
lossless and perfectly 50 Cl in characteristic impedance.
Thus, their S n and S 22
parameters are identically zero, and their S 12 and S21 parameters are both equal to e'iP1,
where 1= 1t for the through line and 1= 1d for the delay line measurement Secondly, the
connectors are assumed to be lossless, reciprocal two-port networks [29]. Therefore,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Automatic Network Analyzer
Microstrip
Line
Electro-optic
Device
Under Test
Connector
figure A.1 Technique for measuring the one-port scattering parameter
port electro-optic device in a microwave test fixture.
of a one-
S21 ^ -----------•An
r
f
Connector
s ll
5
*
•
A
I
I
B2,
1
vl 1:*\
V B22
11
1
c
I
■•
► S 21
-•
Bl l l
-•
•
Microstrip
Connector
Line
B
c
a 22
Figure A.2 Schematic diagram of test fixture characterization model.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A i 2=A 2 i and B i 2=B 2 i, and the through and delay measurements together yield six
complex equations with which seven unknowns (A n , A 12, ^ 22 , B 11, B 12, B22, and J3)
need to be detennined:
SiiT = A n + A l2Bl2B22e'J2plr;
1 - A22 B22 e-Pfc
(A-l)
Si2T = S21T=
.A tta n e ig . ;
1 —A 22 B22 e-i2PlT
(A-2)
S22T = B n + A l2Bl2A22e'j2Plr;
1 - A 22 B22 e'j2Ph
(A-3)
S11D = A u + A12B12B22e~j2PlD ;
1 —A22 B22 e-i2P,D
(A-4)
S,2D = S21D----- ;
1 - A22 B 22 e-J2P1t>
(A-5)
S22D = B u + Al2Bl2A 22e'j2PlD.
1 —A22 B22 e-J2PlD
(A-6)
Another assumption has been shown to be valid for most high-quality connectors—that is,
that their through parameters would be roughly equal: Ai 2=Bi 2. This reduces the number
of unknowns to six, so that the equations above suffice. However, they can be further
simplified by assuming that the second- and higher-order reflections are of negligible
magnitude, so that IA22 B22l « l ; thus:
Si i t = A n + A22 B 22 e-J2PlT ;
(A-7)
S 12T = S 21T = A22 e-iP11;
(A-8)
S 22T = B n + A j 2 A 22 e*J2PlT ;
(A-9)
S iid = A n + Aj2 B 22 e-J2PlD ;
(A -10)
Si 2D = S 21D = A22 e-JPfe;
(A -ll)
S 22D = B n + A22 A 22 e'J2PlD ;
(A -12)
From equations (A-8) and (A-11) the solutions for (3 and A 12 are readily derived:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
254
P«
Z S21T —Z S21D
It - I
(A-13)
d
and
Al2 =
(A-14)
V e 'j ^ T + e - i^ D
From equations (A-9) and (A-12) the solutions for A22 and B n are derived:
A a . - l - S a T ~ S22D
A j2 e_j2PlT + e~j2P’D
(A-15)
B 11 = j [ S22T + S22D - Ax2 A22 (e'J2PlT + e-j2P1o)].
(A-16)
and
Solutions for A n and B22 are derived from equations (A-7) and (A-10):
B22 = - 1------ 11T.~..S-UDA j2 e-i2?1* + e-J2PlD
(A-17)
A n = 2 f S iit + Siid - A j2 B22 (e-J‘2PlT + e-J2Pio)] .
(A-18)
and
When the electro-optic device is tested using tne set-up shown in Fig. A.1, S n is
embedded in the measures S n ' as follows:
S'n = A n +
S u A^2 e~j2pl
.
(A-19)
1 - A 22 S n e-J2Pi
At each measured frequency, S n is determined by searching for the value that causes the
calculated S n ' to match the measured Sn'Table A.1 shows by example how this procedure was used to characterize the test
fixture that enabled de-embedding of device parameters from the measured one-port
scattering parameters of the devices in the fixture. Tables A.2-A.7 give the measured oneport scattering parameters of the devices in each of the six links, along with the results of
the de-embedding procedure.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
255
rcq .
SU T
SU T
; h i ) M ag. An*. (°) M ag. An*. O
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
10
2.1
0.006
0.008
0.009
0.011
0.012
0.012
0.013
0.012
0.012
0.010
0.008
0.006
0.003
0.000
0.003
0.006
0.010
0.012
0.015
0.017
0.019
14.2
223
24.4
226
18.4
12.8
6.2
-15
-8.7
-16.6
-24.8
-32.9
-40.8
205
118.7
110.6
102.0
93.1
84.2
75.2
66.2
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
-9.4
-18.8
•28.2
-37.7
-47.1
-45.5
-655
-253
-85.7
-94.2
•103.6
-113.0
-12Z4
-131.8
-1415
-150.6
-160.1
-1695
-178.9
171.7
16Z3
M ag.
S11D
S22T
An*. (°) M a*. An*. O
125
20.0
212
205
165
11.1
4.7
-14
-9.9
-17.8
-25.8
-34.0
-41.7
195
117.8
109.7
101.1
913
83.3
745
655
0.006
0.007
0.009
0.010
0.011
0.012
0.012
0.011
0.011
0.009
0.008
0.005
0.003
0.000
0.003
0.006
0.009
0.011
0.013
0.015
0.016
0.006
0.008
0.009
0.010
0.011
0.011
0.011
0.010
0.009
0.006
0.004
0.000
0.003
0.007
0.010
0.014
0.017
0.020
0.022
0.023
0.024
135
205
21.4
185
13.4
6.8
-0.8
-9.0
-17.6
-26.4
-35.1
•34.8
1235
1145
104.8
95.0
855
755
65.3
555
455
M a*.
S22D
S12D
An*. (°) M a*. An*. (°) M a*.
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0.994
0594
0.994
0.994
0.994
0.994
0.994
0.994
0.994
-10.4
•20.8
-315
-41.7
-511
-625
-72.9
-835
-93.7
-1045
-1145
-125.0
-135.4
-145.8
-1565
-166.7
-177.1
1725
1611
151.7
1415
0.006
0.007
0.009
0.010
0.010
0.011
0.010
0509
0.008
0.006
0.003
0.000
0.003
0.006
0.009
0.013
0.015
0.018
0.019
0.021
0.021
115
18.0
195
165
11.6
5.1
-25
-10.3
-18.8
-275
•365
-35.9
1225
113.4
103.9
945
845
74.4
64.4
54.4
44.4
sir
An*. (°)
0.765
0.768
0.773
0.778
0.783
0.783
0.792
0.795
0.798
0.800
0.804
0.809
0.816
0.824
0.832
0.841
0.851
0.857
0.863
0.869
0.872
151.9
124.0
965
685
41.1
-625
-13.7
-41.4
-614
-975
-125.9
-154.4
177.3
149.1
1205
919
665
385
11.3
-16.3
-45.0
S ll
A ll
B22
B ll
A22
beta
AU
F raq.
(GHz) (1/m etcr) M a*. An*. (•) M ag. An*. (°) M ag. An*. (°) M ag. An*. (•) M ag. An*. (•) M ag. An*. (”
0.1
05
0.3
0.4
05
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
15
1.6
1.7
1.8
1.9
2.0
11
4.9
9.8
14.7
195
245
83.4
34.4
395
395
49.1
54.0
585
63.8
68.7
74.1
79.0
83.4
885
935
985
103.6
Table A.1
0597
0.997
0.997
0597
0597
0597
0.997
0597
0597
0.997
0.997
0.997
0.997
0597
0.997
0.997
0.997
0.997
0.997
0.997
0.997
-3.0
-6.0
-9.0
•110
-15.0
-17.9
-20.9
-23.9
•26.9
-29.9
-319
-35.9
-38.9
-41.9
•44.9
-47.9
-50.8
-53.8
-56.8
-59.8
-618
0.003
0.004
0.005
0.006
0.006
0.007
0.008
0.009
0.010
0.011
0.011
0.012
0.012
0.013
0.013
0.013
0.013
0.013
0.013
0.012
0.012
185
318
41.4
465
48.6
495
495
48.8
47.6
46.1
44.3
414
405
38.0
35.7
335
30.8
285
25.7
23.1
20.4
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.012
0.013
0.014
0.014
0.014
0.014
0.015
0.014
0.014
0.014
0.013
206
35.1
43.6
485
50.4
515
51.0
50.1
485
47.3
45.4
43.4
415
39.0
36.6
345
31.7
29.1
265
235
215
0.003
0.004
0.005
0.006
0.006
0.007
0.008
0.009
0.010
0.011
0.011
0.012
0.012
0.013
0.013
0.013
0.013
0.013
0.013
0.012
0.012
185
318
41.4
465
48.6
495
495
48.8
47.6
46.1
445
414
405
38.0
35.7
33.3
30.8
285
25.7
23.1
20.4
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.010
0.011
0.012
0.012
0.013
0.014
0.014
0.014
0.014
0.015
0.014
0.014
0.014
0.013
206
35.1
436
485
50.4
515
51.0
50.1
485
475
45.4
43.4
415
39.0
36.6
345
31.7
29.1
265
235
215
0.773
0.775
0.777
0.780
0.783
0.787
0.792
0.797
0.802
0.808
0.814
0.820
0.827
0.833
0.839
0.845
0.852
0.858
0.863
0.869
0.874
165.0
150.1
135.1
120.2
105.3
90.4
755
606
45.7
30.8
15.9
1.0
-13.9
-28.8
-43.8
-58.8
-73.9
-89.0
-1045
-119.6
-135.0
Example of how the one-port scattering parameter S n of the semiconductor
laser in the narrowband 900 MHz direct modulation link was de-embedded
from the measured scattering parameter S n ' of the device in its test fixture.
(a)
Measured parameters.
(b)
Results of calculations using measured parameters of (a) in equations (A13) through (A-19).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
256
F riq w acjr
(GHz)
0.1
0.2
03
CM
03
03
0.7
03
0.9
1.0
1.1
13
13
M
13
1.6
1.7
13
1.9
2.0
2.1
Table A.2
L m r S ll (M tm n A
Mac. RBse(deg.)
0.774
0.775
0.777
0.780
0.784
0.789
0.794
0300
0306
0312
0319
0325
0331
0337
0343
0349
0354
0359
0364
0368
0372
1653
150.1
135.1
1203
1053
903
75 3
603
45.7
303
15.9
1.0
•13.9
•283
•433
•583
•73.9
•893
•1043
•119.6
•135.0
L aatr S ll (D H a M d id )
Mag. Pbaae(deg.)
0.773
0.775
0.777
0.780
0.783
0.787
0.792
0.797
0302
0308
0314
0320
0327
0333
0339
0345
0352
0358
0363
0369
0374
•1793
•179.6
•1793
•1793
•179.1
-179.0
•1793
-1793
•179.0
•179.1
•1793
•1793
•179.6
•1793
1793
1793
1793
1783
1783
178.1
1773
D etector S ll (M cam red)
Mag. Pbaae(deg.)
0.999
0.998
0.997
0.995
0.993
0.991
0.988
0.985
0.982
0.978
0.975
0.972
0.969
0.966
0.963
0.961
0.959
0.957
0.955
0.953
0.952
-163
•33.0
•493
•66.1
-82.7
-993
-116.0
-132.7
-1493
•1663
1763
160.1
1433
1263
1093
93.1
763
60.0
43.6
273
11.1
D etector S ll (Dc-cmbec
Mag. R a te (deg.)
0.999
0.999
0.998
0.998
0.997
0.996
0.995
0.994
0.993
0.991
0.989
0.988
0.986
0.984
0.981
0.979
0.976
0.974
0.971
0.968
0.965
•13
-2 3
•33
•5.1
•63
•7.6
•8.9
•10.1
•1 U
-12.7
•13.9
•153
•163
-17.7
•19.0
•203
•213
•223
-24.1
•25.6
•26.6
Scattering parameters of the semiconductor laser diode and p-i-n photodiode
in the L-band direct modulation link described in section 4.2.2.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
Fr*qo*acy
«»>
8.00
8.23
8.30
8.7S
9.00
9.25
9X
9.7S
10.00
1035
10X
10.75
11.X
11.25
1130
11.75
12.X
1235
1230
12.75
13.X
1335
1230
13.75
14.X
Table A.3
L a w S ll (M carartd)
Mag. f% ue(deg.)
0431
0440
0444
0.845
0440
0430
0416
0.798
0.782
0.774
0.777
0.791
0411
0431
0448
0461
0469
0172
0471
OJ63
04X
0431
0408
0.789
0.783
9.6
-254
•594
•943
•1294
-166.1
155.1
113.7
694
234
•23.0
•674
-109.7
•1484
175.1
140.7
1074
744
414
7.1
•294
•68.9
•1124
-1594
1504
L w r S ll (D ^cB b^dad)
Mag. Pfaaae<dBg.)
0407
0409
0410
0412
0413
0415
0416
0418
0419
0421
0423
0424
0426
0428
0429
0431
0433
0434
0436
0438
0440
0441
0443
0445
0447
161.1
1X 4
1594
1593
158.7
158.1
1573
1564
1563
155.7
155J
1543
1534
1533
1523
1524
1514
1504
1X 3
1493
1494
1484
147.7
147.1
1463
D etector S ll (M canred)
Mag. P late (<fcg.)
0496
0489
0487
0489
0494
0499
0.902
0.903
0.9X
0492
0479
0459
0434
0409
0.792
0.790
0401
0417
0433
0445
0451
0452
0445
04X
0.804
1554
1X 3
64 3
21.9
•18.1
•554
•91.9
•1273
•1623
1614
1243
84 4
41.0
•6.0
-553
•1044
•1513
1653
1264
90.0
55 3
21 4
-13 0
•46.9
•843
D etector S ll (De-ombedded)
Mag. P late (deg.)
0.917
0.912
0.906
0.90!
0496
0490
0484
0478
0472
0466
04X
0454
0448
0442
0436
0429
0423
0417
0411
0405
0.798
0.792
0.786
0.780
0.775
•583
•603
•623
•644
•663
•68.6
•70.7
-72.9
■75.1
•773
•793
•81.7
•84.0
-863
•883
•90.9
•933
•95.6
-983
•1 X 4
• 1024
•1053
•107.7
-110.1
-112.6
Scattering parameters of the semiconductor laser diode and p-i-n photodiode
in the Ku-band direct modulation link described in section 4.2.3.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
258
F rcqM tey
(GHr)
2.00
225
230
2.75
3.00
3.25
330
3.75
4.00
4.25
430
4.75
5.00
525
5.50
5.75
6J00
625
6$ 0
6.75
7.00
725
750
7.75
8.00
Table A.4
Lm v S ll (M ta m d )
Mag. Pbue(deg.)
0.795
0.790
0.784
0.780
0.778
0.779
0.784
0.792
0.801
0.809
0216
0220
0221
021*
0212
0202
0.791
0.782
0.778
0.780
0.790
0203
0218
0.831
0J4 2
-1302
-1704
1493
1084
673
263
•14.1
-53.7
-922
•129.9
•166.8
1564
1200
82.9
44.7
S.l
-36.1
-78.9
-1224
-1662
151.1
1102
713
342
•1.6
L aser S ll (P i im bedded)
Mag. Phase (deg.)
0.786
0.788
0.789
0.790
0.791
0.793
0.794
0.796
0.798
0200
0201
0204
0206
0208
0210
0212
0215
0217
0220
0222
0225
0227
0230
0232
0235
1664
1654
1633
161.7
160.1
1584
1562
1552
1534
1524
1504
1484
1473
1452
1442
142.7
1412
139.7
1382
1362
1353
1334
1324
1314
1294
D ttod or S ll (M«— rad)
Mag. Fbase(deg.)
0.943
0.937
0.930
0.921
0.908
0290
0268
0242
0215
0.792
0.775
0.764
0.758
0.752
0.744
0.730
0.709
0.678
0.639
0397
0362
0346
0352
0374
0.601
19.7
-21.7
-62.7
-103.7
•1454
1722
1293
842
38.9
-7 3
•53.7
•984
-1424
1763
135.7
9 54
552
13.6
-302
•762
-1263
-177.9
1313
832
392
Detector S ll (Pt-em bedded)
Mag. raae< d rf.)
0.954
0.942
0.929
0.913
0297
0279
0260
0239
0217
0.795
0.772
0.748
0.724
0.701
0.679
0.658
0.638
0.620
0.605
0392
0382
0375
0371
0369
0370
-333
-384
•424
•474
•523
•573
-62.6
-68.0
•733
-793
•854
-914
•984
•104.7
•1114
-1182
-126.1
•1334
•1412
-148.9
-1564
•1642
-1712
-179.1
173.7
Scattering parameters of the semiconductor laser diode and p-i-n photodiode
in the S/C-band direct modulation link described in section 4.2.4.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
259
rn q w a c jr
(GHz)
0.10
0.20
030
0.40
030
030
0.70
030
0.90
1.00
1.10
130
130
130
130
130
1.70
130
1.90
2.00
2.10
T able A.5
M adalilof S ll (M iaasnd)
Mag. Ftoae(deg.)
0.999
0.997
0.994
0.989
0.9S3
0.976
0.969
0.962
0.956
0.951
0.946
0.942
0.939
0.937
0.935
0.933
0.932
0.931
0.929
0.928
0.927
•303
•60.7
•903
•1203
•1493
•177.9
1543
1273
101.1
75 3
50.7
263
2.7
•203
-43.1
•653
•873
•109.1
•130.6
•151.9
•173.1
M odslator S ll (D r embedded)
Mag. Roae(deg.)
0.999
0.999
0.999
0.997
0.993
0.987
0.981
0.973
0.965
0.957
0.949
0.941
0.934
0.927
0.921
0.915
0.910
0.906
0.902
0398
0395
•11.1
•22.1
-323
•43.0
-52.7
•61.7
•703
•773
-843
-90.7
•963
•1013
-106.0
•110.1
-113.9
-1173
-1203
•1233
•125.9
•1283
•1303
D etector S ll (M easured)
Mag. Roae(deg.)
0.999
0.999
0.998
0.996
0.994
0.991
0.988
0.985
0.982
0.979
0.975
0.972
0.969
0.967
0.964
0.962
0.096
0.958
0.957
0.956
0.955
•163
•33.7
•50.6
•673
•843
•1013
•1183
•1353
•1523
•1693
1733
1553
1383
121.7
104.7
87.7
703
54.0
373
203
43
D etector S ll (De-cmbec
Mag. Place (deg.)
0.999
0.999
0.999
0.999
0.998
0.997
0.996
0.995
0.993
0.992
0.990
0.988
0.986
0.984
0.981
0.979
0.976
0.974
0.971
0.968
0.965
•1.6
•3 3
•4.9
•6 3
•8.1
•9.7
•113
•13.0
•143
•163
-173
•193
•21.0
•22.6
•243
•25.9
•273
-29.1
-30.7
•323
•33.9
Scattering parameters of the Iumped-element electro-optic modulator and pi-n photodiode in the L-band external modulation link described in section
4.3.2.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
260
Fw qw xy
(GHz)
25.00
25JO
2640
26J0
27.00
27JO
28.00
28JO
29.00
29JO
30.00
30J0
31.00
31 JO
3240
32J0
33.00
33JO
34.00
34JO
3540
Table A.6
M odulator S ll (M i— rid )
M is. Flw e(dBS)
0445
0450
0455
0459
0463
0466
0468
0.270
0470
0470
0470
0469
0467
0464
0462
0459
0455
0452
0448
0445
0441
1704
1514
1314
112.7
93J
74J
55.2
35.9
16J
-2.7
-2 2 J
-414
-613
•81J
-1 01J
-121.9
•142J
-153.1
1754
154J
1324
M odaU tor S ll <D »cabedded)
M if. Fhaae (deg.)
0.153
0.156
0.159
0.171
0.175
0.178
0.180
0.184
0.185
0.189
0.192
0.195
0.199
0401
0404
0408
04 10
0414
0417
0420
0423
1144
114.1
U 3J
1134
1124
1124
112J
111.7
1113
111.1
1103
1104
110.1
109.7
1094
109.1
1094
108.7
1084
1084
1074
D etector S ll (M t— rid )
M if. Pfawe (deg.)
0.750
0.755
0.750
0.746
0.742
0.738
a735
0.732
0.729
0.725
0.723
0.720
0.717
0.714
0.711
0.708
0.705
0.701
0.598
0.595
0J92
-1393
•1714
I5 6 J
124J
924
504
28J
-3 4
•3 5 J
•67.1
•98.9
•130J
•1623
1564
1343
1023
70.7
38.9
7.0
•24.9
•56.9
D etector S ll (P i imbed
M if. R a te (deg)
0.754
0.759
0.754
0.750
0.745
0.741
0.737
0.733
0.729
0.725
0.723
0.719
0.716
0.713
0.710
0.708
0.70S
0.703
0.701
0.699
0.69?
1144
114.1
1134
1134
1124
1124
112.1
111.7
1113
111.1
UOJ
1104
110.1
109.7
1093
109.1
1094
108.7
1084
1084
1074
Scattering parameters of the traveling-wave electro-optic modulator and p-in photodiode in the millimeter-wave external modulation link described in
section 4.3.3.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
261
fn q w a c v
(GHi)
5.00
SJO
6.00
6.50
7.00
7X0
8.00
850
9.00
9.50
10X0
10X0
11X0
11X0
12X0
12X0
13.00
13X0
14X0
14X0
15X0
Table A.7
Modalatoc S it (M iaeurad)
M is. R ase (deg.)
0.046
0.044
0X53
0.057
0.031
0.016
0.055
0X61
0X73
0X92
0X99
0X74
0X40
0.035
0X61
0.109
0.149
0.153
0.127
0.104
0.092
-72.7
•95X
•111.7
•151.4
159.1
-87.1
•U SX
-173X
161.2
129X
SOX
19.9
-58.1
•151.1
15SX
mx
59 X
8.1
-37X
-78.9
-134X
M odoUtor S ll (De-«aibaddsd)
Mag. R use (deg.)
0X30
0X21
0X26
0X38
0X44
0X37
0X25
0X21
0X32
0X44
0X44
0X32
0X21
0X25
0X39
0X47
0X40
0X25
0X21
0X33
0X47
176X
177X
179.1
178.9
176.9
174.9
175X
177X
178X
176X
174X
173.2
174.5
176.7
176X
174X
I72X
172X
174X
176.1
174.7
Detector S ll (M«—a n d )
Mag. R ose (dag.)
0.941
0.929
0.914
0X99
0X82
0X63
0X44
0X23
0X02
0.780
0.758
0.737
0.718
0.700
0X84
0X70
0X59
0X51
0X45
0.641
0.639
90.9
63.6
36.1
8X
•19.4
•47X
-76.1
•105.0
•134.1
•163X
166X
136X
106.1
75X
44.9
14.1
•I6X
•47X
-77X
•108.1
•138X
D etector S ll (De-oabec
Mag. R ose (dbg.)
0.940
0.927
0.913
0X97
0X80
0X62
0X43
0X23
0X03
0.782
0.762
0.742
0.723
0.705
0X88
0X74
0X62
0X53
0X46
0X41
0X39
-43.9
•48X
•54.0
•59X
•64X
•70X
•76.4
-82X
•88.9
•95X
-102X
-109.4
•116.7
-124.2
-131X
•139X
•147X
•155.1
•162X
•170.4
•177X
Scattering parameters of the traveling-wave electro-optic modulator and p-in photodiode in the wideband (6-12 GHz) external modulation link
described in section 4.3.4.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
262
APPENDIX B
DETERMINATION O F ELECTRO -O PTIC DEVICE
FREQUENCY RESPONSES
This appendix describes how the frequency responses of the semiconductor lasers
and p-i-n photodiodes used in the experimental links of Chapter 4 were measured to enable
determination of (Or, y, and f3dB.
The HP Lightwave Signal Analyzer allows direct measurement of the frequency
response of an electronic-to-photonic transducer (directly-modulated semiconductor laser or
externally-modulated laser) or a photonic-to-electronic transducer (photodetector). The
experimental set-ups for performing these two measurements are shown in Fig. B.l (a) and
(b), respectively.
In the semiconductor laser frequency response measurement set-up, the analyzer
feeds a range of RF frequencies between 130 MHz and 20 GHz into a test fixture
consisting of a fiber-pigtailed semiconductor laser attached to a 50 £2 transmission via a
bondwire. It is important that the laser’s equivalent circuit model be already determined
using the technique described in Appendix A. The RF-modulated optical signal in the
optical fiber is fed directly into the analyzer, where it is detected by an MSM photodetector
whose frequency response and parasitic circuit response have been calibrated into the
analyzer’s computer software. The analyzer automatically adjusts the detected RF
photocurrent using the correction factors that have been programmed into its measurement
routine, so that the data it displays represents the ratio of the RF modulation power on the
optical output of the laser to the RF input current to the device at electrical port 1. This ratio
has units of dB (W/A)2.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
263
The measured laser response (called ‘E-O* by the analyzer screen) depends upon
the known values of the laser’s junction resistance Rjl >junction capacitance C jl , parasitic
contact resistance R p l , parasitic bondwire inductance L p l , and upon the heretofore
unknown relaxation oscillation frequency and damping rate as follows:
E-O (in dB [W/A]2) = 10 log
ISzipI2|i - rj2tiglHi]2
(B-l)
|l -S 2 2 I> I lF
where [Sjjp] is the two-port scattering matrix of the circuit consisting of C jl , R p l , and
L pl . The equations for Tl as a function of R jl and IHl I2 as a function of (Or and y were
given in Chapter 3. The E -0 measurement thus enables the laser’s frequency response
IHL(lL,co)l2 to be determined at all RF frequencies and DC bias currents of interest Fitting
the shape of the frequency response as a function of frequency for any bias current to the
expression for IHl (Il »©)I2 [equation (3-23)] yields values of (Or and y for that bias current
For each of the three experimental direct modulation links of Chapter 4, part (a) of Tables
B .l, B.2, and B.3, respectively, gives the E -0 measured at each bias current of interest
Using [Syp] and I I calculated from the equivalent circuit models, the calculated frequency
response IHl (Il ,©)I2 is also given for each bias current followed by the model-fit values
of (Of and y.
In a similar fashion, Fig. B .l (b) shows how the detector’s ‘O-E’ response is
measured. This is related to the device’s frequency response and parasitic circuit response
as follows:
(B-2)
where [Syp] is the two-port scattering matrix of the circuit consisting of Cjd , R p d » and
Lpp. The equations for I' d as a function of Rjd and IHd I2 as a function of f 3<jB were given
in Chapter 3. The O-E measurement thus enables the detector’s frequency response
IHD(<o)l2 to be determined at all RF frequencies of interest Fitting the shape of the
frequency response as a function of frequency to the expression for IHd (g>)I2 [equation (3-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
24)] yields the value of f3<jB- For each of the three experimental direct modulation links of
Chapter 4, part (b) of Tables B .l, B.2, and B.3, respectively, gives the measured O-E
data. For each of the three experimental external modulation links of Chapter 4, Tables
B.4, B.5, and B.6, respectively, give the measured O-E data. Using [Syp] and T o
calculated from the equivalent circuit models, the calculated frequency response IHd (cd)P is
also given, followed by the model-fit value of f3<jB-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
265
HP Lightwave Signal Analyzer
D
jSemiconduto{
i Laser or i
| Laser-Driven*
, External |
i Modulator ■
!_ynderTestJ
RF-modulated
optical out
(a)
HP Lightwave Signal Analyzer
RF-modulated
optical in
RFout
Optical
• Under T e s t1
i___________i
(b)
Figure B.1 Experimental set-up for measuring the microwave frequency responses of
electro-optic devices.
(a) Set-up for measuring the frequency response of a directly-modulated
semiconductor laser.
(b) Set-up for measuring the frequency response of an optical detector.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
266
E -O
r
(GHz)
dB (W/A]2)
0.1
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
-18.5
-27.9
-37.2
-43.7
-48.6
-52.5
-55.8
-58.6
-61.1
-63.3
-65.4
-67.3
-69.0
-70.7
-72.2
-73.7
-75.1
-76.5
-77.7
-79.0
-80.1
Im S22P 1-S22PGLI:
IHLI2
IS21PI2
I1-GLI2
ctaL
(W/A)
R eS22P
0.2424
0.0606
0.0185
0.0086
0.0049
0.0031
0.0022
0.0016
0.0012
0.0010
0.0008
0.0006
0.0005
0.0005
0.0004
0.0003
0.0003
0.0003
0.0002
0.0002
0.0002
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0 .0 0 5 6 0 3 4 2 2
0 .0 0 7 2 0 3 2 2 1
0 .0 0 0 3 0 4 3 4 8
0 .0 0 0 8 1 7 7 1 3
0 .0 0 0 0 7 1 5 4 2
1 .0 0 0 0 4 2 0 3 0
1 .0 0 0 0 8 1 5 0 7
1.000104701
1.000110461
1.0 0 0 1 2 0 3 3 3
1.0 0 0 1 3 6 1 4 3
1.0 0 0 1 4 0 9 2 8
1 .0 0 0 1 4 4 3 1 2
1.0 0 0 1 4 6 6 0 3
1 .0 0 0 1 4 8 3 3
1.0001 4 0 4 0 1
1.0001 5 0 0 3 1
1.00015031
1 .0 0 0 1 5 0 3 0 6
1 .0 0 0 1 5 0 0 6 6
1 .0 0 0 1 4 9 6 3 2
-0 .0 1 2 1 8 5 3 5
-0 .0 1 0 4 0 0 1 2
-0 .0 0 5 5 6 2 1 5
-0 .0 0 3 7 4 6 3
-0 .0 0 2 8 1 6 5 3
-0 .0 0 2 2 5 2 0
-0 .0 0 1 6 7 4 5 4
- 0 .0 0 1 0 0 2 0 0
-0 .0 0 1 3 0 8 4 1
-0 .0 0 1 2 3 8 6 1
-0 .0 0 1 1 1 0 2 2
-0 .0 0 1 0 0 4 7 1
-0 .0 0 0 0 1 6 3 8
- 0 .0 0 0 8 4 1 2 0
- 0 .0 0 0 7 7 6 6 2
-0 .0 0 0 7 2 0 3
-0 .0 0 0 6 7 0 7 7
-0 .0 0 0 6 2 6 8 6
-0 .0 0 0 5 8 7 6 3
-0 .0 0 0 5 5 2 3 5
-0 .0 0 0 5 2 0 4 4
3.1042
3.1924
3.1985
3.1997
3.2001
3.2003
3.2004
3.2005
3.2005
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
0.9887
0.4649
0.1770
0.0859
0.0491
0.0311
0.0211
0.0150
0.0111
0.0084
0.0065
0.0051
0.0040
0.0033
0.0027
0.0022
0.0018
0.0015
0.0013
0.0011
0.0009
R e S llP
I m S llP
1 -S llP G L l:
IHDI2
-0 .0 0 0 4 2 6 9 5
-0 .0 1 0 4 9 0 1 2
- 0 .0 0 5 5 6 2 1 5
-0 .0 0 3 7 4 6 3
-0 .0 0 2 6 1 6 5 3
-0 .0 0 2 2 5 2 8
- 0 .0 0 1 8 7 4 5 4
-0 .0 0 1 6 0 2 9 9
-0 .0 0 1 3 9 6 4 1
-0 .0 0 1 2 3 8 6 1
-0 .0 0 1 1 1 0 2 2
-0 .0 0 1 0 0 4 7 1
-0 .0 0 0 9 1 6 3 8
- 0 .0 0 0 8 4 1 2 9
-0 .0 0 0 7 7 6 6 2
-0 .0 0 0 7 2 0 3
- 0 .0 0 0 6 7 0 7 7
-0 .0 0 0 6 2 6 8 6
-0 .0 0 0 5 8 7 6 3
-0 .0 0 0 5 5 2 3 S
- 0 .0 0 0 5 2 0 4 4
3.0924
3.1924
3.1985
3.1997
3.2001
3.2003
3.2004
3.2005
3.2005
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
3.2006
0.9998
0.9846
0.9412
0.8767
0.8000
0.7191
0.6400
0.5664
0.5000
0.4414
0.3902
0.3459
0.3077
0.2747
0.2462
0.2215
0.2000
0.1813
0.1649
0.1506
0.1379
(a)
r
O-E
(GHz)
dB [A/W])2
0.1
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
-13.1
-18.2
-23.6
-27.2
-30.0
-32.4
-34.5
-36.4
-38.1
-39.7
•41.1
-42.5
-43.8
-45.0
-46.1
-47.2
•48.3
-49.2
-50.2
-51.1
-51.9
IS21PI2
GL
ctaD
(A/W)
0.1864
0.0606
0.0185
0.0086
0.0049
0.0031
0.0022
0.0016
0.0012
0.0010
0.0008
0.0006
0.0005
0.0005
0.0004
0.0003
0.0003
0.0003
0.0002
0.0002
0.0002
-0.8
-0.8
-0.8
-0.8
•0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9 6 1 4 7 6 5 2 1
0 .9 9 7 2 0 3 2 2 1
0 .9 9 9 3 6 4 3 4 8
0 .9 9 9 8 1 7 7 1 3
0 .9 9 9 9 7 1 5 4 2
1 .0 0 0 0 4 2 9 3 9
1.0 0 0 0 6 1 5 9 7
1.000104701
1.000119461
1 .0 0 0 1 2 9 3 3 3
1 .0 0 0 1 3 6 1 4 3
1 .0 0 0 1 4 0 9 2 6
1.0 0 0 1 4 4 3 1 2
1 .0 0 0 1 4 6 6 9 3
1 .0 0 0 1 4 8 3 3
1.000149401
1.000150031
1.0001S031
1 .0 0 0 1 5 0 3 0 6
1 .0 0 0 1 5 0 0 6 6
1 .0 0 0 1 4 9 6 3 2
(b)
Table B .l
Calculation of the frequency responses for the devices in the L-band direct
modulation link described in section 4.2.2: (a) calculation of the
semiconductor laser frequency response from measured E -0 data; (b)
calculation of the p-i-n photodetector response from the measured O-E data.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
267
f
(GHz)
IS21P12
E-O
dB (W/A]2)
-18.3
-18.6
-19.4
-20.4
-21.4
-22.4
-23.4
-24.3
-25.1
-26.0
-26.9
-27.9
-29.1
-30.3
-31.6
-33.0
-34.4
-35.8
-37.3
-38.6
-40.0
0.1
1.0
2.0
3.0
4.0
S.O
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
0.2498
0.2330
0.1935
0.1508
0.1152
0.0883
0.0686
0.0543
0.0437
0.0358
0.0297
0.0250
0.0213
0.0183
0.0159
0.0139
0.0122
0.0108
0.0096
0.0086
0.0078
I1-GLI2
etaL
(W/A)
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
R eS22P
Im S22P 1-S22PGLI:
IHLI2
1.0000
0 .9 6 1 6 6 3 3 4 9
0 .9 7 0 1 7 6 4 9 7
0 .9 6 2 3 6 2 4 1 6
0 .9 6 9 7 7 7 4 3 9
0 .9 9 3 7 6 1 6 9
0 .9 9 6 0 4 6 0 6 7
0 .9 9 7 4 1 3 9 5 1
0 .9 9 6 2 9 1 5 8
0 .9 9 8 8 6 3 8 2 4
0 .9 9 9 2 9 9 7 1 2
0 .9 9 9 6 0 2 0 8 2
0 .9 9 9 8 2 7 9 3
1 .0 0 0 0 0 0 4 9
1 .0 0 0 1 3 4 6 3 6
1 .0 0 0 2 4 1 0 7 7
1 .0 0 0 3 2 6 1 8 6
1 .0 0 0 3 9 5 0 9 7
1 .0 0 0 4 5 1 3 7 5
1 .0 0 0 4 9 7 6 5 2
1 .0 0 0 5 3 5 9 0 2
1 .0 0 0 5 6 7 6 2 8
- 0 .0 0 2 1 1 9 8 6
-0 .0 1 6 6 0 4 2 7
- 0 .0 2 0 0 3 9 1 7
-0 .0 1 8 0 6 7 6 7
- 0 .0 1 5 4 7 3 0 6
- 0 .0 1 3 2 2 8 9 7
- 0 .0 1 1 4 4 1 0 8
- 0 .0 1 0 0 2 5 7
-0 .0 0 6 8 9 2 4 7
-0 .0 0 7 9 7 0 8 5
- 0 .0 0 7 2 0 9 3 9
- 0 .0 0 6 5 7 0 9 5
- 0 .0 0 6 0 2 6 S 5
- 0 .0 0 5 5 6 2 3
-0 .0 0 5 1 5 7 3 1
-0 .0 0 4 6 0 2 2 7
-0 .0 0 4 4 6 6 4 4
- 0 .0 0 4 2 0 8 9 6
- 0 .0 0 3 9 5 6 4 9
-0 .0 0 3 7 3 2 6 2
- 0 .0 0 3 5 2 7 8 7
3.0929
3.1167
3.1509
3.1716
3.1828
3.1892
3.1930
3.1954
3.1971
3.1983
3.1991
3.1997
3.2002
3.2006
3.2009
3.2011
3.2013
3.2015
3.2016
3.2017
3.2018
1.0050
1.0198
1.0440
1.0767
1.1156
1.1570
1.1949
1.2201
1.2218
1.1899
1.1196
1.0148
0.8878
0.7539
0.6264
0.5133
0.4177
0.3392
0.2759
0.2253
R e S llP
I m S llP
1-S llP G L l:
IHDI2
3.0925
3.0829
3.0416
2.9796
3.3876
3.2828
3.2479
3.2319
3.2230
3.2175
3.2138
3.2112
3.2093
3.2079
3.2068
3.2059
3.2052
3.2046
3.2041
3.2037
3.2033
0.9975
0.9901
0.9780
0.9615
0.9412
0.9174
0.8909
0.8621
0.8316
0.8000
0.7678
0.7353
0.7030
0.6711
0.6400
0.6098
0.5806
0.5525
0.5256
0.5000
(a)
r
(GHz)
1S21PI2
O-E
dB [A/W])2
GL
ctaD
(A/W)
0.2055
0.2052
0.2042
0.2027
0.2006
0.1979
0.1947
0.1911
0.1871
0.1828
0.1782
0.1733
0.1683
0.1632
0.1580
0.1528
0.1476
0.1424
0.1373
0.1323
0.1274
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
•0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
•0.8
-0.8
-0.8
-0.8
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.1
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
-12.7
-12.7
-12.7
-12.7
•13.4
-13.4
-13.5
-13.7
-13.9
-14.2
•14.4
-14.7
-15.1
-15.4
-15.7
-16.1
-16.4
-16.8
-17.2
-17.6
-17.9
0 .9 6 1 5 2 0 8 7 3
0 .9 5 8 0 4 4 2 2 3
0 .9 4 3 0 5 3 2 7 6
0 .9 1 7 8 3 9 4 7 6
1 .0 6 5 1 4 3 5 1 7
1 .0 2 9 0 8 2 1 9
1 .0 1 6 8 2 9 4 9 7
1 .0 1 1 1 9 2 2 2 4
1 .0 0 8 0 6 4 2 8 9
1 .0 0 6 1 2 2 3 0 2
1 .0 0 4 8 2 3 2 4 3
1 .0 0 3 9 0 6 7
1 .0 0 3 2 3 3 5 6 9
1 .0 0 2 7 2 3 4 4 3
1 .0 0 2 3 2 6 9 4 3
1 .0 0 2 0 1 2 2 6 4
1 .0 0 1 7 5 8 1 0 3
1 .0 0 1 5 4 9 7 2 9
1 .0 0 1 3 7 6 6 7
1 .001231311
1 .0 0 1 1 0 7 9 9 4
-0 .0 0 0 2 7 5 8 8
-0 .0 0 3 3 1 2 3 1
- 0 .0 1 2 9 6 6 5 6
-0 .1 0 6 6 1 1 7 1
- 0 .0 3 6 6 1 2 7 8
-0 .0 0 7 9 0 3 8 8
-0 .0 0 3 0 9 4 1 2
-0 .0 0 1 5 8 3 9 7
- 0 .0 0 0 9 3 6 6 7
- 0 .0 0 0 6 0 8 3
- 0 .0 0 0 4 1 7 7
- 0 .0 0 0 3 0 1 2 5
-0 .0 0 0 2 2 5 0 4
- 0 .0 0 0 1 7 2 8 9
-0 .0 0 0 1 3 5 B 9
-0 .0 0 0 1 0 8 8 6
-8 .8 6 2 6 E -0 S
-7 .3 1 6 1 E -0 5
- 6 .1 1 2 4 E -0 5
-5 .1 6 1 1 E -0 S
-4 .3 9 B 8 E -0 S
1.0000
(b)
Table B.2
Calculation of the frequency responses for the devices in the Ku-band direct
modulation link described in section 4.2.3: (a) calculation of the
semiconductor laser frequency response from measured E -0 data; (b)
calculation of the p-i-n photodetector response from the measured O-E data.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
268
E -O
r
(GHz)
dB (W/A]2)
0.1
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
-18.3
-18.3
-18.5
•18.8
-19.2
-19.7
-20.1
-20.7
-21.3
-22.0
-22.8
-23.8
-24.9
•26.1
-27 J
-29.0
-30.5
-32.0
-33.5
-35.0
-36.4
Im S22P 1-S22PGLI:
IHLI2
IS21PI2
I1-GLI2
ctaL
(W/A)
R cS22P
0.2500
0.2453
0.2321
0.2128
0.1902
0.1667
0.1442
0.1237
0.1056
0.0900
0.0767
0.0654
0.0558
0.0478
0.0410
0.0353
0.0305
0.0265
0.0230
0.0201
0.0175
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0 .8 6 1 5 8 5 3 2 3
0 .9 6 4 5 5 2 8 3 7
0 .9 7 1 5 8 0 0 4 8
0 .9 7 9 2 5 4 1 5 3
0 .9 8 5 7 1 0 8 8 5
0 .9 9 0 5 8 7 6 6 4
0 .9 9 4 1 2 4 7 9 1
0 .9 9 6 6 6 2 2 8 4
0 .9 9 8 4 8 3 8 9 3
0 .9 9 9 7 9 6 5 7
1 .0 0 0 7 4 5 1 0 7
1 .0 0 1 4 3 0 1 0 1
1 .0 0 1 9 2 1 9 7 7
1.0 0 2 2 7 0 7 0 1
1 .0 0 2 5 1 2 2 8 6
1.0 0 2 6 7 3 0 8 2
1 .0 0 2 7 7 2 6 4 8
1 .0 0 2 8 2 5 6 8 6
1 .0 0 2 8 4 3 3 6 5
1 .0 0 2 8 3 4 2 4 7
1 .0 0 2 8 0 4 9 4
- 0 .0 0 1 2 0 6 9 7
-0 .0 1 1 2 6 9 5 2
- 0 .0 1 8 7 4 4 7 8
- 0 .0 2 1 8 8 5 2 7
- 0 .0 2 2 1 5 4 3 9
-0 .0 2 1 0 0 3 8 2
- 0 .0 1 9 3 0 5 8 7
-0 .0 1 7 4 9 0 0 4
- 0 .0 1 5 7 4 4 3 9
-0 .0 1 4 1 4 0 6 1
-0 .0 1 2 6 9 7 6 6
- 0 .0 1 1 4 1 1 8 7
- 0 .0 1 0 2 7 0 7 8
- 0 .0 0 9 2 5 9 3 2
-0 .0 0 8 3 6 2 5
- 0 .0 0 7 5 6 6 4 8
-0 .0 0 6 8 5 8 8 9
- 0 .0 0 6 2 2 8 6 7
- 0 .0 0 5 6 6 6 9 6
-0 .0 0 5 1 6 4 9 1
- 0 .0 0 4 7 1 5 5 6
3.0927
3.1010
3.1207
3.1422
3.1603
3.1740
3.1839
3.1910
3.1961
3.1997
3.2024
3.2043
3.2057
3.2067
3.2073
3.2078
3.2081
3.2082
3.2082
3.2082
3.2081
1.0000
1.0050
1.0198
1.0440
1.0767
1.1156
1.1570
1.1949
1.2201
1.2218
1.1899
1.1196
1.0148
0.8878
0.7539
0.6264
0.5133
0.4177
0.3392
0.2759
0.2253
R e S llP
I m S llP
1-SU PG L l:
IHDI2
3.1300
3.1031
3.1690
3.3342
3.2809
3.2634
3.2554
3.2509
3.2482
3.2464
3.2451
3.2442
3.2435
3.2430
3.2426
3.2422
3.2420
3.2417
3.2415
3.2414
3.2412
1.0000
0.9956
0.9825
0.9615
0.9336
0.9000
0.8621
0.8212
0.7785
0.7353
0.6923
0.6503
0.6098
0.5711
0.5344
0.5000
0.4678
0.4377
0.4098
0.3840
0.3600
(a)
f
(GHz)
IS21PI2
O-E
dB [A/W])2
0.1
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
-13.0
-13.0
-13.2
-13.6
-13.9
-14.2
-14.7
-15.1
-15.7
-16.2
-16.8
-17.4
-18.1
-18.7
-19.3
-19.9
-20.6
-21.2
-21.8
-22.4
-23.0
0.1951
0.1939
0.1904
0.1847
0.1774
0.1688
0.1594
0.1495
0.1395
0.1297
0.1202
0.1112
0.1028
0.0950
0.0878
0.0812
0.0752
0.0697
0.0646
0.0600
0.0559
GL
ctaD
(A/W)
•0.8
-0.8
•0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0 .9 6 1 4 7 3 8 6 6
0 .9 5 1 9 3 0 5 5 9
0 .9 7 1 3 8 7 2 3 2
1 .0 3 2 4 4 5 2 5 3
1.0141 4 2 4 5 1
1 .0 0 8 1 2 1 2 1 4
1.0 0 S 3 3 4 1 96
1 .0 0 3 7 9 3 6 4 2
1 .0 0 2 8 4 5 0 6 6
1 .0 0 2 2 1 6 7 3
1 .0 0 1 7 7 7 8 4 2
1 .0 0 1 4 5 8 6 2 8
1 .0 0 1 2 1 8 9 1 6
1.0 0 1 0 3 4 1 7 5
1 .0 0 0 8 8 8 7 0 3
1.0 0 0 7 7 2 0 5 6
1 .0 0 0 6 7 7 0 5 9
1.0 0 0 5 9 8 6 4 6
1 .0 0 0 5 3 3 1 5 7
1 .0 0 0 4 7 7 8 9
1 .0 0 0 4 3 0 8 1 8
-0 .0 0 0 5 4 5 9 3
-0 .0 0 6 8 7 7 4 2
-0 .1 3 0 4 9 6 7 1
- 0 .0 1 2 3 9 1 1 3
- 0 .0 0 2 9 0 5 9 9
-0 .0 0 1 1 8 0 5 7
-0 .0 0 0 6 0 7 9 8
-0 .0 0 0 3 S 7 8 6
-0 .0 0 0 2 2 9 7
-0 .0 0 0 1 5 6 7 4
-0 .0 0 0 1 1 1 9 5
-8 .2 6 6 1 E -0 5
-6 .3 1 0 S E -0 5
-4 .9 2 E -0 5
-3 .9 1 2 E -0 5
-3 .1 6 2 9 E -0 5
-2 .5 9 4 3 E -0 5
-2 .1 5 4 7 E -0 5
-1 .B 0 9 5 E -0 5
-1 .5 3 4 4 E -0 5
-1 .3 1 2 6 E -0 5
(b)
Table B.3
Calculation of the frequency responses for the devices in the S/C-band
direct modulation link described in section 4.2.4: (a) calculation of the
semiconductor laser frequency response from measured E -0 data; (b)
calculation of the p-i-n photodetector response from the measured O-E data.
R eproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
269
O-E
(dB (A/W])2
O-E
(A/WJ2
IS21PI2
GL
cu D
(A/W)
R e S llP
Im S llP
I1-SUPGLI2
IHDI2
-13.9
-13.8
•14.4
-14.5
-14.8
-15.1
-15.5
•16.0
•16.5
-17.0
-17.6
-18.2
-18.8
-19.3
-19.9
-205
-21.1
-21.7
-22.3
-22.9
-235
0.0408
0.0414
0.0364
0.0356
0.0335
0.0309
0.0281
0.0252
0.0224
0.0198
0.0174
0.0153
0.0133
0.0116
0.0101
0.0088
0.0077
0.0067
0.0059
0.0051
0.0045
0.1577
0.1566
0.1533
0.1480
0.1413
0.1335
0.1250
0.1163
0.1077
0.0993
0.0914
0.0839
0.0771
0.0708
0.06S1
0.0599
0.0552
0.0509
0.0470
0.0435
0.0404
-O.S
•0.8
-0.8
-0.8
-0.8
•0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
•0.8
-0.8
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.86139001
0.83S23735
1.04463921
1.01266434
1.00627722
1.00380568
1.00256895
1.00185603
1.00140584
1.00110271
1.000888S6
1.00073155
1.00061292
1.00052108
1.00044849
1.00039013
1.00034248
1.00030308
1.00027012
1.00024227
1.00021852
-0.00054S4
-0.0169566
-0.0150169
-0.00171
-0.000558
*0.0002561
-0.00014
-8.525E-0S
-5.589E-05
-3.S68E-05
-2.791 E-OS
-2.081 E-05
-1.593E-05
-1.248E-05
-9.953E-06
-6.069E-06
-6.633E-06
-5.519E-06
-4.642E-06
-3.941 E-06
-3.375E-06
3.1298
3.0564
3.3700
32166
3.2581
32510
32474
32453
32441
32432
32426
3.2421
32418
32415
32413
32411
3.2410
3.2409
32408
3.2407
3.2406
1.0000
0.9969
0.9878
0.9730
0.9529
0.9284
0.9000
0.8686
0.8351
0.8000
0.7642
0.7281
0.6923
0.6572
0.6231
05902
05586
05285
05000
0.4730
0.4475
Table B.4
Calculation of the frequency responses for the p-i-n photodetector in the Lband external modulation link described in section 4.3.2 from measured 0 Edata.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
270
O-E
r
(GH*)
dB (A/W])2
0.1
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
-12.7
-12.7
-12.7
-12.7
-12.6
-13.6
-13.5
-13.6
-13.7
-13.9
-14.1
-14.4
-14.6
-14.9
-15.1
-15.4
-15.7
-16.0
-16.3
-16.6
-16.9
Table B.5
IS21PI2
GL
etaD
(A/W)
0.2093
0.2092
0.2088
0.2083
0.2076
0.2067
0.2055
0.2042
0.2027
0.2010
0.1992
0.1972
0.1950
0.1928
0.1904
0.1879
0.1853
0.1826
0.1798
0.1769
0.1740
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
•0.8
-0.8
-0.8
-0.8
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
R e S llP
0 .9 6 1 5 3 5 9 7 5
0 .9 5 9 7 4 8 9 9 5
0 .9 5 3 2 2 5 9 2 2
0 .9 3 8 7 0 7 5 4 7
0 .6 9 7 1 4 0 2
1 .1 0 6 1 9 5 0 1 5
1.05073B 202
1 .0 2 8 6 4 7 0 5 4
1 .0 1 8 9 1 9 4 2
1.0 1 3 6 3 6 5 0 4
1 .0 1 0 3 6 6 4 3 9
1 .0 0 6 2 1 6 6 6 3
1.0 0 6 6 8 6 6 8 6
1.0 0 5 5 6 2 6 4 3
1.004706671
1 .0 0 4 0 3 9 0 0 8
1 .0 0 3 5 0 7 1 3 6
1 .0 0 3 0 7 5 9 2 2
1 .0 0 2 7 2 1 0 6 3
1 .0 0 2 4 2 5 2 6 7
1 .0 0 2 1 7 5 9 3 7
I m S llP
-0 .0 0 0 1 5 9 5 8
-0 .0 0 1 7 5 4 1 8
-0 .0 0 4 8 1 2 2 2
-0 .0 1 3 9 6 5 3 1
-0 .0 7 5 9 7 2 1
-0 .1 0 4 0 6 4 1 7
-0 .0 1 6 9 S 2 5 1
-0 .0 0 6 0 4 9 0 6
-0 .0 0 2 9 6 6 4 6
-0 .0 0 1 7 3 9 6 5
-0 .0 0 1 1 1 9 6
-0 .0 0 0 7 7 0 7 5
-0 .0 0 0 5 5 6 7 2
-0 .0 0 0 4 1 7 0 6
-0 .0 0 0 3 2 1 5 2
- 0 .0 0 0 2 5 3 6 7
- 0 .0 0 0 2 0 4
-0 .0 0 0 1 6 6 7 3
-0 .0 0 0 1 3 8 1 5
-0 .0 0 0 1 1 5 6 4
-9 .8 1 5 B E -0 5
1-S11PGLI:
1HDI2
3.1302
3.1251
3.1067
3.0604
2.9542
3.5600
3.3880
3.3231
3.2947
3.2794
3.2700
3.2637
3.2593
3.2560
3.2536
3.2516
3.2501
3.2489
3.2478
3.2470
3.2463
1.0000
0.9972
0.9890
0.9757
0.9576
0.9352
0.9093
0.8805
0.8494
0.8167
0.7831
0.7490
0.7149
0.6811
0.6481
0.6160
0.5851
0.5554
0.5270
0.5000
0.4744
Calculation of the frequency responses for the p-i-n photodetector in the
millimeter-wave external modulation link described in section 4.3.3 from
measured O-E data.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
271
r
O-E
(GHz)
dB [A/W])2
0.1
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
-12.8
-12.8
-13.0
-13.2
-14.1
-14.4
-14.8
-15.4
-15.9
-16.5
-17.1
-17.7
-18.3
-18.9
-19.5
-20.0
-20.6
•21.2
-21.7
-22.3
-22.8
Table B.6
1S21PI2
GL
etaD
(A/W)
0.2029
0.2026
0.2016
0.2001
0.1979
0.1952
0.1920
0.1884
0.1843
0.1799
0.1753
0.1704
0.1654
0.1602
0.1550
0.1498
0.1446
0.1394
0.1343
0.1293
0.1244
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
-0.8
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
R e S llP
0 .9 6 1 5 1 8 2 5 3
0 .9 S 7 7 3 2 9 8 8
0 .9 4 0 6 2 1 7 6 7
0 .9 3 4 4 1 7 1 1 2
1 .0 5 7 2 7 1 6 7 4
1.02589B 9S6
1 .0 1 5 2 1 9 2 3 3
1 .0 1 0 2 0 4 2 6 4
1 .0 0 7 3 8 7 7 4
1 .0 0 5 6 2 5 8 7 9
1 .0 0 4 4 4 1 4 0 7
1 .0 0 3 6 0 2 7 6 2
1 .0 0 2 9 8 5 3 0 6
1 .0 0 2 5 1 6 4 6
1 .0 0 2 1 5 1 5 0 5
1 .0 0 1 8 6 1 5 2 3
1.0016 2 7 0 9 1
1 .0 0 1 4 3 4 7 4 3
1 .0 0 1 2 7 4 8 9 4
1 .0 0 1 1 4 0 5 5 9
1 .0 0 1 0 2 6 5 4 3
Ir a S llP
1-S11PGLI:
IHDI2
- 0 .0 0 0 2 7 8 3 3
- 0 .0 0 3 3 9 2 9 6
- 0 .0 1 4 2 4 2 0 2
- 0 .1 4 0 6 4 7 7 3
- 0 .0 2 7 6 7 6 7 6
- 0 .0 0 6 2 5 0 3 8
-0 .0 0 2 5 4 1 9 6
-0 .0 0 1 3 2 5 4
-0 .0 0 0 7 9 1 9 6
-0 .0 0 0 5 1 6
-0 .0 0 0 3 5 7 0 5
- 0 .0 0 0 2 5 8 3 2
-0 .0 0 0 1 9 3 4 2
-0 .0 0 0 1 4 8 6 6
- 0 .0 0 0 1 1 7 1 6
-9 .3 9 6 E -0 5
-7 .6 5 6 2 E -0 5
-6 .3 2 4 6 E -0 5
-5 .2 8 7 3 E -0 5
-4 .4 6 6 6 E -0 5
-3 .8 0 8 S E -0 5
3.1301
3.1194
3.0719
3.0665
3.4075
3.3150
3.2840
3.2695
3.2613
3.2562
3.2528
3.2504
3.2486
3.2473
3.2462
3.2454
3.2447
3.2441
3.2437
3.2433
3.2430
0.9999
0.9878
0.9529
0.9000
0.8351
0.7642
0.6923
0.6231
0.5586
0.5000
0.4475
0.4010
0.3600
0.3240
0.2924
0.2647
0.2404
0.2189
0.2000
0.1833
0.1684
Calculation of the frequency responses for the p-i-n photodetector in the
wideband (6-12 GHz) external modulation link described in section 4.3.4
from measured O-E data.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
272
APPENDIX C
DETERMINATION OF LASER RELATIVE INTENSITY NOISE
This appendix describes how the microwave output noise of the optical sources
used in the experimental links of Chapter 4 were measured to enable determination of
RIN sl« o) [in the case of the semiconductor lasers used in the three direct modulation links]
and RIN ssl (g>) [in the case of the solid-state laser used in the three external modulation
links].
An HP RF Spectrum analyzer is used for measurement of the laser’s noise, as
detected by a well-characterized p-i-n photodetector. Because the noise can be below the
spectrum analyzer’s range of sensitivity it is usually necessary to amplify the RF output
noise of the detector with a broadband LNA before the input of the spectrum analyzer.
The measured noise power depends upon all of the following: the known values of
the detector’s junction resistance Rjd , junction capacitance Cjd , parasitic contact resistance
RpD, parasitic bondwire inductance Lpo, and frequency response IHd I2; the measured DC
photocurrent Id ; the spectrum analyzer resolution bandwidth setting B; the known gain and
noise figure of the LNA (Glna and NFlna . respectively); and the optical source’s relative
intensity noise (the single unknown). The following equation expresses the noise power
fed into the calibrated RF spectrum analyzer
N 0„ = ( l j R I N + 2 q I D)
falp p
„ 1hd P b z 0g 1j ^ f ln a .
[l - S l i p I^J"
(C-l)
where [Syp] is the two-port scattering matrix of the circuit consisting of Cjd, Rpd. and
Lpd- The equations for To as a function of Rjd and IHdI2 as a function of f 3dB were given
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
273
in Chapter 3. The noise output power measurement thus enables the optical source’s
relative intensity noise to be determined at all RF frequencies and bias settings of interest
For the semiconductor laser in each of the three experimental direct modulation
links of Chapter 4, Tables C .l, C.2, and C.3, respectively, gives the RF noise power
measured at each laser bias current of interest Using [Sijp] and To calculated from the
equivalent circuit models along with measured IHd I2, I d . G l n a . NF l n a . and B values, the
calculated value of RIN sl (o ) is then given for each bias current
For the one fiber-pigtailed Nd:YAG solid-state laser used in the three experimental
external modulation links of Chapter 4, Table C.4 gives the measured RF noise power
Again using [Syp] and To calculated from the equivalent circuit models along with
measured IHdI2, Id . G l n a . N F l n a . and B values, the calculated value of RIN S s l C©) is
then given in the table.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
274
f
(G H z)
N o u t/B
(dB m /M H z)
ID
(m A )
GRX
IHDI2
GLNA
(d B )
NFLNA
(d B )
RIN
(d B /H z)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
-70.3
-70.3
-70.3
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
-70.2
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
-141.4
-141.4
-141.4
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
-141.3
Table C .l
Calculation of the relative intentity noise of the semiconductor laser used in
the L-band direct modulation link described in section 4.2.2 from RF noise
power measurements.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
275
f
(G H z)
N o u t/B
(dB m /M H z)
ID
(m A )
GRX
IHDI2
GLNA
(dB )
NFLNA
(d B )
RIN
(dB /H z)
0.1
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
-77.9
-78.6
-78.2
-78.0
-77.6
-77.3
-77.4
-77.0
-77.1
-76.8
-75.7
-75.5
-75.4
-75.3
-74.9
-75.2
-75.9
-76.5
-76.9
-77.9
2.6000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
2.4000
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.9
0.9
0.9
0 .9
0.9
0.9
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
-150.2
-150.2
-149.8
-149.5
-149.1
-148.8
-148.8
-148.4
-148.5
-148.1
-146.9
-146.7
-146.5
-146.4
-146.0
-146.2
-146.9
-147.5
-147.9
-149.0
Table C.2
Calculation of the relative intentity noise of the semiconductor laser used in
the Ku-band direct modulation link described in section 4.2.3 from RF
noise power measurements.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
276
f
(G H z)
N o u t/B
(dB m /M H z)
ID
(mA)
GRX
IHDI2
GLNA
(dB )
NFLNA
(d B )
R IN
(d B /H z)
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
4.25
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
6.50
6.75
7.00
-74.8
-74.2
-73.7
-73.1
-72.6
-72.2
-71.9
-71.7
-71.6
-71.6
-71.5
-71.4
-71.3
-71.1
-71.0
-70.9
-70.9
-71.0
-71.3
-71.7
-73.2
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
2.1000
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
-144.9
-144.3
-143.7
-143.1
-142.6
-142.2
-141.9
-141.7
-141.6
-141.6
-141.5
-141.4
-141.3
-141.1
-140.9
-140.8
-140.8
-140.9
-141.2
-141.6
-143.2
Table C.3
Calculation of the relative intentity noise of the semiconductor laser used in
the S/C-band direct modulation link described in section 4.2.4 from RF
noise power measurements.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
277
f
(G H z)
N o u t/B
(dB m /M H z)
ID
(m A )
GRX
IHDI2
GLNA
(d B )
NFLNA
(d B )
RIN
(d B /H z)
0.10
1.00
2.00
3.00
4.00
S.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
15.00
16.00
17.00
18.00
19.00
20.00
-80.2
-80.2
-80.2
-80.2
-80.2
-80.2
-80.2
-80.2
-80.2
-80.3
-80.3
•80.3
-80.3
-80.4
-80.4
-80.4
-80.5
-80.5
-80.5
-80.6
-80.6
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.4753
0.47S3
0.4753
0.4753
0.4753
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.9
0.9
0.9
0.9
0.9
0.9
0.9
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
17.4
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
2.3
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
-155.5
T able C.4
Calculation of the relative intentity noise of the Nd:YAG laser used as a CW
optical source in the three external modulation links described in Chapter 4
from RF noise power measurements.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
278
APPENDIX D
ANALYTICAL MODEL OF L-BAND (900 MHz) DIRECT
MODULATION LINK
This appendix contains the details of the analytical model for the L-band direct
modulation link described in section 4.2.2 of this thesis.
Figure D .l shows the equivalent circuit model for this link, including the
impedance-matching circuitry and the electro-optic devices. Table D.l lists the parameters
needed for modeling of the link performance as calculated using the model set forth in
Chapter 3. Part (a) of Table D.l lists frequency-independent device parameters; part (b) is
a spreadsheet in which the frequency-dependent link performance calculation was carried
out
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Analytical model of direct modulation fiber-optic link optimized across a narrow bandwidth at
L-band (900 MHz).
(a)
(b)
(c)
(d)
Equivalent circuit of semiconductor laser-based optical transmitter.
Equivalent circuit of p-i-n photodiode-based optical receiver.
Signal flow diagram of semiconductor laser-based optical transmitter.
Signal flow diagram of p-i-n photodiode-based optical receiver.
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(a)
Table D .l
Calculation of the L-band direct modulation link’s performance using the
model rendered in section 3.1 (Fig. 3.1 and Tables 3.1 and 3.2).
(a)
Frequency-independent device parameters necessary for calculation of the
L-band direct modulation link performance.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Rt(YlhL) ImfYlhL)
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•134.1
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•134.4
•134.4
•134.9
•136.1
•138.1
•140.6
•143.2
•146.1
•148.1
•141.4
•141.4
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33.1
33.1
33.2
322
33.2
335
33.4
33.7
34.1
344
33.6
328
324
314
315
315
323
34.0
362
346
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434
SFDR <dI«Mlli)2/3
CDR<dB‘MHt)
315
309
302
296
294
300
314
314
35.6
342
394
(b)
Table D .l
Calculation of the L-band direct modulation link’s performance using the model rendered in section 3.1 (Fig. 3.1 and
Tables 3.1 and 3.2).
(b)
Frequency-dependent device parameters necessary for calculation of the L-band direct modulation link performance.
Parameter values are rendered for frequencies between 500 MHz and 1.5 GHz in 100 MHz steps.
to
00
282
APPENDIX E
ANALYTICAL MODEL OF Ku-BAND (12.0 GHz) DIRECT
MODULATION LINK
This appendix contains the details of the analytical model for the Ku-band direct
modulation link described in section 4.2.3 of this thesis.
Figure E .l shows the equivalent circuit model for this link, including the
impedance-matching circuitry and the electro-optic devices. Table E .l lists the parameters
needed for modeling of the link performance as calculated using the model set forth in
Chapter 3. Part (a) of Table E.1 lists frequency-independent device parameters; part (b) is
a spreadsheet in which the frequency-dependent link performance calculation was carried
out.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Figure E .l
Analytical model of direct modulation fiber-optic link optimized across a narrow bandwidth at
Ku-band (12 GHz).
(a)
(b)
(c)
(d)
Equivalent circuit of semiconductor laser-based optical transmitter.
Equivalent circuit of p-i-n photodiode-based optical receiver.
Signal flow diagram of semiconductor laser-based optical transmitter.
Signal flow diagram of p-i-n photodiode-based optical receiver.
NO
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(a)
Table E .l
Calculation oi the Ku-band direct modulation link’s performance using the
model rendered in section 3.1 (Fig. 3.1 and Tables 3.1 and 3.2).
(a)
Frequency-independent device parameters necessary for calculation of the
Ku-band direct modulation link performance.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
286
APPENDIX F
ANALYTICAL MODEL OF S/C-BAND (3-6 GHz) DIRECT
MODULATION LINK
This appendix contains the details of the analytical model for the S/C-band direct
modulation link described in section 4.2.4 of this thesis.
Figure F .l shows the equivalent circuit model for this link, including the
impedance-matching circuitry and the electro-optic devices. Table F.l lists the parameters
needed for modeling of the link performance as calculated using the model set forth in
Chapter 3. Part (a) of Table F .l lists frequency-independent device parameters; part (b) is
a spreadsheet in which the frequency-dependent link performance calculation was carried
out.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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h-0.005"
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Sim
(c)
Figure F .l
(d)
Analytical model of direct modulation fiber-optic link optimized across a broad bandwidth at
S-C bands (3-6 GHz).
(a)
(b)
(c)
(d)
Equivalent circuit of semiconductor laser-based optical transmitter.
Equivalent circuit of p-i-n photodiode-based optical receiver.
Signal flow diagram of semiconductor laser-based optical transmitter.
Signal flow diagram of p-i-n photodiode-based optical receiver.
to
OO
288
R jl_______________________________________________5.6 Q
50 Q
Zo
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Il =50 mA
I l =70 mA
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T
B
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nL
CtL
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Rl
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45.2 GHz
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82.3 GHz
56.5 GHz
66.0 GHz
88.0 GHz
13 mA
0.66 mA
1.30 mA
2.00 mA
15 GHz
1.38x10*23 J/K
298 K
1 MHz
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3nA
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250 }im
0.3
0.3
0.5 Jim
d
4xl07 A/m2
Jth
Vol
6.3xl0*17 m3
(a)
Table F .l
Calculation of the S/C-band direct modulation link’s performance using the
model rendered in section 3.1 (Fig. 3.1 and Tables 3.1 and 3.2).
(a)
Frequency-independent device parameters necessary for calculation of the
S/C-band direct modulation link performance.
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289
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290
APPENDIX G
ANALYTICAL MODEL OF L-BAND (900 MHz) EXTERNAL
MODULATION LINK
This appendix contains the details of the analytical model for the L-band external
modulation link described in section 4.3.2 of this thesis.
Figure G .l shows the equivalent circuit model for this link, including the
impedance-matching circuitry and the electro-optic devices. Table G.l lists the parameters
needed for modeling of the link performance as calculated using the model set forth in
Chapter 3. Part (a) of Table G .l lists frequency-independent device parameters; part (b) is
a spreadsheet in which the frequency-dependent link performance calculation was carried
out
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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(a)
(b)
(c)
(d)
(d)
Analytical model of external modulation fiber-optic link optimized across a narrow bandwidth
at L-band (900 MHz).
Equivalent circuit of electro-optic modulator-based optical transmitter.
Equivalent circuit of p-i-n photodiode-based optical receiver.
Signal flow diagram of electro-optic modulator-based optical transmitter.
Signal flow diagram of p-i-n photodiode-based optical receiver.
to
VO
292
C m ______________________________________________ 3.1 pF
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v*
ffcJB
kB
T
B
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(a)
Table G .l
Calculation of the L-band external modulation link’s performance using the
model rendered in section 3.2 [Fig. 3.2 and Tables 3.3 (a) and 3.4 (a)].
(a)
Frequency-independent device parameters necessary for calculation of the
L-band external modulation link performance.
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Frequency-dependent device parameters necessary for calculation of the L-band external modulation
performance. Parameter values are rendered for frequencies between 0.5 and 1.5 GHz in 100 MHz steps.
CN
link
293
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
294
APPENDIX H
ANALYTICAL MODEL OF MILLIMETER-WAVE (32.5 GHz)
EXTERNAL MODULATION LINK
This appendix contains the details of the analytical model for the millimeter-wave
external modulation link described in section 4.3.3 of this thesis.
Figure H .l shows the equivalent circuit model for this link, including the
impedance-matching circuitry and the electro-optic devices. Table H.1 lists the parameters
needed for modeling of the link performance as calculated using the model set forth in
Chapter 3. Part (a) of Table H.1 lists frequency-independent device parameters; part (b) is
a spreadsheet in which the frequency-dependent link performance calculation was carried
out
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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(b)
(c)
(d)
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tl-l
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(d)
Equivalent circuit model of millimeter-wave external modulation link optimized across a
narrow bandwidth surrounding a millimeter-wave frequency (32.5 GHz)
Equivalent circuit of electro-optic modulator-based optical transmitter.
Equivalent circuit of p-i-n photodiode-based optical receiver.
Signal flow diagram of electro-optic modulator-based optical transmitter.
Signal flow diagram of p-i-n photodiode-based optical receiver.
N
>
VO
U\
296
Zg_________________________________________________ 50 Q
Zc
43 Q
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lo o m
Rjd
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19 GHz
1.38x10-23 J/K
29$ K
1 MHz
1.6xl0 -19 Coul
q
10 pA
Ijadc
(a)
T able H .l
Calculation of the millimeter-wave (32.5 GHz) external modulation link’s
performance using the model rendered in section 3.2 [Fig. 3.2 and Tables
3.3 (b) and 3.4 (b)].
(a)
Frequency-independent device parameters necessary for calculation of the
millimeter-wave external modulation link performance.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
S 2 1 M S 2 2 M S 2 2 M R c (Z t) lm (Z l)
r
(on/) (Mag.) (Mag.)
(11)
(11)
25.0
25.5
26.0
26.5
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27.5
28.0
28.5
29.0
29.5
30.0
30.5
31.0
31.5
32.0
32.5
33.0
33.5
34.0
34.5
35.0
0.981
0.981
0.981
0.981
0.981
0.981
0.981
0.981
0.980
0.980
0.980
0.979
0.979
0.978
0.977
0.976
0.974
0.972
0.971
0.968
0.966
0.185
0.185
0.185
0.185
0.185
0.185
0.185
0.186
0.187
0.188
0.189
0.192
0.195
0.199
0.203
0.209
0.215
0.222
0.230
0.239
0.248
0.8
-5.3
-11.6
-18.0
-24.7
-31.6
-38.7
-45.9
-53.4
-61.0
-68.8
-76.7
-84.7
•92.8
-100.8
-108.8
-116.7
-124.5
-132.2
-139.7
-147.1
50.034
50.610
51.212
51.829
52.452
53.069
53.666
54.229
54.745
55.199
55.576
55.864
56.052
56.131
56.095
55.941
55.670
55.286
54.797
54.212
53.545
9.069
9.251
9.358
9.387
9.331
9.187
8.953
8.631
8.221
7.731
7.167
6.541
5.866
5.158
4.433
3.711
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2.348
1.743
1.210
0.763
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69.6 1356.5
69.6 1383.1
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69.6 1436.2
69.6 1462.8
69.6 1489.4
69.6 1516.0
69.6 1542.6
69.6 1569.2
69.6 1595.8
69.6 1622.4
69.6 1649.0
69.6 1675.6
69.6 1702.2
69.6 1728.8
69.6 1755.4
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69.6 1835.2
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(Mag.) (Mag.) ^ ( ° )
(dB)
0.750
0.748
0.747
0.744
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0.738
0.734
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0.703
0.695
0.685
0.675
0.665
0.653
0.641
0.629
0.616
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0.109
0.088
0.067
0.047
0.035
0.041
0.061
0.086
0.115
0.145
0.176
0.208
0.241
0.274
0.308
0.341
0.375
0.408
0.440
0.471
0.502
153.5
146.4
135.9
117.5
82.0
38.7
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(11)
(11)
(H)
(11)
28.0
28.2
29.5
31.9
35.5
40.6
46.8
53.9
60.4
64.6
65.3
62.9
58.8
54.7
51.7
50.1
50.3
52.3
56.4
62.2
69.3
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1.4
6.6
11.5
15.9
19.5
21.4
20.9
17.4
11.4
4.5
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0.0
3.1
6.1
8.2
8.3
4.9
6.7
6.5
7.4
9.8
15.7
32.0
89.8
188.6
93.4
46.7
32.0
28.0
29.3
35.2
44.4
50.0
44.6
35.1
28.7
26.8
30.1
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23.2
41.8
68.3
99.3
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4.5
6.7
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3.3
15.4
31.1
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(dD)
SFDR
(dDMIlz)2/3
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41.4
41.2
41.1
41.0
41.1
41.2
41.4
41.7
42.1
42.5
42.9
43.5
44.0
44.7
45.4
46.1
47.0
47.8
48.7
49.7
50.7
(b)
Table H .l
Calculation of the millimeter-wave external modulation link’s performance using the model rendered in section 3.2 [(Fig.
3.2 and Tables 3.3 (b) and 3.4 (b)].
(b)
Frequency-dependent device parameters necessary for calculation of the millimeter-wave external modulation link
performance. Parameter values are rendered for frequencies between 25 and 35 GHz in 500 MHz steps.
298
APPENDIX I
ANALYTICAL MODEL OF WIDEBAND MICROWAVE
(6-12 GHz) EXTERNAL MODULATION LINK
This appendix contains the details of the analytical model for the wideband
microwave external modulation link described in section 4.3.4 of this thesis.
Figure 1.1 shows the equivalent circuit model for this link, including the
impedance-matching circuitry and the electro-optic devices. Table 1.1 lists the parameters
needed for modeling of the link performance as calculated using the model set forth in
Chapter 3. Part (a) of Table LI lists frequency-independent device parameters; part (b) is a
spreadsheet in which the frequency-dependent link performance calculation was carried
out.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Equivalent circuit model of external modulation link optimized across a wide microwave
bandwidth (6-12 GHz)
Figure 1.1
(a)
(b)
(c)
(d)
Equivalent circuit of electro-optic modulator-based optical transmitter.
Equivalent circuit of p-i-n photodiode-based optical receiver.
Signal flow diagram of electro-optic modulator-based optical transmitter.
Signal flow diagram of p-i-n photodiode-based optical receiver.
io
vo
vo
300
Zg________________________________________
50 fl
Zc
2 5Q
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IMG
lD(Vb=0)=L.MLFKFDTlDPsSiy2
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no
2.2
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0.85
Teo
Ge
X
N
7.6 |xm
1.3 [im
2
0.8 mm
Z0
B
10.5 mm
14.6 mm
5.6 V
9.0 GHz
1.38X10’23 J/K
298 K
1 MHz
q
1.6X10' 19 Coul
zi
Z2
V*
ffcffi
ks
T
10 |lA
Idadc
(a)
Table 1.1
Calculation of the wideband (6-12 GHz) microwave external modulation
link’s performance using the model rendered in section 3.2 [Fig. 3.2 and
Tables 3.3 (b) and 3.4 (b)].
(a)
Frequency-independent device parameters necessary for calculation of the
wideband microwave external modulation link performance.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S2IM S22M S22M
f
(C.Hz) (Mag.) (Mag.) Z (° )
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
14.5
15.0
0.951
0.957
0.957
0.951
0.943
0.935
0.933
0.935
0.942
0.950
0.955
0.954
0.948
0.939
0.933
0.931
0.936
0.945
0.953
0.956
0.952
0.297
0.278
0.279
0.298
0.324
0.344
0.351
0.344
0.324
0.301
0.285
0.288
0.308
0.333
0.351
0.354
0.341
0.317
0.292
0.282
0.296
178.3
-179.0
-174.8
-172.4
-173.3
-176.9
178.3
173.7
170.5
170.1
172.9
177.1
179.2
178.0
174.2
169.5
165.2
163.0
164.3
168.9
173.4
Re(Zt)
(ft)
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
28.128
Im(Zt)
(ft)
1.704
1.875
2.045
2.216
2.386
2.556
2.727
2.897
3.068
3.238
3.409
3.579
3.749
3.920
4.090
4.261
4.431
4.602
4.772
4.943
5.113
S21D SUD SUD
(Mag.) (Mag.)
0.897
0.893
0.888
0.882
0.874
0.864
0.851
0.834
0.813
0.788
0.757
0.723
0.685
0.645
0.603
0.560
0.519
0.478
0.440
0.404
0.371
0.053
0.041
0.041
0.060
0.094
0.137
0.187
0.243
0.304
0.367
0.432
0.496
0.558
0.616
0.670
0.717
0.759
0.795
0.826
0.853
0.875
-81.5
-66.3
-34.5
-9.4
-0.6
0.2
-2.4
-6.9
-12.4
-18.4
-24.8
-31.4
-37.9
-44.4
-50.6
-56.6
-62.3
-67.6
-72.6
-77.2
-81.5
G Re(ZthM)
(dB)
(ft)
-31.8
-31.8
-31.8
-31.8
-31.8
-31.5
-31.1
-30.8
-30.7
-30.8
-31.1
-31.7
-32.6
-34.2
-36.2
-38.3
-40.3
-42.1
-44.0
-46.1
-48.4
51.2
49.4
47.8
45.1
47.1
50.1
46.2
42.7
43.5
44.0
50.7
57.4
52.0
47.0
44.6
45.3
56.1
67.7
60.4
50.9
43.6
ImlZthM)
(ft)
-4.5
-4.4
-4.8
-2.5
1.1
-1.6
-3.7
-0.6
2.1
6.3
9.9
2.9
-3.5
-1.6
2.1
9.3
14.7
3.0
-9.6
-10.5
-5.8
Re|ZthD)
(ft)
2.9
7.5
36.4
1132.0
38.8
13.5
8.2
6.5
6.2
6.8
8.8
13.5
25.9
65.7
116.8
55.4
25.6
15.7
11.8
10.6
11.2
Im(ZthD)
(ft)
65.7
109.7
235.6
-502.0
-199.1
-99.1
-60.1
-37.5
-21.3
-7.5
5.9
20.9
39.9
56.9
-7.8
-46.5
-28.5
-11.2
3.5
17.7
33.7
NF
(dB)
SFDR
Re(ZJQR)
44.7
44.7
44.8
45.0
45.2
45.3
45.3
45.4
45.7
46.1
46.5
46.6
46.8
47.3
48.0
48.7
49.3
49.8
50.5
51.4
52.6
(b)
Table 1.1
Calculation of the wideband (6-12 GHz) external modulation link’s performance using the model rendered in
section 3.2 [(Fig. 3.2 and Tables 3.3 (b) and 3.4 (b)[.
(b)
Frequency-dependent device parameters necessary for calculation of the wideband external modulation link
performance. Parameter values are rendered for frequencies between 5 and 15 GHz in 500 MHz steps.
302
APPENDIX J
LIST O F SYMBOLS
ai
argument of Bessel functions; normalized RF signal amplitude at
frequency ©, (unitless)
agD
normalized incident traveling wave intensity from source of two-port
network comprised of Cjd , Rp d , Lp d , and impedance matching circuit in
p-i-n detector-based optical receiver (mW1^ )
a gL
normalized incident traveling wave intensity from source of two-port
network comprised of impedance matching circuit in semiconductor
laser-based optical transmitter (mW1/2)
a gM
normalized incident traveling wave intensity from source of two-port
network comprised of impedance matching circuit in electro-optic
modulator-based optical transmitter (mW1/2)
am
normalized incident traveling wave intensity at load of two-port network
comprised of Cjd »R pd . Lp d , and impedance matching circuit in p-i-n
detector-based optical receiver (mW1^ )
aiL
normalized incident traveling wave intensity at load of two-port network
comprised of Cs, Rs» Rp l , L p l > and impedance matching circuit in
semiconductor laser-based optical receiver (mW1^2)
aiM
normalized incident traveling wave intensity at load of two-port network
comprised of Rp m » Lp m , and impedance matching circuit in external
modulator-based optical transmitter (mW1/2)
A
rate of phase change with respect to voltage in electro-optic modulator
(V -l)
b
term defined by Su et al. [92] for calculation of directly modulated
semiconductor laser noise behavior (m 3-s_1)
bgD
normalized incident traveling wave intensity from source of two-port
network comprised of Cjd , Rpd . Lpd , and impedance matching circuit in
p-i-n detector-based optical receiver (mW1/2)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
303
bgL
normalized traveling wave intensity launched into the semiconductor
laser-based optical transmitter from the generator (mW 'C)
bgM
normalized traveling wave intensity launched into the external
modulator-based optical transmitter from the generator (mW1^ )
biD
normalized reflected traveling wave intensity from load of two-port
network comprised of Cjd , Rp d , Lp d , and impedance matching circuit in
p-i-n detector-based optical receiver (mW*/2)
b iL
normalized reflected traveling wave intensity from load of two-port
network comprised of Cs, Rs, R p l , Lp l , and impedance matching circuit
in semiconductor laser-based optical transmitter (mW1^ )
b iM
normalized reflected traveling wave intensity from load of two-port
network comprised of R p m , L p m , and impedance matching circuit in
external modulator-based optical transmitter (mW1^2)
bR X
normalized traveling wave intensity launched into the load of the p-i-n
detector-based optical receiver (mW1# )
bsL
normalized incident traveling wave intensity from source of two-port
network comprised of Cs, Rs, R p l , L pl , and impedance matching circuit
in semiconductor laser-based optical transmitter (mW1/2)
b SM
normalized incident traveling wave intensity from source of two-port
network comprised of R p m , L p m , and impedance matching circuit in
external modulator-based optical transmitter (mW1/2)
B
instantaneous receiver bandwidth (MHz)
c
speed of light in a vacuum (m-s'1)
Cjd
capacitance of p-i-n photodetector reverse-biased junction (pF)
CS
substrate capacitance of forward-biased semiconductor laser diode (pF)
Cm
capacitance of lumped-element electro-optic modulator electrodes (pF)
CDR
compression-limited dynamic range (dB-MHz)
C D R d ir
compression-limited dynamic range of direct modulation link (dB-MHz)
C D R ext
compression-limited dynamic range of external modulation link
(dB-MHz)
d
thickness of semiconductor laser active region (pm)
f
RF frequency (GHz)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
304
fb
center frequency within operating band of fiber-optic link (GHz)
f3dB
3 dB bandwidth of optical detector (GHz)
fjugh
highest frequency in the band o f frequencies across which reactive
impedance matching is to be attempted (GHz)
fj
tone i (i=l,2) of two-tone intermodulation distortion experiment (GHz)
flF
intermediate frequency mixed with high-frequency local oscillator to
generate RF frequencies f=fLO±fiF (MHz)
fjj0
local oscillator frequency mixed with intermediate-frequency signal to
generate RF frequencies f=fLO±flF (GHz)
fjlC
resonant frequency due to parasitic resistive and capacitive elements in
the equivalent circuit of a device (GHz)
go
differential optical gain coefficient in the semiconductor laser active
region (n r3)
G
RF insertion gain (dB)
Gc
Fabry-Perot semiconductor laser amplifier signal gain (dB)
Gdir
RF insertion gain of direct modulation link (dB)
Gs
gap between coplanar electrodes of electro-optic modulator (mm)
Gext
RF insertion gain of external modulation link (dB)
Gr x
RF insertion gain of p-i-n detector-based optical receiver (dB)
Gs
single-pass gain of laser active medium (unitless)
GTX.dir
RF insertion gain of semiconductor laser-based optical transmitter (dB)
G tx ext
RF insertion gain of electro-optic modulator-based optical transmitter
(dB)
h
Planck's constant (6.626 x 10' 34 J-s)
IHdI2
normalized response of optical detector at given frequency and DC bias
voltage (dB)
Hdir
normalized direct modulation link current transfer function at given
frequency (dB)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
305
Hext
normalized external modulation link current transfer function at given
frequency (dB)
IHlI2
normalized response of semiconductor laser at given frequency and DC
bias current (dB)
io(coi)
amplitude of RF current at junction o f p-i-n detector at frequency coi
(mA)
i'L(coi)
amplitude of RF current at junction of semiconductor laser at frequency
C0i (mA)
<i2dark>
spectral current density of noise in the optical receiver o f a fiber-optic
link due to p-i-n photodetector dark current (A^Hz*1)
<i 2RIN>
spectral current density of noise in the optical receiver o f a fiber-optic
link due to laser relative intensity noise (A 2-Hz_1)
<i2RIN,dir>
spectral current density o f noise in the optical receiver o f a direct
modulation fiber-optic link due to semiconductor laser relative intensity
noise (A2 -Hz_1)
<j 2RlN,ext>
spectral current density of noise in the optical receiver o f an external
modulation fiber-optic link due to laser relative intensity noise (A2 -HzJ)
<j 2shot>
spectral current density o f noise in the optical receiver o f a fiber-optic
link due to shot noise at the p-i-n photodetector (A^Hz*1)
<l2shot,dir>
spectral current density of noise in the optical receiver o f a direct
modulation fiber-optic link due to shot noise at the p-i-n photodetector
(A 2 -Hz-1)
<i2shot,ext>
spectral current density of noise in the optical receiver o f an external
modulation fiber-optic link due to shot noise at the p-i-n photodetector
(A 2 -Hz*l)
<*2th,TX,dir> spectral current density o f noise in the optical receiver o f a direct
modulation fiber-optic link due to thermal noise in the optical transmitter
(A 2-Hz*l)
Id
DC photocurrent measured at p-i-n photodetector (mA)
Idark
dark current generated by p-i-n detector (mA)
Ik(aj), In(ai) hyberbolic Bessel functions o f the kth and n ^1 kind, with argument a*
(unitless)
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
306
II
semiconductor laser or light-emitting diode forward DC bias current
(mA)
Ith
semiconductor laser threshold current (mA)
IMD/C
ratio o f third-order intermodulation product power to fundamental
frequency signal power (dB)
Jk(a0
ordinary Bessel functions of the k 1*1 kind, with argument ai (unitless)
Jth
threshold current density of the material comprising the active region of
a semiconductor laser (A*cm*2)
kB
Boltzmann's constant (1.381 x 10*23 J K*1)
Kfd
fiber-to-detector optical coupling efficiency (dB)
Klf
semiconductor laser-to-fiber optical coupling efficiency (dB)
L
length of semiconductor laser active region (fim)
Le
length of external modulator electrodes (mm)
Lf
optical loss in fiber, including loss at all connectors and attenuation over
length (dB)
Lm
optical insertion loss of electro-optic modulator (dB)
Lpd
parasitic series inductance of reverse-biased p-i-n photodetector (nH)
L pl
parasitic series inductance of forward-biased semiconductor laser (nH)
L pm
parasitic series inductance of lumped-element electro-optic modulator
electrodes (nH)
mi cp ,dir
modulation index of direct modulation link at the RF input power for
which the link response is compressed by 1 dB (unitless)
micp,ext
modulation index of external modulation link at the RF input power for
which the link response is compressed by 1 dB (unitless)
nidir
modulation index of direct modulation link (unitless)
mext
modulation index of external modulation link (unitless)
mint,dir
modulation index of direct modulation link at the RF input power for
which the link output power at the fundamental and third-order
intermodulation product frequencies are equal (unitless)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
307
mint,ext
modulation index of external modulation link at the RF input power for
which the link output power at the fundamental and third-order
intermodulation product frequencies are equal (unitless)
IMI^
response of semiconductor laser at frequency co=2 jrf and bias current II,
relative to DC response at the same bias (dB)
n
refractive index of an optical medium (unitless)
nL
refractive index of forward-biased semiconductor laser active region
(unitless)
no
effective index of traveling wave in modulator at optical frequencies
(unitless)
N
number of phaser-reversed sections in the electrodes of a re verse-A (J
traveling-wave modulator (unitless)
Ne
inverted population density of electrons in semiconductor laser active
region (m*3)
NF
noise figure (dB)
NFdir
noise figure of direct modulation link (dB)
NFext
noise figure of external modulation link (dB)
No
electron density at which the active region is transparent(n r3)
N 0p,dir
all noise in the optical receiver o f a direct modulation link arising from
the electronic-to-photonic and photonic-to-electronic energy conversion
processes (dBm)
^op,ext
nil noise in the optical receiver of an external modulation link arising
from the electronic-to-photonic and photonic-to-electronic energy
conversion processes (dBm)
NoutjtX
total noise power at the output of a p-i-n detector-based optical receiver
(dBm)
Nout,RX,dir
total noise power at output of p-i-n detector-based optical receiver in
direct modulation link (dBm)
Nout,RX,ext total noise power at output of p-i-n detector-based optical receiver in
external modulation link (dBm)
N th,R X
noise power at link output due to thermal noise in the p-i-n detectorbased optical receiver (dBm)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
308
Nth,TX,dir
noise power at output of direct modulation link due to thermal noise in
semiconductor laser-based optical transmitter (dBm)
Nth,TX,ext
noise power at output of external modulation link due to thermal noise
in electo-optic modulator-based optical transmitter (dBm)
Pin,lCP
RF input power at which link response is compressed by 1 dB (dBm)
Pin,lCP,dir
RF input power at which direct modulation link response is compressed
by 1 dB (dBm)
Pin,lCP,ext
RF input power at which external modulation link response is
compressed by 1 dB (dBm)
P in,int
RF input power at which link output power at the fundamental and thirdorder intermodulation product frequencies are equal (dBm)
Pin4nt,dir
RF input power at which direct modulation link output power at the
fundamental and third-order intermodulation product frequencies are
equal (dBm)
Pin,int,ext
RF input power at-which external- modulation 4:-nk output power at the
fundamental and third-order intermodulation product frequencies are
equal (dBm)
Pin,TX
RF input power to optical transmitter (dBm)
P:~
RF input power to semiconductor laser-based optical transmitter in a
direct modulation link (dBm)
Pin,TX,ext
RF input power to external modulator-based optical transmitter in an
external modulation link (dBm)
P o p t,d ir(0
RF amplitude of optical carrier modulated at output of semiconductor
laser in direct modulation link (dBm)
P o p t,ex t(® )
RF amplitude of optical carrier modulated at frequency eo at output of
electro-optic modulator in external modulation link (dBm)
Pout,lCP
RF output power at which link response is compressed by 1 dB (dBm)
Pout,lCP,dir
RF output power at which the direct modulation link response is
compressed by 1 dB (dBm)
P o u t, 1CP,ext
RF output power at which the external modulation link response is
compressed by 1 dB (dBm)
P out,int
RF output power at which the fundamental and third-order
intermodulation frequency plots intersect (dBm)
t v
a ; — U l ) X / l fU U
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
309
P ouw nt,dir
direct modulation link third-order intercept R F output power (dBm)
P out,int,ext
external modulation link third-order intercept R F output power (dBm)
Pout,op
output optical power (dBm)
Pout,RX
RF power at output of p-i-n detector-based optical receiver (dBm)
PSSL
optical power at output o f fiber-pigtailed solid-state laser in external
modulation link (dBm)
q
electronic charge (1.602 x 10*19 Coul)
Qext
external quality factor of a device (unitless)
rjj
electro-optic tensor in electro-optic external modulator (m-V*1)
R j, R2
reflectivities of front and rear facets of semiconductor laser cavity
(unitless)
Rjd
resistance of reverse-biased p-i-n photodetector junction (£2)
Rjl
resistance of forward-biased semiconductor laser junction (£2)
Rpd
parasitic series resistance of reverse-biased p-i-n photodetector (£2)
R pl
parasitic series resistance of forward-biased semiconductor laser (£2)
Rpm
parasitic series resistance of electro-optic modulator (£2)
Rs
substrate resistance of forward-biased semiconductor laser (£2)
Rsp
rate at which spontaneous emission o f photons occurs in semiconductor
laser active region (m^s*1)
RIN
relative intensity noise (dB-Hz*1)
RINsl
relative intensity noise o f semiconductor laser in direct modulation link
at given frequency and DC bias current (dB-Hz*1)
RINssl
relative intensity noise of solid-state laser in external modulation link at
given frequency (dB-Hz*1)
S
photon density in semiconductor laser active region (m*3)
Si
photon density of the i^-order optical mode in the semiconductor laser
active region (m*3)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
310
[SijD]
scattering parameters of two-port network comprised of Cjd , Rpd , Lpd ,
and impedance-matching circuit in p-i-n detector-based optical receiver
(unitless)
[SijL]
scattering parameters of two-port network comprised of Cs, Rs, Rp l »
L p l , and impedance-matching circuit in semiconductor laser-based
optical transmitter (unitless)
[SijM]
scattering parameters o f two-port network comprised o f
R p m , L p m » and
im p e d a n c e -m atch in g circuit in electro-optic modulator-based optical
transmitter (unitless)
S /N
signal-to-noise power ratio (dB)
(S /N )in
signal-to-noise power ratio at the input to a fiber-optic link (dB)
(S/NJjn^ir
RF signal-to-noise power ratio at input to direct modulation link (dB)
(S /N )in ,e x t
RF signal-to-noise power ratio at input to external modulation link (dB)
( S / N ) 0u t
signal-to-noise power ratio at output of an external modulation fiber­
optic link (dB)
( S /N ) 0ut,dir
RF signal-to-noise power ratio at output to direct modulation link (dB)
( S / N ) 0ut,ext
RF signal-to-noise power ratio at output to external modulation link
(dB)
SFDR
spurious-free dynamic range (dB-MHz2^3)
SFDRdir
spurious-free dynamic range of direct modulation link (dB-MHz2^3)
SFD R ext
spurious-free dynamic range of external modulation link (dB-MHz2^3)
T
absolute temperature (K)
vg
group velocity of photons in the laser cavity (m-s*1)
vg
RF generator voltage (V)
VM(©i)
RF amplitude of voltage at electrodes of electro-optic modulator at
frequency coj (V)
<v2th,RX>
spectral voltage density of noise in the optical receiver o f a fiber-optic
link due to thermal noise in the receiver (V^Hz*1)
<v 2th,TX,ext>
spectral voltage density o f noise in the optical transmitter of an
external modulation link due to thermal noise in the transmitter (V^Hz*
*)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
311
Vb
electro-optic modulator DC voltage bias (V)
Vd
p-i-n detector DC voltage bias (V)
Vm
total of DC bias and RF modulation voltages at modulator electrodes
(V)
Vol
volume of semiconductor laser active region (jim^)
Vrt
electro-optic modulator voltage required for 100% modulation (V)
w
width of semiconductor laser active region (fim)
Y
total admittance presented to the equivalent thermal noise current
source in a semiconductor-laser based optical transmitter (£2_1)
YrhT.
admittance of the semiconductor laser-based optical transmitter circuit
as seen from the output (mS)
z
distance from the modulator electrode load termination (mm)
Z
total impedance presented to the equivalent thermal noise voltage
source in an external modulator-based optical transmitter (£2)
Zo
system impedance at the input and output of a link (£2)
Zc
characteristic impedance of traveling-wave electrode waveguides (£2)
Z m ( z)
impedance of electrodes in a traveling-wave modulator, as seen at a
distance z from the load impedance (£2)
Zt
load termination impedance in a travelin-wave modulator (£2)
ZthD
impedance of detector termination as seen from the reverse-biased
junction (£2)
ZthM
modulator source impedance as seen from the input to the electrodes
(Q )
cte
real (lossy) part of microwave propagation constant (mm-1)
<*l
optical attenuation in semiconductor laser active region (mm'1)
(3
fraction of spontaneously emitted photons coupled into the lasing modes
(unitless)
pe
imaginary (transmissive) part of microwave propagation constant (mm*
l)
y
semiconductor laser relaxation oscillation damping rate (GHz)
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
312
Ye
complex microwave propagation constant (mm"1)
Yi
relaxation oscillation damping rate of the ith-order optical mode in a
semiconductor laser’s active region (GHz)
T
semiconductor laser optical confinement factor (|im2)
rD
reflection coefficient at p-i-n photodetector junction (unitless)
roevice
de-embedded scattering parameter o f an electro-optic device (unitless)
Fee
overlap integral between applied electric field and optical mode in
external modulator (unitless)
rgD
reflection coefficient at generator feeding a p-i-n photodetector-based
optical receiver (unidess)
rgL
reflection coefficient at generator feeding a semiconductor laser-based
optical transmitter (unidess)
rgM
reflection coefficient at generator feeding an external modulator-based
optical transmitter (unidess)
r id
reflection coefficient at load of p-i-n photodetector-based optical receiver
(unitless)
r il
reflection coeffient at load of two-port network comprised of Cs, Rs, Rpl ,
L pl , and impedance-matching circuit in semiconductor laser-based
optical transmitter (unidess)
I' d
reflection coefficient at semiconductor laser junction (unidess)
r im
reflection coeffient at load of two-port network comprised of Rpm , Lpm ,
and impedance-matching circuit in electro-optic modulator-based optical
transmitter (unitless)
rm
reflection coefficient at electro-optic modulator electrodes (unitless)
^Measured
measured scattering parameter of an electro-optic device in its test
fixture (unidess)
in 2min
minimum achieveable reflection coefficient
8
“walk-off’ coefficient in traveling-wave external modulator (unidess)
8fsT
Schawlow-Townes linewidth of a semiconductor laser (GHz)
Af
band of frequencies across which reactive impedance matching is to be
attempted (GHz)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
313
Af3dB
3 dB modulation bandwidth (maximum operating frequency) o f an
electro-optic modulator (GHz)
Ap-Lg
frequency-dependent phase shift caused by electro-optic effect in
external modulator (unitless)
80
nonlinear gain coefficient in a semiconductor laser with a single
longitudinal mode (pm2)
eeff
effective dielectric constant o f transmission line formed by travelingwave modulator electrodes (unitless)
tid
p-i-n detector responsivity (mA-mW*1)
TjL
semiconductor laser external differential quantum efficiency (mA-mW*1)
Tir p n
semiconductor LED internal differential quantum effiency (mA-mW*1)
0,
random microwave phase (rad)
X
optical wavelength (nm or pm)
v
optical frequency (THz)
vo
resonant mode frequency o f laser cavity (THz)
Tp
photon lifetime in cavity of semiconductor laser (ps)
Ts
spontaneous emission lifetim e o f charge carriers in cavity of
semiconductor laser (ps)
<t>(a0
term used in calculation o f direct modulation link distortion, evaluated at
a; (unitless)
£0
2 n f (G H z)
© h ig h
2 jc f h ig h ( G H z )
C0i
2k fi (G H z )
© ri
2 jt frj ( G H z )
©RC
27C fRC
(G H z)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
VITA
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
314
VITA
Edward Ackerman was bom on May 28, 1965, in Binghamton, New York, where
he attended a public high school. He received a Bachelor of Science degree in Electrical
Engineering from Lafayette College in Easton, Pennsylvania, in 1987.
In September 1989, Mr. Ackerman was awarded a Master of Science in Electrical
Engineering from Drexel University, where he is currently completing his Ph.D. studies.
The topic of his M.S. thesis was the design of a high-speed, low-loss fiber-optic link.
While a full-time student at Drexel from 1987-89, he was employed as a teaching/research
assistant in the Electrical and Computer Engineering Department, where he assisted in
teaching Electromagnetics classes and Fiber Optics laboratories. Mr. Ackerman is currently
employed as a Microwave Photonics Engineer at Martin Marietta Laboratories*Syracuse,
where he develops photonic systems for feeding high-fidelity RF signals to and from
phased array antennas in radar and communications applications. He has authored or co­
authored 21 publications in this field.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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