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HIGH SPEED INTEGRATED - OPTIC SAMPLER FOR TRANSIENT RADIOFREQUENCY AND MICROWAVE SIGNALS (ELECTROOPTIC, LASER, PHOTODETECTOR, DIRECTIONAL COUPLER)

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Vi/
’IMversHy
Mcrofilins
, Internationa]
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8603043
Ridgway, Richard William
HIGH SPEED INTEGRATED-OPTIC SAMPLER FOR TRANSIENT RADIO
FREQUENCY AND MICROWAVE SIGNALS
The Ohio State University
University
Microfilms
International
Ph.D.
1985
300 N. Zeeb Road, Ann Arbor, Ml 48106
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HIGH SPEED INTEGRATED-OPTIC SAMPLER
FOR TRANSIENT RF AND MICROWAVE SIGNALS
DISSERTATION
Presented in Partial Fulfillment of the Requirements
for the Degree Doctor of Philosophy
in the Graduate School of The Ohio State University
by
Richard William Ridgway, BSE, MSE
The Ohio State University
1985
Reading Committee
Approved By
Professor D. T. Davis
Professor R. T. Compton
Professor H. Hsu
Advisor
Department of
Electrical Engineering
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To my wife Judy, whose inspiration, patience, and sacrifice have made
our dream a reality.
ii
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ACKNOWLEDGMENTS
I would like to thank my research
his help and friendship throughout my
advisor Dr. Dean T. Davis for
studies and research.
I wonld
also like to thank Dr. R. T. Compton and Dr. H. Hsu for their helpful
suggestions and comments while serving on my advisory committee.
I also owe a great debt to Battelle for the Doctoral Fellowship
and the financial assistance which made this whole program possible.
Especially to Mr. E. R. Leach, Mr. M. R. Seiler, and Dr. J. D. Hill
who fnlly supported me through my frequent absence.
Gratitude is expressed to my friend Dr. Carl M. Verber who
introduced my to the world of integrated optics and graciously
reviewed my manuscript.
Also to Dr. Paul J. Cressman for his many
helpful suggestions and discussions in the laboratory.
would like to thank Barbara Lubberger
Finally, I
for all of her help in preparing
and editing this manuscript, Jan Burdette for
her
excellent
illustrations, and Jim Busch and Tim Shortridge for their assistance
in fabricating the integrated optic devices.
iii
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VITA
March 3, 1956
Born - Detroit, Michigan
April 1978
BSE - The University of Michigan
Ann Arbor, Michigan
August 1979
MSE - The University of Michigan
Ann Arbor, Michigan
September 1979 - Present..........Principal Research Scientist
Battelle Columbus Laboratories
Columbus, Ohio
Publications
"Fiber-Optic High-Sensitivity Interferometer", co-author E. R. Leach
Battelle Columbus Laboratories, Contract No. DAAH01-83-D-A008,
December,1984.
"Studies of Millimeter-Wave Diffraction Devices and Materials",
co-author M. R. Seiler, Battelle's Columbus Laboratories, Contract
No. F49620-82-C-0099, December 28,1984.
"Light Beam Scanning System with SAW Transducer", co-inventors
C. M. Verber, R. P. Kenan, U. S. Patent No. 4,394,060, July 19, 1983
"Integrated Optics", Battelle Columbus Laboratories, Contract
No. F33657-81-C-2070, May 6,1983.
Fields of Study
Major Field: Electrical Engineering
Studies in Communications . . . .
Professor Dean T. Davis
Professor R. T. Compton
Professor F. Garber
Studies in Optics
Professor H. Hsu
iv
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Studies in Digital Electronics.
.
Professor F. Ozgener
Studies in Mathematics............. Professor Stefan Drobot
Professor Omar Hijab
v
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TABLE OF CONTENTS
ACKNOWLEDGMENTS ..............................................
iii
VITA...........................................................
iv
LIST OF
LIST OF
F I G U R E S ..................................... viii
TABLES....................................
CHAPTER
I.
xii
PAGE
INTRODUCTION ................................
1
II.PHYSICAL PRINCIPLES OF SYSTEM COMPON E N T S ..............
12
Optical Waveguides ...............................
Planar Optical Waveguides .....................
Channel Waveguides
...........................
Effective Index Method
.......................
Electrooptic Effect
.............................
The Directional Coupler .........................
Asymmetric Couplers ...........................
Coupling Coefficient
.........................
Microwave Stripline
.............................
Traveling Wave Devices
.......................
Electrode Design .............................
R e f e r e n c e s .......................
13
16
18
19
29
41
46
49
65
55
61
66
THE INTEGRATED-OPTIC SAMPLER ........................
68
Theory of Operation...............................
Case 1: Sampler with Arbitrary Sine Wave
I n p u t ....................................
Case 2: Sampler with Electrical Pulse
Input......................................
Case 3: Intensity Modulated Optical Signal
and a Square Electrical Pulse. . . . . . .
Case 4: Arbitrary Optical and Electrical
Signals....................................
Sampling Rate and A p e r t u r e .......................
Electrical Considerations
.......................
Integrating Detector
.........................
Coupler Considerations ...........................
70
III.
70
84
88
96
104
108
116
126
vi
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Sampler
Step
Step
Step
Step
Step
IV.
V.
Design Procedure .........................
1: Optical Waveguide Design .............
2: Coupling Coefficient
...............
3: Coupler L a y o u t ........................
4: Sampler P a r a m e t e r s ...................
5: Detector Requirements.................
128
128
129
130
130
131
Sampler Design Example ...........................
R e f e r e n c e s ........................................
133
142
EXPERIMENTAL PROCEDURES AND RESULTS.................
143
Integrated Optical Device Fabrication.............
Optical Waveguide Fabrication .................
Surface Preparation ...........................
Titanium Evaporation...........................
Titanium Photolithography .....................
D i f f u s i o n ......................................
P o l i s h i n g ......................................
Buffer Layer Fabrication.......................
Electrode Fabrication .........................
Chrome-Gold Evaporation .......................
Chrome-Gold Photolithography...................
Fundamental Experiments ...........................
Mode Structure..................................
Endfire Coupling...............................
Coupler Characterization.......................
Sampler Electronics...............................
Proof-of-Principle Demonstration .................
Experimental Results .............................
143
144
145
145
146
146
147
148
148
149
149
152
152
157
161
167
169
179
CONCLUSIONS AND RECOMMENDATIONS
...................
180
B I B L I O G R A P H Y ................................................
184
vii
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LIST OF FIGURES
FIGURES
1.
PAGE
RF and Microwave Sampler Utilizing Integrated
Optic T e c h n o l o g y ....................................
3
2.
Photoconductive Sample and Hold Circuit.............
5
3.
Photoconductive Sampler with Spatially Determined
Sample Points........................................
7
4.
2-Bit Analog-to-Digital Converter....................
8
5.
Planar Waveguide on the Surface of a Substrate . . .
14
6.
Channel Waveguide....................................
15
7.
Planar Waveguide Between Two Lower Index
S u b s t r a t e s ..........................................
17
Channel Waveguide with Vertical and Horizontal
Diffusion............................................
20
9.
Optical Path in a Graded Index W a v e g u i d e ...........
22
10.
Propagation Vectors for the optical wave in the
diffused waveguide ..................................
24
(a) Cross Section of Channel Waveguide
(b) Channel Waveguide with Sides Extended
(c) Channel Waveguide with Top and Bottom Extended .
28
12.
Index Ellipsoid for Uniaxial Crystal ................
31
13.
Ellipse Representing the Crystal's Birefringence . .
31
14.
Electrooptic Phase Shifters Utilizing
rgg Electrooptic Coefficient .......................
38
Electrooptic Phase Shifters Utilizing
* 1 3 Electrooptic Coefficient .......................
39
8.
11.
15.
viii
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16.
Optical Directional Coupler..........................
42
17.
Electrically controlled Directional Coupler.........
44
18.
Voltage-to-Coupling Curve for Symmetric Coupler.
47
19.
Asymmetric Coupler ..................................
48
20.
Voltage-to-Coupling Curve for Asymmetric Coupler . .
50
21.
Cross-Section of Rectangular Waveguide used in
Harcatili's Analysis ................................
52
22.
Traveling Wave M o d u l a t o r ............................
57
23.
(a) Symmetric and (b) Asymmetric RF Striplines on
Electrooptic Coupler ................................
63
Electrooptic Coupler with an Alternate Electrode
Structure...................
64
25.
Sampler Example - Case 1 ............................
71
26.
Input and Output Signals for an Integrated Optic
Sampler Comprised of Three Symmetric Couplers.
The input optical signal is a 15 picosecond pulse
and the electrical signal to be sampled is a
sine wave............................................
79
Input and Output Signals for an Integrated Optic
Sampler Comprised of Three Asymmetric Couplers.
A short optical pulse is interacting with an
electrical sine w a v e ................................
81
28.
Sampler Example - Case 2 ............................
85
29.
Input and Output Signals for the Sampler - Case 2.
A short optical pulse interacts with a square
electrical pulse.....................................
89
30.
Sampler Example - Case 3 ............................
91
31.
Input and Output Signals for the Sampler - Case 3.
An intensity modulated optical signal being
sampled by a short optical pulse ...................
94
32.
Sampler Example - Case 4 ............................
97
33.
Input and Output Signals for the Sampler - Case 4.
An intensity modulated optical signal is
interacting with a sine electrical waveform to
produce three optical output signals ...............
100
24.
27.
. .
ix
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34.
Ideal Sampler.........................................
105
35 o
Conventional Photodiode Circuit......................
Ill
36.
Minimum Detectable Signal as a Function of
Frequency............................................
115
37.
Integrating Optical Detector ........................
117
38.
Frequency Response of Real Integrator...............
119
39.
Signal-to-Noise Ratio for Integrating Optical
Detector as a Function of Incident Optical Power . .
125
Normalized Output Power of Last Coupler as a
Function of the Number of Sample Points.............
127
Voltage-to-Coupling Curves for a Symmetric Optical
Coupler. The distance between the waveguides is
varied from 2 microns to 5 m i c r o n s .................
137
Voltage-to-Coupling Curves for a Symmetric Optical
Coupler. The interaction length varied from
2 millimeters to 1/2 millim e t e r s ...................
138
Voltage-to-Coupling Curves for a Asymmetric Optical
Coupler.
The distance between the waveguides is
varied from 2 microns to 5 m i c r o n s .................
139
Voltage-to-Coupling Curves for a Asymmetric Optical
Coupler. The interaction length varied from
2 millimeters to 1/2 millimeters ...................
140
45.
Schematic Drawing of Experimental Device ...........
151
46.
(a) Photograph of Titanium In-diffused Optical
Waveguides in Directional Coupler Configuration,
(b) Photograph of Chrome-Gold Electrodes over
Optical Waveguides ..................................
153
Photographs of Integrated Optic Directional
Coupler..............................................
155
Experimental Arrangement for Determining the Mode
Structure of Optical Waveguides.....................
156
49.
Laboratory Arrangement for Endfire Coupling.........
158
50.
Oscilloscope Photograph of Detected TM Light from
the End of the C r y s t a l .............................
160
40.
41.
42.
43.
44.
47.
48.
x
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51.
Detected Light out of the Optical Waveguides using
IE Polarized light, (a) Real-Time Oscilloscope
Output, (b) Integrated Output using Multichannel
Analyzer ..........................................
52.
Laboratory Arrangement for Endfire Coupling
Experiments using Laser Diodes .....................
53.
Detected Light out of the Optical Waveguides using
TM Polarized Light in Laser Diode Coupling
Experiments..........................................
54.
Measured Voltage-to-Coupling Curve .................
55.
Network Analyzer Configuration for Testing Frequency
Response of the Laser Diode and Optical Detector . .
56.
Amplitude and Phase vs Frequency for Laser Diode
and Detector Combination ...........................
57.
Laboratory Arrangement for Time Domain Testing of
Laser Diode and Optical Detection...................
58.
Time Domain Response of Laser Diode and Optical
Detector, (a) Pulse into Laser Diode, (b)
Electrical Signal from APD Photodetector ...........
59.
Laboratory Arrangement for Proof-of-Principle
Experiment ..........................................
60.
Photograph of Proof-of-Principle Experiment.
Left: Laser Diode, Center: Integrated-Optic Device
Right: APD and Preamplifier.........................
61.
Detected Outputs for Proof-of-Principle
Experiments with DC voltage on Electrodes..........
62.
Detected Optical Pulses from Proof-of-Principle
Experiments with Sinusoidal Signal on Electrodes . .
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LIST OF TABLES
TABLE
1.
PAGE
Refractive Indices and Electrooptic
Coefficients for Lithium Niobate ...................
. . .
40
2.
Typical Parameters for CommercialPhotodiodes.
114
3.
Integrating Detector Example ........................
124
'4.
Device Parameters....................................
134
5.
Waveguide Fabrication Parameters ....................
134
6.
Results of Effective Index Method...................
135
xii
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CHAPTER I
INTRODUCTION
The sampling of electrical signals in order to detect or analyze
their properties has been important to the field of communications for
many years. In 1928 Nyqnist noted the necessity of sampling a signal
at a rate greater than twice the bandwidth of the signal 1 . Later
Shannon gave a mathematical proof of Nyqnist's theory and showed that
as long as the signal occupied a bandwidth no greater than
W, the
signal could be completely determined by means of a series of samples
taken at intervals 1/2W seconds apart 3 . Modern communications systems
using time-multiplexing as well as digital processing of broadband
signals have led to a need for methods of sampling at very high rates.
A variety of technology advances through the years have yielded
faster methods of sampling an electrical signal.
Such advances
include the advent of the transistor as well as the realization of
high speed GaAs circuits. The latest development that has led to a
significant increase in the sampling rate is the pulsed laser.
Although pulsed lasers have been available for some time, it was not
until recently that the pulses have been produced with durations short
enough to yield a significant improvement over other types of sampling
systems. Also, until recently, short-pulse lasers were large and
expensive mode-locked or Q-switched lasers.
Recent advances in diode
lasers have produced more economical devices capable of generating
short pulses at high repetition rates.
1
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Another major contribution to sampling technology has been the
microcomputer 1 . The microcomputer has enabled stand-alone sampling
systems to incorporate various signal processing schemes, as veil as
computer controlled measurement, calibration and data storage. A
microcomputer can, as an example, perform deconvolution on the sampled
points of an electrical signal to compensate for distortion that is
added during the signal acquisition.
This advantage will be discussed
further in the later sections.
The work reported here presents the analysis and experimental
demonstration of a novel high-speed integrated-optic sampling system
which uses a pulsed laser source to achieve a high sampling rate
as well as a microcomputer for removal of some of the inherent signal
distortion. The integrated-optic sampler has the potential for both a
very short sampling aperture and a very high sampling rate. This
should lead to a device that has the capability of sampling transient
(single shot) RF or microwave signals.
The high speed sampler is pictured schematically in Figure 1.
The
device consists of a series of optical couplers that are fabricated on
an electrooptic material along a coplanar RF stripline so that the
electric field across each coupler is determined by the local voltage
along the stripline and the associated ground strip. A short optical
pulse, which propagates in a direction opposite to a traveling wave
electrical signal, passes sequentially through the couplers causing a
small amount of light to couple into one of the output optical
waveguides and propagate to the optical detectors.
The amount of
coupled light is dependent on the local electric field.
The sampling
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OPTICAL PULSE-
ELECTROOPTIC
VOLTAGE ON
STRIPLING
PROPAGATION
DIRECTION
OF ELECTRICAL
SIGNAL
TRAVELING
WAVE
ELECTRODE
PROPAGATION
DIRECTION
OF OPTICAL
PULSE
GROUND
STRIP
&
OUTPUT
OPTICAL
WAVEGUIDES
COUPLED
OPTICAL
PULSE
TO OPTICALDETECTORS
FIGURE 1.
RF AND MICROWAVE SAMPLER UTILIZING INTEGRATED OPTIC TECHNOLOGY
CO
4
rate of the device is determined by the spatial distance between the
optical couplers and the velocities of both the optical pulse and the
RF signal.
There are several other pulsed laser based sampling techniques
being pursued in the United States. Researchers at the University of
Rochester 4 are using a fast laser pulse to activate a semiconductor
switch (Cr:GaAs) to enable the electrical signal to propagate onto a
coplanar strip transmission line on an electrooptic crystal (LiTaOg).
A second pulse is then used to probe the birefringence induced by the
gated electrical signal on the electrooptic crystal. The temporal
resolution of the sampling system is determined by the convolution
time of the traveling electrical signal and the optical pulse that is
used for probing s. Recent changes in the geometry have enabled the
demonstration of electrical sampling with a temporal resolution of
less than 500 femtosec *. The sampling rate of the device is
determined by the pulse repetition rate of the laser source, which is
currently limited to 100 MHz. Although this technique has tremendous
resolution potential,
its low repetition rate, and thus sampling rate,
limits its usefulness to repetitive signals.
Another high speed sampling system which uses short laser pulses
and semiconductor switches is being considered at both Lincoln
Laboratories 7 and Bell Laboratories *. In these samplers, shown in
Figure 2, a fast semiconductor switch is activated by a laser pulse to
allow the electrical signal on the stripline to proceed to the
detector. In one case an InP switch with a 50 picosecond effective
response time is demonstrated and a sampling system is proposed.
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LASER PULSE
INPUT SIGNAL
FIGURE 2.
V7//77Z
HHI'
METAL STRIPLINE
SEMICONDUCTOR.
MATERIAL
GROUND PLANE'
PHOTOCONDUCTIVE SAMPLE AND HOLD CIRCUIT [7]
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6
In a related device Dr. John Meadors, then of Battelle, suggested
a sampler consisting of a series of fast semiconductor switches that
are located along a stripline, as shown in Figure 3. The switches are
simultaneously strobed with a short optical pulse which spatially
samples a signal traveling down the stripline. Due to the speed of the
switches and the short distance between the switches, it was presumed
that a sampling rate of 40 GHz and a sampling aperture of 25
picoseconds could be achieved
In 1975, H.F. Taylor suggested the use of an electrooptic
modulator in channel waveguides for analog-to-digital conversion 10.
Since then numerous laboratories have demonstrated this concept
xhe most recent, shown in Figure 4, is a sampler that is
able to convert a 500 MHz bandwidth signal to a 2-bit digital code at
a rate of 1 gigasample per second 14.
There are several reasons for investigating the present topic.
First, the electrooptic effect, which is the fundamental physical
principle of this sampler, is an extremely fast phenomenon which has a
potential bandwidth in excess of 10^2 Hz.
In addition the integrated
optic device presented herein can be interfaced to optical fibers for
use in the growing fiber communications field.
Furthermore,
integrated optic devices will eventually be fabricated in mass
production and become low in cost, and thus provide a cost-effective
method of sampling and characterizing high frequency electrical
signals.
Finally, this work will include a more general look at
the interaction between high frequency electrical signals and
amplitude modulated optical signals in electrooptic couplers and
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7
LASER PULSE
PHOTOCONDUCTIVE
SWITCH
METAL STRIPLINE
FIGURE 3.
PHOTOCONDUCTIVE SAMPLER WITH SPATIALLY DETERMINED
SAMPLING RATE [9]
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8
LSB
LASER PULSE
" in
MSB
FIGURE 4.
2-BIT ANALOG TO DIGITAL CONVERTER [10]
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introduce other possible applications.
These applications will
include the sampling of an amplitude modulated optical signal with a
short electrical pulse.
The presented paper is divided into five chapters.
Chapter II
presents the physical principles employed in modeling and designing
the integrated-optic sampler.
Chapter III includes a theoretical
discussion of the sampler and derivations of the expressions for the
output signals.
Chapter IV contains a description of the experimental
work completed during the investigation including the fabrication
procedures and the proof-of-principle demonstrations of the device.
Finally* Chapter V provides the conclusions of the work and
recommendations for future studies.
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10
References
1.
Nyquist, H., "Certain factors affecting telegraph speed", Bell
System Tech. Jour., Vol. 3, p. 324, April 1924
2.
Shannon, Claude E., "Communications in the Presence of Noise",
Proceedings of the IEEE, Vol.72, No. 9, September, 1984.
3.
Nahman, Norris S., "Picosecond-Domain Waveform Measurements",
Proceedings of the IEEE, Vol. 66, No. 4, April, 1978.
4.
Valdmanis, J.A., Mourou, G.A., Gabel, C.W., "Picosecond
electro-optic sampling system", Appl. Phys. Lett., Vol.
August 1, 1982.
5.
6.
14, No. 3,
Valdmanis, J.A., Mourou, G.A., Gabel, C.W., "Subpicosecond
electrical sampling", IEEE J. Quantum Electron., Vol. QE-19,
No. 4, April 1983.
Mourou, G.A., Meyer, K.E., "Subpicosecond electro-optic sampling
using coplanar strip transmission lines", Appl. Phys. Lett.,
Vol. 45, No. 5, Sept. 1, 1984.
7.
Leonberger, F.J., "Applications of InP photoconductive switches",
SPIE, High Speed Photodetectors, Vol. 272, 1981.
8.
Auston, D.H., Johnson, A.M., Smith, P.R., and Bean, J.C.,
"Picosecond optoelectronic detection, sampling, and correlation
measurements in amorphous semiconductors", Appl. Phys. Lett.,
Vol. 37, No. 4, August 15, 1980.
9.
Meadors, J., Personal correspondence, 1984.
10. Taylor, H.F., "An electrooptic analog-to-digital converter",
Proc. IEEE, Vol. 63, pp. 1524-1525, 1975.
11. Taylor, H.F., Taylor, M.J., and Bauer, P.W., "Electro-optic
analog-to-digital conversion using channel waveguide modulators",
Appl. Phys. Lett., Vol. 32, No. 9, May 1, 1978.
12. Leonberger, F.J., Woodward, C.E., Becker, R.A., "4-bit
828-megasample/s electro-optical guided analog-to-digital
converter", Appl. Phys. Lett., Vol. 40, No. 7, April 1, 1982.
13. Dokhikyan, R.G., Zolotov, E.H., Karinskii, S.S., Maksimov, V.F.,
Popkov, V.T., Prokhorov, A.M., Sisakyan, I.N., Shcherbakov, E.A.,
"Prototype of an integrated-optics four-digit analog-to-digital
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11
converter", Sov. J. Quantum Electron., Vol. 12, No. 6, p. 806,
June 1982.
14. Becker, R.A., Johnson, L.M., "Low-loss multiple-branching circuit
in Ti-indiffused LiNbO channel waveguides". Optics Letters,
Vol. 9, No. 6, June, 1984.
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CHAPTER II.
PHYSICAL PRINCIPLES OF SYSTEM COMPONENTS
This chapter discusses the principles of physics applied in
modeling and designing the integrated-optic sampler.
important points discussed in this chapter.
There are four
The first is that a
diffused channel waveguide, which has an index of refraction profile
that is nonlinear with depth, can be modeled as a waveguide with a
constant index and its propagation constant and mode structure can be
characterized by a quantity called its effective index.
The second
important point of this chapter is that if the waveguide is fabricated
in an electrooptic material, then its index of refraction can be
varied by applying an electric field.
Thirdly, this chapter shows
that if two parallel waveguides are fabricated in proximity then light
from one waveguide can be coupled into the other waveguide.
It is
also shown that the amount of coupled light can be controlled via the
electrooptic effect.
Finally, this chapter demonstrates that the
electrodes can be designed in a stripline configuration where the
impedance is matched to the required source or load impedance.
These
topics are discussed in the following sections.
12
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13
Optical Vavegnides
Optical waveguides are a fundamental part of integrated optical
circuits in that they are used to transfer the optical energy from one
portion of the circuit to another x .
Although optical waveguides can
take on a variety of forms and can be fabricated using a variety of
techniques, they can be categorized into two basic types.
The first
type is the planar waveguide which, as shown in Figure 5,
has
boundaries only in one (y) direction and extends to infinity in the
other two directions (x and z). In an actual device, of course, the
waveguide cannot extend to infinity.
However, the assumption of the
infinite boundaries does simplify the theory and is therefore often
used in analysis.
The second type of waveguide is the channel waveguide which, as
shown in Figure 6, has boundaries in two directions and propagates
light in the third direction.
At this point the axes x, y, and z have
little significance in that they are simply the axes in a
3-dimensional picture.
It will later be shown that when
these axes
refer to coordinates of an electrooptic crystal, their orientation,
both crystal cut and propagating direction, will be important in terms
of the refractive index and the electrooptic coefficients.
Optical waveguides are often fabricated in electrooptic materials,
such as lithium niobate.
An electrooptic material has a refractive
index that varies as a function of applied electric field.
This
property, which is explained more fully in later sections, is often
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14
HIGH INDEX LAYER
SUBSTRATE
z
FIGURE 5.
PLANAR WAVEGUIDE ON THE SURFACE OF A SUBSTRATE
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15
HIGH INDEX CHANNEL
SUBSTRATE
FIGURE 6.
CHANNEL WAVEGUIDE
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16
exploited in integrated optics to provide such functions as optical
phase shifters and directional couplers.
Although the high speed sampler discussed in this work uses
channel waveguides, the following discussion includes planar
waveguides in order to give insight in the understanding of channel
waveguides as well as their significance in the use of the effective
index method for calculating the propagation constant of a channel
waveguide.
Planar Optical Waveguides
Planar optical waveguides play a very important role in integrated
optics.
In many devices, such as the acousto-optic
modulators which
use surface acoustic waves (SAW) devices to diffract the laser
light 2, the optical signal must be capable of propagating in many
directions and therefore cannot be confined in the lateral direction.
For this reason planar waveguides are used since they allow the light
to propagate in any direction in the plane but still offer the
confinement required in many applications.
Planar waveguides consist
of a high index slab of material between two lower-index materials, as
shown in Figure 7.
In a symmetric planar waveguide the indices of the
two outside materials (n^ and n 3 ) are equal.
waveguide the outside materials are not equal.
In an asymmetric
Most integrated optic
waveguides are asymmetric since they are usually formed on the surface
of the material and have air above the guide.
A planar waveguide is
fabricated using a number of techniques which can be divided into two
classes.
First are the waveguides that are fabricated by depositing a
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17
FIGURE 7.
PLANAR WAVEGUIDE BETWEEN TWO LOWER INDEX SUBSTRATES
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
18
higher index material on the substrate and second ure the waveguides
that are fabricated within the substrate itself by producing a
higher index region by some chemical or physical reaction *.
In the
first type, there is an index discontinuity at the interface between
guide and the substrate.
In the second type of waveguide the index
gradually changes through the substrate.
The optical waveguides
considered in this work are of the second type in which the index
varies as a function of depth.
This type of waveguide is often
fabricated by diffusing a transition metal, such as titanium, into an
electrooptic crystal.
The index profile of the waveguide after
diffusion can be described by a variety of functions including
Gaussian, exponential, and the complementary error function4 .
One way of characterizing a diffused planar waveguide is by means of
its effective index.
The effective index is essentially the index of
an equivalent slab waveguide which would have the same propagation
constant and mode structure as the diffused waveguide.
This will be
discussed in greater depth in the next sections of this chapter.
Channel Waveguides
A channel waveguide may be required in an integrated optical
circuit simply to guide the light from one point to another, in which
case it is analogous to a metal strip in an integrated electrical
circuit.
On the other hand, a channel waveguide may be required to
confine the optical beam in order to modulate the optical phase
efficiently.
In this case, which is a fundamental part of this work,
the channel waveguide confines the light and enables the generation of
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19
very large electric fields using electrodes with reasonably small
voltages.
This effect is described in the electrooptic section of
this chapter.
Channel waveguides can he fabricated using the same techniques
used in planar waveguides.
In the fabrication of titanium diffused
channel waveguides, the titanium is first laid down on the surface of
the crystal and the pattern of the waveguide channels is formed using
photolithography. Once the waveguide pattern is defined, the titanium
is diffused into the crystal forming the graded index waveguides.
In
reality, the index varies in both the vertical and horizontal
directions due to the vertical and horizontal diffusion of the
titanium, as shown in Figure 8.
The diffused channel waveguide can again he characterized by its
effective index.
A procedure for calculating the effective index of a
diffused channel waveguide was developed by Hocker and Burns5 and will
be discussed in the next section.
The Effective Index Method
When designing an optical system, it is important to know the
propagation constants and the number of modes in the optical
waveguides.
In graded index optical waveguides, the analytic
expressions for these parameters may he extremely complicated, if not
impossible to solve.
Hocker and Burns * developed a straightforward
method for calculating the propagation constant in a diffused optical
waveguide with an arbitrary index profile.
The method determines the
effective index of a diffused planar waveguide, which is the index
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20
FIGURE 8.
CHANNEL WAVEGUIDE WITH VERTICAL AND HORIZONTAL
DIFFUSION
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21
that an equivalent constant index planar waveguide would need in
order to have the same propagation constant and mode structure as the
graded index waveguide. To determine the effective index, neff, of a
diffused planar waveguide, one compares the parabolic path that the
optical beam would take through the graded index, with the straight
path that an optical beam might take if the guide had a constant index
neff*
When the phase shift associated with each of these paths is
equal over a complete cycle of the parabolic path, then the transverse
component of the parabolic path phase shift is equal to zero and the
beam is propagating in its lowest order mode.
When the two paths
differ by a multiple of 2n the beam is propagating at a higher order
mode.
To calculate the total phase shift that an optical beam
experiences in an entire cycle, one must consider (1) the phase shift
of the beam as it propagates along the parabolic path, (2) the phase
shift associated with the reflection along the surface of the crystal,
and (3) the phase associated with the reflection of the graded
structure, as shown in Figure 9.
The phase shift that an optical beam experiences traveling a
distance d in a medium with index n is equal to:
9 - nkQd ,
(1)
where kQ = 2n/k is the freespace phase constant and k is the freespace
wavelength of the optical beam.
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22
—
► ]
—
DIRECTION OF
PROPAGATION
y
FIGURE 9. OPTICAL PATH IN A GRADED INDEX WAVEGUIDE [18]
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An approximate way to determine the phase shift that the optical
beam experiences in its parabolic shaped path is to divide the path
into piecewise linear segments and assume that the index is constant
over each segment with a value determined by the index grading
function.
The length of the individual segments vary as a function of
depth and can be determined from the two propagation vectors, one of
which always points in the x-direction corresponding to an optical
beam propagating in a constant index medium with index neff, and one
that propagates in a direction differing from the x-direction by an
angle
where n(y^) is the index in the graded waveguide at a depth yj.
This
index is given by the equation
(3)
n(y) = n^ + An f(y) ,
where n^ is the index of the bulk crystal. An is total index change
through the waveguide, and f(y^) is the function that describes the
variation of the index through the waveguide.
The two propagation
vectors shown in Figure 10 are given by
(4)
(5)
For a given Ax the beam penetrates the waveguide by a depth Ay given
by
Ay. = Ax tan 6,.
'i
i
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(6 )
24
y
FIGURE 10.
PROPAGATION VECTORS FOR THE OPTICAL WAVE IN THE
DIFFUSED WAVEGUIDE.
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25
The transverse component of the phase shift is given by
i
= n(y.) k sinG.Ax tanO,.
i
o
i
i
(7)
The total transverse phase shift can be determined by summing all of
the components over one complete cycle.
The phase shift associated with the reflection at the crystal
surface must also be considered.
For a wave with an electric field
perpendicular to the plane of incidence (TE), the phase shift due to a
reflection at the interface between two materials with index n^ and
> nj) is given by 7
9.
=2
tan
-1
sin^Gj -
In
(8)
cosG,
where G^ is the angle between the incident wave vector and the normal
to the surface.
Similarly, for a wave with the magnetic field perpendicular to the
plane of incidence (TM), the phase shift due to the reflection at the
interface is given by
1^
=2
tan
-1
[ s i n ^ - n22 /ni2 ]*
(9)
( n ^ / n j 2 ) cosGj
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26
The angle of incidence is determined by the assumed effective index
and the surface index of the graded structure.
Equations 8 and 9 can also be used to determine the phase shift
due to the reflection in the graded index.
In this case, as Hocker
and Burns point out, the angle of incidence approaches 90 degrees and
the indices become almost equal.
When the beam is at the lowest point
in the path its angle is almost parallel to the surface.
Therefore
(10)
In order to use the above equation one must treat the two indices as
= n(yt - 6) and nj = u(yt + 6).
This can be shown to have a phase
shift given by
(11)
for both TE and TM modes8 .
The phase difference of the straight and parabolic paths over one
complete cycle is the sum of (1) the transverse components of the
phase shifts for the piecewise linear segments,
(2) the phase shift
due to the reflection at the surface of the waveguide, and (3) the
phase shift due to the reflection in the graded structure.
The total
phase difference is given by
AK As various values of
J
+ »! + «2 .
(12)
are used in Equations 2 through 7 the
total phase difference will change.
For one value of ue£f, which is
somewhere between the bulk index of the crystal and the maximum index
on the surface, the phase difference will be zero. This is the
effective index for the lowest order mode.
A computer can be used to
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27
try various effective indices and find the best value for a given
bulk index n^ and total index change An.
The effective index method discussed so far can be used to
calculate the effective index of a planar waveguide which has
essentially infinite boundaries in two directions.
A channel
waveguide, on the other hand, is confined in two directions and
therefore requires additional considerations.
Hocker and Burns published a second paper that addresses this
issue9 . The problem with channel waveguides is that the diffusion
occurs in two dimensions, both perpendicular and parallel to the
surface, as shown in Figure 8.
In this work, as a first
approximation, it is assumed that the diffusion occurs only in the
direction perpendicular to the surface.
To estimate the effective index of a channel waveguide one must
extend the side walls of the waveguide to infinity, as shown in Figure
lib.
Then the effective index of waveguide with infinite boundaries
can be calculated just as it was for the planar waveguide.
In other
words, using the exact method described for planar waveguides, one
must calculate the effective index
Now the walls are placed on
the sides of the waveguides and the top and bottom are extended to
infinity, as shown in Figure 11c.
The waveguide is now represented by
a guiding layer with index &eff and an outer material on both sides
with index n^.
The effective index of this configuration n'eff which
is the effective index of the channel waveguide, can be determined
using the method used for diffused planar waveguides except this time
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28
n2
"3
"l
n3
"4
(a)
(b)
(c)
FIGURE 11 (a) CROSS SECTION OF CHANNEL WAVEGUIDE,
(b) CHANNEL WAVEGUIDE WITH SIDES EXTENDED,
(c) CHANNEL WAVEGUIDE WITH TOP AND BOTTOM EXTENDED.
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29
the optical beam just zigzags back and forth between the' two
interfaces.
Again, a computer can be used to determine the phase shift that
the optical beam experiences and the value of the effective index of
the channel waveguide n'eff.
The Electroontic Effect
An electric field, when placed across an electrooptic crystal, can
cause the refractive index of the crystal to change.
This fundamental
property of many crystalline structures, known as the electrooptic
effect, provides a means of controlling the phase of an optical beam.
This phase shifting ability can be used to make optical intensity
modulators, and optical beam deflectors, as well as many other optical
devices.
The electrooptic effect occurs in anisotropic materials in which
the velocity of the optical beam depends on the polarization of the
optical signal and the relative orientation of the optical signal to
the crystal.
In all crystals there is at least one axis, called the
optic axis, in which the velocity of light is the same for all optical
polarizations.
In a cubic crystal, every direction is an optic axis
and therefore has transmission characteristics similar to an isotropic
material.
Uniaxial crystals, which could have tetragonal, trigonal or
hexagonal symmetry, have just one optical axis which lies along one of
its crystallographic or c axis. Biaxial crystals, which could have
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triclinic, monoclinic or orthorhombic symmetry, have two optical
axes 10.
Most linear electrooptic devices are of the uniaxial type,
and therefore this type will he emphasized in this section.
The
refractive indices of a crystal can be represented by the index
ellipsoid
where n^, H 2 , and n 3 are the refractive indices for the x, y, and z
directions. For a uniaxial crystal this can be described by an
ellipsoid shown in Figure 12.
With the optical axis in the z
direction the refractive indices that an optical beam experiences can
be determined by intersecting the ellipse with a plane perpendicular
to the direction of propagation.
As an example, the indices of an
optical beam propagating along the z-axis can be represented by the
intersection of the ellipsoid and the xy plane, which in this case is
a circle.
The circle verifies that since the light is propagating
along the optical axis, the refractive index is independent of
the optical polarization.
polarization.
This is known as the ordinary direction of
The radius of the circle is the ordinary index nQ .
if,
on the other hand, the optical beam is propagating in the x direction,
then the indices can be represented by the intersection of the
ellipsoid and the yz plane, which in this case is an ellipse.
known as the extraordinary direction.
This is
The index changes elliptically
between the value of the ordinary index nQ , when the optical wave is
polarized perpendicular to the optic axis, to a value of the
extraordinary index np when the optical wave is polarized parallel to
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OPTIC AXIS
y
FIGURE 12.
INDEX ELLIPSOID FOR UNIAXIAL CRYSTAL
t
FIGURE 13.
OPTIC AXIS
ELLIPSE REPRESENTING THE CRYSTAL'S BIREFRINGENCE
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32
the optical axis, as shown in Figure 13.
birefringence.
This is referred to as
If the ordinary index nQ is larger than the
extraordinary index ne , the birefringence is negative.
extraordinary index is larger
If the
than the ordinary indexthe
birefringence is positive 1 1 .
Thegeneral equation for the
index
ellipsoid is given by 13
b11x2 + t»22y2 + b33z2 + 2b23yz + 2b13xz + 2b12xy = 1 ’
where
Because of the symmetry of all electrooptic crystals there are, at
most, 18 independent elements in the electrooptic tensor that describe
the interaction between the indices and the electric fields.
For this
reason it is customary to reduce the subscripts in the coefficients to
a single subscript.
Namely,
b l = b ll
b2
=
b22
b3
°
b33
b4
=
b23
b5
=
b13
b 6 = b 12
The
ellipsoid equation then becomes
2
b lx
2
+ b2y
2
+ b3z
+ 2b4yz + 2b5xz + 2bfixy = 2 *
When an electric field is applied to the crystal the coefficients
change by the amount
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6 and j = 1, 2, 3, r^j is the appropriate
where i = 1, 2,
electrooptic coefficient* and E- is the jth component of the electric
field. The electrooptic tensor* which is represented by a 3 by 6
matrix, contains the values of r
ij
The following example will help
illustrate how the above equations can be used to determine the
indices as a function of applied electric field.
Consider the uniaxial crystal lithium niobate.
is larger than the extraordinary index ne .
The ordinary index
Therefore, lithium
niobate is a crystal with negative birefringence.
Lithium niobate has
3m symmetry with a electrooptic tensor given by:
0
0
r22
r13
r 22
r13
0
0
0
r51
51
“r22
r33
(17)
0
0
0
0
0
Assuming that the z-axis is defined as the optic axis, the ellipsoid
equation given above has coefficients given by:
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where n^ is the index for a wave polarized in the x-direction, n2 is
the index for a wave polarized in the y-direction, and ng is the index
for a wave polarized in the z-direction.
Since lithinm niobate is
uniaxial with the optic axis in the z direction, the following
equalities hold.
nl = n2 = n0 = ordinary index of refraction
n3 = ne = extraordinary index of refraction
The electrooptic tensor shows that many of the elements in the
matrix are zero and others have equal value.
Substituting the matrix
elements into Equation 18 gives:
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Suppose that an electric field was applied to the crystal in the
z direction.
The ellipsoid equation would become
+ r13E z
x2 +
+ 'l3Ez
y2 +
+ r E
,
33 z
z
=
1 .
(20)
Since the principal axis did not change, there are no cross terms and
the new indices can be determined directly from the coefficients b^,
t>2 , and b g :
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Therefore, the refractive index for an optical beam polarized in the
x direction is given by
1
n
+
r
1 + n
E
13 z
o
(24)
x1 aE
13 z
Differentiating this equation with respect to the electric field E
3n
3E
which, assuming
x
-1
2
z
.
2
B v3/2
(1 + n r19E )
O
13
no r13 '
(25)
Z
^qTi 2 E z << 1, can be reduced to
3n
BE
i
-1
x
2 0
z
a
3
(26)
13
The refractive index for the x~polarized light is approximately equal
to
n
= n
x
o
1
3
_
n r19E
.
j ° 13 z
(27)
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Similarly, the indices for the y and z polarizations are approximately
equal to
n
y
n
z
(28)
n
r
= n - 1 n 3 raoE
o j o 33 z
(29)
For lithium niobate the magnitude of rgg is over three times larger
than r^g.
For this reason, z polarized light is often used with z
oriented electric fields to insure maximum index change for a given
electric field.
Figure 14 shows two examples of electrooptic phase
shifters which use z-polarized light and z-oriented electric fields.
Note that one device uses IE (Transverse Electric) polarized light
and the other uses TM (Transverse Magnetic) polarized light.
In
integrated optics TE polarized light refers to light polarized
parallel to the surface of the crystal and TM polarized light refers
to light polarized perpendicular to the surface of the crystal. Figure
15 shows two electrooptic modulations that use the smaller
electrooptic coefficient
Table 1 summarizes the crystal cuts and
modulation directions as well as the corresponding electrooptic
coefficients.
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38
.J
x
ELECTRIC
FIELD Ez
POLARIZED
LIGHT
y
ELECTRIC
FIELD
POLARIZED
LIGHT
/
FIGURE 14.
ELECTROOPTIC PHASE SHIFTERS UTILIZING r „ ELECTROOPTIC
COEFFICIENT
dd
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FIELD
TE
POLARIZED
LIGHT
mm.
isM
ELECTRIC
FIELD
y
POLARIZED
LIGHT
FIGURE 15 . ELECTROOPTIC PHASE SHIFTERS UTILIZING r1Q ELECTROOPTIC
COEFFICIENT
13
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40
TM nodes
TE Dodea
Modulation
Modulation
Crystal
Cut
X
X
Propagation
Direction
Z
Y
Ex
b
n=n0
n=n0
n»n0
n»n0
r-r2i-0
r°r22
I“rl1“0
*“r12“r22
n«n0
n«n„
r-r31»0
I
Z
n=n0
r-ru
Y
*“ *•33
r=r12— r22
n=n#
X
n=n0
X
r“r22
Z
Y
n=n0
r=ru
TABLE 1.
=0
Ey
n=n0
r-rjl-0
r=ri3
t“ r2i*‘0
r=r22
r“r22
r“r33
n=ne
n-nD
1 = 1 3 2 “°
r“r23“r13
r«r13
n-n0
n=n0
n=ne
n=n0
Ez
n=n0
n=n0
n=n0
r=r32=0
Z
Ez
Ex
n-ne
r»r31«0
n=n0
r=r23=r13
n=ne
r«r33
n=n8
r=r33
REFRACTIVE INDICES AND ELECTROOPTIC COEFFICIENTS FOR
LITHIUM NIOBATE.
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41
The Directional Coupler
If two parallel channel waveguides are fabricated close together
in such a way that their evanescent fields overlap, the optical
signals will couple between the waveguides.
This is the fundamental
principle of the directional coupler, shown in Figure 16.
The amount
of light that couples between them is dependent on: (1) the distance
between the waveguides,
(2) the interaction length, and (3) the index
of each of the waveguides and the substrate.
The first two parameters are determined during the design phase
and are fixed once the coupler is fabricated.
The index of the
waveguides, on the other hand, can be adjusted using the electrooptic
effect described in the previous section, thereby making a voltagecontrolled optical coupler.
The coupling between waveguides can be described using the coupled
wave equations13
= j ^
dz
A
- jKA
dA2 = -i APA,- jKA, ,
dz
2 2
where
(30)
2
(31)
and A 2 are the amplitudes of the optical fields in waveguides
1 and 2 respectively, A0 is the difference in propagation constants,
(f?2 “ Pj.)> of the waveguides, K isthe coupling coefficient, and z
is
the direction of propagation.
in
If all of the light is propagating
waveguide 1 at time t=0 then the power in each of the waveguides.
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42
/
d
/
r *
DISTANCE BETWEEN
WAVEGUIDES
INTERACTION LENGTH
SUBSTRATE
OPTICAL
WAVEGUIDES
FIGURE 16.
OPTICAL DIRECTIONAL COUPLER
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43
after propagation over the length of the interaction region L, is
given by
14
(32)
P2 = A2A2
* A '
2K
1
P1
A 1A 1
(33)
1 " P 2 '
assuming that the optical power is normalized to 1.
The amount of
coupling between waveguides can be controlled by adjusting the
propagation constants of the waveguides using the electrooptic effect.
The propagation constant is given by
2
where
nn
(34)
X is the freespace wavelength and n is the effective index in
the waveguide as calculated in an earlier section.
It was also shown
that the index could be changed by applying an electric field.
From
Equation 27
(35)
where E is the electric field and r is the appropriate electrooptic
coefficient.
E~V/d.
A voltage V applied to the electrodes creates a field
If the electrodes are oriented to obtain positive and negative
fields, as shown in Figure 17, then one index will increase and one
will decrease.
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44
METAL ELECTRODES
ELECTROOPTIC
MATERIAL
TM POLARIZED LIGHT
ELECTRODES
"1
= "o “
r\2 =
nQ +
an
ELECTRIC FIELD
FIGURE 17.
ELECTRICALLY CONTROLLED DIRECTIONAL COUPLER
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45
As an example, consider the directional coupler propagating TM
polarized light shown in Figure 17, with a voltage on one of the
electrodes. The voltage generates an electric field which decreases
the index of waveguide
1
, and increases the index in waveguide
ni =
1
+
o
n0 = n
—
roj®.
- £ n ^ raaE .
2
°
z
o
2
2
2
.
<36)
(37)
where rgg is the electrooptic coefficient for z-cnt crystal with TM
polarized light and an electric field in the z direction.
The propagation constants are then
1
3
2n(n + _ n
raaE )
2nn 1
o
_ o
33 z
= ____ =_________ t-----------
a
2nn.
P2 =
2n(n
1 =-
o
- £ n ^ raaE )
. o
33 z
f----------
(38)
(39)
and the difference is given by
3
Ap = p 1 - p
1
= 2nno
1
r33E z .
(40)
X
Substitution of the relation given by Equation 40 into Equations 32
and 33 gives the coupling power as a function of electric field.
Figure 18 shows an example of a directional coupler and its
coupling as a function of voltage.
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46
Asymmetric Coupling
Looking at Equation 40 one sees that the sign of E simply changes
the sign of A0.
However, as shown by Equations 32 and 33, the term is
squared so its sign information is lost.
This means that the coupling
for an electric field +E is identical to the coupling for a field -E.
Therefore, as shown in Figure 18, the coupling is always symmetric
about zero.
In a sampler this leads to two problems.
The obvious one
is that the sampler cannot distinguish between positive and negative
voltages on the electrodes.
Additionally, since the shape of the
coupling curves are flat as the voltage goes through V=0, a small
change in voltage will not change the amount oflight
There are anumber
of
thatis coupled.
ways to overcome these twoproblems.
A
bias
voltage can be used to shift the coupling to a more linear region of
the coupling curve.
However, this method requires extra electrodes
and due to space limitations is probably not practical for the
sampler.
Another way to overcome the symmetric coupling problem is to
fabricate the two waveguides with different widths 14, as shown in
Figure 19.
Increasing the width of the waveguides increases its
effective index.
Rewriting Equations 36 and 37 yields
(41)
nl = n10 + “ n10 r33E z
(42)
n2 = ”20 " “ n20 r33E z '
where n^Q and n2 0 are the effective indices for waveguides
respectively.
1
and
The propagation constants are then
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2
47
>•=0. 8 40 m
Nl= 2.207974
N2= 2.207974
Wi = 4. 0 0 m
W2=4. 0 0 m
LEN=2. 0 0 mu
d=3. 00 m
3 0«80E-12
N B - 2 . 2 04 0
KflP=767.0
•20.0 -15.0 -10.0
.
5 0
0 .0
5.0
10.0
15.0
20.0
Voltage
FIGURE 18.
VOLTAGE-TO-COUPLING CURVE
FOR A SYMMETRIC COUPLER
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48
INPUT
FIGURE 19. ASYMMETRIC COUPLER
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49
2
jrn,
1
(43)
2
nn,
2
(44)
and the difference is given by
Again, substitution of tbis relation in the coupling equations
gives the coupling power as a function of electric field.
however, the coupling is not symmetric about zero.
Now,
Figure 20 shows an
example of the coupling response of an asymmetric coupler.
The coupler shown in Figure 19 clearly offers significant
advantages over symmetric couplers in this sampler application.
First, a small change in voltage will significantly change the amount
of coupling and thus will be easier to detect.
Second, one can
measure the difference between positive and negative voltage across
the electrodes.
For this reason, the couplers that will be described
in the next few sections will be asymmetric.
Coupling Coefficient
The coupling coefficient K, used in the coupling equations in the
last section, has been derived and calculated a number of ways for
dielectric waveguides.
Most methods are derived, at least in part,
from the work of Marcatili 1 4 .
In the classic paper, Marcatili solves
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50
>.=0. 840 m
N l = 2 . 207 9 7 4
N2=2.208285
Wl=4. 0 0 m
W2=5. 00 m
LEN=2.00mm
d=3. 00 m
r=30.80E-12
N B = 2 . 204 0
KAP=767. 0
■20.0 -15.0 -10 .0
-5.0
0 .0
5.0
.
10 0
15.0
20.0
V o 11 age
FIGURE 20. 'VOLTAGE-TO-COUPLING CURVE FOR ASYMMETRIC COUPLER
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51
Maxwell's Equations in closed form to find the transmission properties
of a rectangular dielectric waveguide, surrounded by several
dielectrics with smaller refractive indices, as shown in Figure 21.
In his analysis he assumes that no power is propagating in the shaded
areas and therefore doesn't require that the fields in Region 1
properly match the fields along the shaded areas.
A reasonable
assumption of field distributions in a dielectric waveguide is that
the field in Region 1 varies sinusoidally in both the x and y
directions.
In Regions 2 and 4 the fields vary sinusoidally along x
and exponentially along y.
In regions 3 and 5 they vary sinusoidally
along y and exponentially along x.
Use of these field distributions
yields the transverse propagation constants, k x and ky, as the
solutions to the following transcendental equations.
k a = pn - tan 1 k
X
Z v
- tan
1
k
(46)
E
x 5
2
-1
k b = qn - tan
y
n2
___
2
-1
k n, - tan
n4
2
k q.
(47)
2
nl
“2
where
53
5
q2
4
(48)
Ikx3 I
5
ZL
- k x 3
A3
5
(49)
Iky2 1
4
- ky
A2
4
and
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52
T
b
±
y
A
h - aH
FIGURE 21.
►x
CROSS-SECTION OF RECTANGULAR WAVEGUIDE USED IN
MARCATILIS ANALYSIS
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In these equations, a and b are the dimensions of the rectangular
waveguides and p and q represent the mode numbers.
£ 5 , t\2> and
*14
The variables €3 ,
measure the penetration depth of the field components
in the regions 3, 3, 2, and 4 respectively.
These equations cannot be solved exactly in closed form.
However,
a computer can be used to solve the equations for kz and ky
iteratively given the refractive indices, the physical dimensions and
the mode numbers.
Marcatili offers an approximation, which applies
for well-guided modes in which most of the power travels within medium
1
, that permits the transcendental equations to be solved in closed
form.
However, for directional couplers, in which one relies on the
fact that the modes are not well guided, the approximation may not be
valid.
The propagation constant of the waveguide is given by
(51)
where
(52)
The coupling coefficient of a waveguide coupler consisting of two
rectangular waveguides, was also derived by Marcatili as
- d
K =
2kx2 «5 “ P I
k
z
t5
.
(54)
a
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54
This expression is valid for both TE and TM polarization.
As might be
expected, the coupling between two waveguides decreases exponentially
with the ratio of the waveguide separation, d, to the field
penetration depth in medium 5,
Marcatili's expression for the
coupling coefficient is not very accurate for weakly guiding
modes 17.
Kuznetsov was able to derive the coupling coefficient
without making the assumption of well-guided modes that Blarcatili used
in his derivation.
The improved expression for the coupling
coefficient is given by
2 kx 2
5
S exp
(55)
K = --
This expression was derived assuming TE coupling.
The expression
for TM coupling is similar but has the ratios (nj/ng)^ and (n^/ng)^
throughout the expression.
For integrated optic waveguides made in
lithium niobate, these ratios are typically
neglected.
1.001
and can be
Therefore, for all practical purposes the expression for
the coupling coefficient given in Equation 55 is valid for both TE and
TM modes.
The coupling coefficient can be used to calculate the coupling
length, L, required for complete energy transfer from one waveguide to
the other.
The coupling length is given by
(56)
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55
Often, an optical switch is designed such that with no voltage
applied, light injected into one waveguide will completely transfer to
the other waveguide.
Equation
56.
This requires a coupling length L given by
As an electric field is changed the light can be
transferred back into the first waveguide.
Microwave Strinline
This section describes an electrode structure that has the
capability of propagating RF and microwave type signals.
These
electrodes will carry the electrical signals that are to be sampled.
They will be fabricated and positioned to generate the electric fields
that will induce the electrooptic effect in the crystal and provide
for the sampling.
This section is divided into three parts.
The first part
discusses traveling wave electrodes which will lay the groundwork
the sampler discussion in the next chapter.
for
The second part describes
the design considerations for maintaining the RF impedance.
Traveling Wave Devices
Up to this point the electrodes that were placed on the
piezoelectric crystal to induce the electrooptic effect always
contained voltages that were essentially DC in value.
Because of
this, any photon or group of photons that entered the optical
waveguide would see a constant index of refraction through itsentire
propagation down the optical waveguide.
If the voltage on the
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56
electrodes changed, as it would if one changed the status of an
optical switch, then it was changed at a slow enough rate that any
group of photons would again think the voltage was constant.
type of modulator is considered a lumped electrode.
This
Its frequency
response is limited by its electrode capacitance.
A second type of electrode, which was originally proposed by
Kaminow 18, is referred to as a traveling wave modulator in which the
electrode is an impedance matched stripline which has the capability
of propagating a voltage waveform.
The voltage on the stripline can
be represented as a function of position, z, and time, t, by the
equation:
v(x,t) = V
e
sin
(t +
T
e
— ) +
v
0
o
(57)
e
where V e is the amplitude, Te is the period and v e is the velocity of
the electrical signal.
The term f*0 represents the relative phase at
t=0 .
A typical traveling wave modulator is shown in Figure 22.
In the
usual case the light and the electrical signal are traveling in the
same direction.
A photon entering the optical waveguide at time tQ
will encounter a voltage induced propagation constant which changes as
a function of time and position.
The voltage as a function of
position is given by:
v(x,t ) = V sin
o
e
o
(58)
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57
C D
COPLANAR
STRIP LINE
MATCHED
TERMINATION ,
ELECTRO-OPTIC
CRYSTAL
DRIVING
TRANSMISSION LINE
FIGURE 22. TRAVELING WAVE MODULATOR
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58
where v Q is the velocity of the optical signal.
Note that if the
electrical and optical signal are traveling at the same velocity.
i-e» v e = vc , any given photon sees a constant voltage, and therefore
a constant index, as it propagates down the optical wavegnide.
A
photon that arrives a little later, i.e. t + At, sees a different
voltage.
However, the voltage again appears to remain constant as the
optical signal propagates down the wavegnide.
This velocity matching concept using a traveling wave electrode
has been exploited for a number of integrated optic devices.
Marcatili of Bell Laboratories, describes how this principal can be
applied to generate a fast optical gate for generating, modulating,
multiplexing and demultiplexing short light pulses 1 9 .
It was shown earlier that the amount of coupling between two
optical waveguides was determined in part by the difference in
propagation constants,
A0.
It was shown that the propagation
constants could be controlled by the electrooptic effect using the
electric field generated from the voltage on the electrodes.
The
difference in propagation constants was given by
AP =
.
(59)
Ad
where n is the effective index of the optical waveguide, r is the
appropriate electrooptic coefficient, d is the distance between the
electrodes and the ground plane V is the applied voltage, and X is the
optical wavelength.
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59
The same equation applies to the traveling wave device except now
the voltage is a function of time and position, as given above in
Equation 58.
Substituting Equation 58 into Equation 59, the
difference in propagation constant that is seen by a photon entering
the guide at time t0 is given by:
2nn^rV
Af)(x,t ) =
o
sin
(60)
\d
v
e
v
e
o
The coupling equations given earlier in Equation 30 and 31 cannot
be solved analytically when A0 varies as a function of position.
One
way to get a good approximation of the coupling is to determine the
average Ap that a group of photons see and use this average in the
coupling equations.
The average Ap that a photon entering the guide
at time t0 "sees" over an interaction length L is given by:
, 2ira3 rV
AH<t0 > =
“1
L
o
+L.
(t
sin
dX
T
e
0
v
dx
(61)
e
The power coupled from the main optical waveguide to the output
optical waveguide can be determined by substituting the average Ap
into the solution of the coupling equations.
The optical power out of
the output waveguide is given by:
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Again, assuming the input optical power is normalized to 1, the amount
of light remaining in the main waveguide is given by:
P,(t ) = 1 - P 0 (t )
1
o
z
o
where K is the coupling coefficient.
(63)
These modified expressions for
the power out of the optical waveguides which use the average
propagation constants, will be used in the next chapter to describe
the integrated optic sampler.
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61
Electrode Design
The purpose of the electrode structure in an integrated optic
device is to carry the electrical signal and to confine its electric
field.
Proper design permits the electric field to modify the
propagation constant of an optical waveguide efficiently by means of
the electrooptic effect.
The position and orientation of the
electrodes relative to the optical waveguide determine how efficiently
the electric field can modify the index of refraction.
This section
shows how the electrode position and structure affect the operation of
a directional coupler.
In this configuration, as explained in the
directional coupler section, the electrodes are placed above each of
the waveguides in what is called the push-pull configuration so that
the electric field tends to increase the index of refraction in one
waveguide and decrease it in the other.
There are primarily three things to consider when designing the
electrode structure.
First, the electric field needs to be generated
in the proper orientation.
In an anisotropic material, such as
lithium niobate, the orientation of the electrode relative to the
crystal cut determines which electrooptic coefficient is used.
In
lithium niobate the rgg coefficient is the strongest and is therefore
often used when designing devices.
In this case the electrode would
be designed to orient the electric field in the z direction, as shown
in Figure 14.
The second concern is the electrode impedance.
If an electrode is
going to be used primarily with DC voltages, then the impedance of the
structure is not important.
If, however, the electrode is going to be
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62
propagating RF or microwave signals, then the electrode structure
must act like a transmission line and maintain a nearly uniform
characteristic impedance over its frequency of operation.
There are two principal types of coplanar RF striplines that can
be considered for the sampler.
Namely, a symmetric electrode in which
the width of the ground electrode is equal to the width of the active
electrode, and an asymmetric electrode in which the ground electrode
is actually a ground plane, as shown in Figure 23.
The impedance of
the striplines is determined primarily by the width of the active
electrode w and the gap between the active electrode and the ground
plane g.
For lithium niobate a 50 ohm transmission line can be
obtained for a symmetric electrode configuration by making the ratio
of the electrode width to the electrode gap equal to 1.6 20.
asymmetric configuration this ratio is reduced to w/g =
0.6
For an
21.
When the coupler is designed in the push-pull configuration the
electrode gap is approximately equal to the separation between the two
waveguides, d.
As will be shown in the next chapter, the waveguide
separation for typical electrooptic couplers is between 2 and 5
microns.
This ratio will severely limit the width of the electrodes.
This could cause the DC resistance of the electrode to become
unreasonably high and limit the usefulness of the stripline.
There
are other electrode configurations that may prove beneficial.
One
such configuration is shown in Figure 24.
are not in the push-pull configuration.
In this case the electrodes
Instead the electric field
primarily affects only the waveguide directly beneath the stripline
and the index of the other waveguide remains constant.
This will
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63
GROUND STRIP
TRAVELING WAVE
ELECTRODE
OPTICAL WAVEGUIDE
(a)
GROUND STRIP
TRAVELING WAVE
ELECTRODE
(b)
FIGURE 23.
OPTICAL WAVEGUIDE
(a) SYMMETRIC AND (b) ASYMMETRIC RF STRIPLINES ON AN
ELECTROOPTIC COUPLER
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64
GROUND
STRIP
TRAVELING WAVE
ELECTRODE
ELECTRIC FIELD LINE
OPTICAL
WAVEGUIDES
FIGURE 24.
ELECTROOPTIC COUPLER WITH AN ALTERNATE ELECTRODE
STRUCTURE
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decrease the change in propagation constant, given in Equation 40, by
a factor of 4.
Half of the reduction is due to the fact that the
index changes in only one waveguide.
Furthermore, because the
electrodes are further apart, the electric field for a given voltage
is reduced.
This relationship proves to be very important in the
design of the sampler as shown in the next section.
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66
1.
References
Hunsberger, R.G., Integrated Optics: Theory and Technology,
Springer Series in Optical Sciences, (Springer, Berlin,
Heidelberg, New York), 1982.
2.
Tsai, C.S., "Guided-wave acousto-optic Bragg modulators for
wide-band integrated optic communications and signal processing",
IEEE Trans. Cir. and Sys., Vol. CAS-26, No. 12, pp. 1072-1098,
December 1979.
3.
Zernicke, F . , "Fabrication and Measurement of Passive Components",
in Integrated Optics, Topics in Applied Physics, Vol. 7 (Springer,
Berlin, Heidelberg, New York), 1975.
4.
Hocker, G. Benjamin, Burns, William K., "Modes in Diffused Optical
Waveguides of Arbitrary Index Profile", IEEE J. Quantum Electron.,
Vol. QE-11, No. 6 , June 1975.
5.
Hocker, G. Benjamin, Burns, William K., "Mode dispersion in
diffused channel waveguides by the effective index method".
Applied Optics, Vol. 16, No. 1, January 1977.
6
. Hocker, G. Benjamin, Burns, William K., "Modes in Diffused Optical
Waveguides of Arbitrary Index Profile", IEEE J. Quantum Electron.,
Vol. QE-11, No. 6 , June 1975.
7.
8
Adams, M.J., "Three-Layer Dielectric Slab Waveguides", in An
Introduction to Optical Waveguides, (Wiley, New York), 1981.
. Hocker, G., Benjamin, Burns, William K., "Modes
Optical Waveguides of Arbitrary Index Profile",
Electron., Vol. QE-11, No. 6 , June 1975.
9.
in Diffused
IEEE J. Quantum
Hocker, G. Benjamin, Burns, William K., "Mode dispersion in
diffused channel waveguides by the effective index method".
Applied Optics, Vol. 16, No. 1, January 1977.
10. Mason, W.P., Crystal Physics of Interaction Processes, Academic
Press, 1966.
11. Zernicke, F., Midwinter, J.E., "Linear Optics: Wave Propagation
in Anisotropic Materials", in Applied Nonlinear Optics (Wiley
Sons, New York), 1973.
12. Zernicke, F . , Midwinter, J.E., "Linear Optics: Wave Propagation
in Anisotropic Materials", in Applied Nonlinear Optics (Wiley
Sons, New York), 1973.
13. Schmidt, R.V., Alferness, R.C., "Directional Coupler Switches,
Modulators, and Filters Using Alternating DELTA-BETA Techniques",
TREE Trans, on Circuits and Systems, Vol. CAS-26, No. 12, Dec. 1979.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
67
14. Schmidt, R.V., Alferness, R.C., "Directional Coupler Switches,
Modulators, and Filters Using Alternating DELTA-BETA Techniques",
IEEE Trans. on Circuit* and Systems, Vol. CAS-26, No. 12, Dec. 1979.
15. Holman, R., Personal communication, 1985.
16. Marcatili, E.A.J., "Dielectric Rectangular Waveguide and
Directional Coupler for Integrated Optics", The Bell System
Technical Journal, September, 1969.
17. Kuznetsov, M., "Expressions for the coupling coefficient of a
rectangular-waveguide directional coupler". Optics Letters,
Vol. 8 , No. 9, September, 1983.
18. Kaminow, I.P., and Liu, J., "Propagation characteristics of
partially loaded two-conductor transmission line for
broad-band light modulators". Proceedings of the IEEE,
Vol. 51, 1963, pp. 132-136.
19. Marcatili, E.A.J., "Optical subpicosecond gate". Applied
Optics. Vol. 19, No. 9, May 1, 1980.
20. Izutsu, M., Itoh, T . , and Sueta, T., "10 GHz Bandwidth
Traveling-Wave LiNbOg Optical Wavguide Modulator", IEEE
Journal of Quantum Electronics, Vol. QE-14, No. 6 , June, 1978.
21. Sueta, T. and Izutsu, M., "High Speed Guided-Wave Optical
Modulators", Journal of Optical Communications, Vol. 3, No. 2,
1982.
R eproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
CHAPTER III
THE INTEGRATED-OPTIC SAMPLER
In the last chapter it was shown that when two waveguides were
placed in proximity so that their evanescent fields overlapped, the
light would couple from one waveguide to the other.
Furthermore, it
was shown that if the waveguides were fabricated in an electrooptic
material then the amount of coupling could be controlled via the
electrooptic effect.
This principle serves as a basis for the
integrated-optic sampler.
This chapter will show how the directional coupler can be used to
sample an RF or microwave signal which is propagating along a
stripline.
It was hypothesized that when directional couplers, or
electrooptic switches, were placed in series beneath a coplanar
stripline, as shown in Figure 1, the coupling between the two
waveguides would be determined by the local voltage directly above the
coupler.
It was also hypothesized that a short pulse of light,
traveling in a direction opposite to the RF signal, could pass
sequentially through each of the electrooptic couplers causing a small
amount of light to couple into the output waveguides.
The amount of
coupling would be dependent on the local electric fields and thus on
the local voltages.
Output detectors, which are placed at the ends of
the output waveguide, could integrate the energy of the coupled
68
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69
optical pulses in the respective output waveguides in order to
determine the associated instantaneous values of the electrical
signal.
The sampler will require asymmetric couplers in which the output
optical waveguide is slightly wider than the input optical waveguide.
This provides a voltage-to-coupling curve which is asymmetric about
zero volts, as shown bach in Figure 20 of Chapter 2.
This enables the
sampler to differentiate between positive and negative voltages.
Furthermore, the couplers will be designed so that only a small
percentage (<5%) of the light in the input optical waveguide will
couple to the output waveguide.
This will insure that there is enough
light left in the main waveguide for the subsequent sample points.
The first section of this chapter describes the theory of
operation.
The goal here is to develop a set of equations that
describe the output optical signals as a function of the input optical
and electrical signals.
The second section describes the sampling
rate and aperture of the sampler.
The third section considers the
electrical components in the sampler and discusses the signal-to-noise
ratio.
The final section describes the procedure for designing the
sampler based on the theoretical work and the computer models.
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70
Theory of Operation
This section will develop a set of equations that describe the
output optical signals as a function of the input optical signal and
the electrical signal.
This vill be done for a series of four cases.
The first two cases are examples of samplers in that the input
optical signals are short pulses that interrogate electrical signals
as they propagate down the traveling wave electrodes.
original objective of this work.
This is the
The second two cases are more
general examples in that the optical signals are not pulses but
instead amplitude modulated optical signals.
general application of this device.
This shows a more
It will be shown that this device
not only has the capability of sampling transient electrical signals
but can also be used to sample intensity modulated optical signals.
In this case the electrical signal would be a pulse which samples the
unknown optical signal.
Case 1: Sampler with Arbitrary Sine Wave Input
The first case considers a sampling device where a short optical
pulse propagates down the input optical waveguide and a sine wave
propagates down the traveling wave electrode.
As with the traveling
wave modulators described in the last chapter, the voltage signal is a
function of position, x, and time, t.
If it is assumed that the
voltage is a simple sinewave propagating from right to left, as shown
in Figure 25, then the traveling wave is given by
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
H
ELECTRICAL SIGNAL
ON ELECTRODE
TRAVELING
WAVE
ELECTRODE
INPUT OPTICAL
PULSE
GROUND
STRIP
X=0
X= D
FIGURE 25. SAMPLER EXAMPLE - CASE 1
—j
72
v(x,t) = V fi sin [
+
e
^~) + 0
]
0
,
(64)
e
where V e is the amplitude, T e is the period, and ve is the velocity of
the electrical signal, and
is the relative phase shift at t=0 .
The optical signal is assumed to arrive at the left side of the
device at t=tQ and propagate from left to right.
A perfect optical
pulse can be described by the pulse function
A(x,t) = AQp a [ x - tvc + a/2 ]
*
(65)
2
where Pj)(x) is defined as the rectangular pulse function
PD (x) = U(x + D) - U(x - D) = | J
• |x! < D
'
a is the physical pulse width in meters, A Q is the magnitude of the
optical signal, and vQ is the velocity of the optical signal.
In the last chapter it was shown that the amount of light that
coupled between the two optical waveguides was dependent on the length
of the interaction region, L, the distance between the waveguides, d,
the wavelength of the optical signal, X, the coupling coefficient, K,
and the various indices of refraction, n^,
113 ,
and nj,.
shown that the coupling could be described in terms of
in propagation constants of the two waveguides, A0.
It was
also
the difference
Furthermore, it
was shown that the propagation constant could be controlled via the
electrooptic effect.
In the traveling wave section of the last
chapter it was shown that as a photon propagated down the waveguide,
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73
it encountered a propagation constant that changed as a function of
time and position.
For the simple sine wave case, the voltage on the
traveling wave electrode that a photon encounters is given by
v(x,t
o
) = V
e
sin [ i^r(t
LJl
o
e
+
v
v
e
o
+ J®
o
1
J
(67)
»
where tQ is the time that the photon enters the waveguide. Note that
the sign of the term x/vQ changed from Equation 58 of the last chapter
due to the fact that the optical and electrical signals are now
propagating in opposite directions.
The change in propagation constant was given in Equation 40 as
Ap =
_2nn r .E-
,
. (68)
where n is the index of the optical waveguides, r is the appropriate
electrooptic coefficient, and E is the electric field through the
waveguide.
The electric field produced by the electrodes is
approximately E = V/d where V is the voltage on the electrodes and d
is the distance between the electrodes.
The difference in propagation
constants of the two waveguides as a function of time and position is
given by
Aj)(x,t0 ) =
2
3
nn r
X d
0
sin
2 H (t
+ 2_ +
T
o
v
e
e
£_ ) + *
v '
Fo
o
(69)
Since the propagation constant changes as a function of position and
time, the coupling equations cannot be solved analytically.
However,
as described in last chapter, an average propagation constant can be
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74
calculated by integrating A0 over the interaction length, L.
The
average value of A0 that a propagating optical signal encounters is
given by
L
f A0
A0(t ) = 1
0
L
oJ
(x,t ) dx.
°
(70)
Substituting Equation 69 into 70 gives
„
2
L
3
nn r
J sin
A0(to ) =
2H , t + S_
T u o
v
e
e
+ 5_ %
v
o
dx.
(71)
After performing the integration, this becomes
W
)=
rY. Vea
~ 2 ’,n
t
Lid
0
cos I -
( t
e
2n
cos [
t"
+
eq
(72)
to + 0o ]
e
where
v v
e o
eq
v
e
+ v
(73)
o
Using trigonometric identities to combine the terms with t
A0 (tQ) =
0
*o
T
2
e
n
v
sin
eq
JtL
Tv
e eq
2
yields
nt
(74)
sin
T v
e eq
where
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
2nn3 rV_
(75)
Po =
Ad
This again is the average difference in propagation constant
enconntered by a photon during its propagation dovn the first
coupler.
The variable tQ is the time the photon enters the main
channel waveguide.
To determine the optical intensity out of the
first output waveguide one must substitute Equation 74 into the
solutions to the coupling equations given in Equations 32 and 33 in
the last chapter.
However, in this case the input optical power
cannot be arbitrarily normalized to
a pulse function.
1
since the optical signal is now
The optical intensity from the first output
waveguide is given by:
•
•
2
i
a
Ap (t )
. 2
sin
EL
1
0
+
2
K
. (76)
P,,(t ) = AA (t )
12
o
o
1
+
Ap(t )
o
2K
where again E is the coupling coefficient and L is the interaction
length.
Under the assumption of a lossless optical waveguide, the
intensity of light remaining in the main optical waveguide after the
first coupler is simply the initial input light minus the light out of
the first coupler.
In other words
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For these equations, the first subscript refers to the coupler number
and the second subscript refers to the main (1 ) or output (2 )
waveguides.
It is important to note that these two output powers are
given as functions of time, tQ , which is again the time the light
enters the main channel waveguide.
Therefore, as time changes,
i.e. the electrical and optical signals move, the amount of light
that couples into the output waveguides changes.
However, the optical
signal doesn't arrive at the detector until it has had a chance to
propagate down the output optical waveguide.
Therefore, assuming a
lossless optical waveguide and an ideal optical detector, the actual
detected signal would be a delayed version of Equations 76 and 77.
In these derivations the equations are all referenced to the time
that the photon initially enters the main optical waveguide, t0 .
The
optical power was described in Equation 65 as a function of time
and position.
However the photon enters the waveguide at z = 0.
Therefore, the equation for the optical power that must be used in the
Equations 76 and 77 is given by:
“ *(V “ U o
'l [ 1/2 - *o] •
(7S)
2
This can be substituted into Equations 76 and 77 to give expressions
for the power out of the first optical coupler.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
77
The amount of light that is coupled at the second coupler is
determined in a similar fashion.
The limits of integration, however,
must be changed when averaging A0.
For the second coupler the average
Ap becomes
D + L
AP 2 <to ) =
-
J
A0 <x>to ) dx
(79)
,
where x=D is the location of the second coupler as shown back in
Figure 25.
For a pure sinusoidal signal this becomes
—
P
T v
AP„(t ) = — --- 6 C3. sin
2
°
L 2n
2
nt
2nD
nL
T v
e eq
T v
e eq
sin
nL
(80)
T v
e eq
For D=0 this equation reduces to Equation 74.
Another major consideration in deriving a function for the coupled
light is the amount of light available for coupling at a given
coupler.
In the first coupler it was assumed that the light in the
input waveguide was a ideal pulse with amplitude AQ .
However, since
the first coupler couples some of the light out of the input
waveguide, there is less entering coupler
1.
2
than was entering coupler
Therefore, the expression for the amount of light that couples out
of the second coupler is dependent on how much light is available
after the first waveguide.
This is given by
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
78
■
1
a
2
. 2
sin KL
P22(V
a
P,,(t )
11
AW
+
1
'
2K
, (81)
0
1
+
^
2
(to>
2
K
and the amount of light remaining after the second coupler is given by
P2 1 (to> " Pll'to> - P22 (t„>
•
<82)
Similar equations can be derived for the remaining couplers in the
sampler.
Figure 26 shows an example of the integrated optic
this example the electrical signal is a sine wave with
amplitude and a period of 600 picoseconds (1.67 GHz).
sampler.
a
2
In
volt
The optical
pulse is 15 picoseconds in duration with a normalized intensity of
1.
The top graph shows the values of the voltage and optical signals
at t=0.
The sampler consists of three couplers each placed 10
millimeters apart.
The output consists of three optical pulses that
represent the light out of each of the couplers.
The delay due to the
optical propagation down the output waveguides has been neglected.
The three pulses are simply delayed by the propagation time of the
input pulse down the main optical waveguide.
symbols (x) represent the voltage samples.
The output voltage
They are calculated using
the DC characteristics of the coupler which are stored
table.
in a look-up
The calculations take into consideration not only the
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79
O
o
A(t)
- CO
tom
C .
o
v(t)
•—i
•O
133. 4
66. 7
Time
2 00. 1
266.8
333. S ™
(c i c o s e c o n d s )
a
o
in
cn
“ n
- in
lh ™
a
a
a.
66. 7
133. 4
Time
200. l
fO
266. 6
333.5 '
(picoseconds)
X=0. 8400m
Nl=2.207974
N2=2.207974
H 1=4. 00m
N2=4. 00m
LEN=1.00mm
d = 5 . 00 m
r=30. 80E-12
KflP=2l9. 00
FIGURE 26.
INPUT AND OUTPUT SIGNALS FOR AN INTEGRATED OPTIC SAMPLER
COMPRISED OF THREE SYMMETRIC COUPLERS. THE INPUT
OPTICAL SIGNAL IS A 15 PICOSECOND PULSE AND THE
ELECTRICAL SIGNAL TO BE SAMPLED IS A SINE WAVE.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
non-linearity of the voltage-to-coupling curve but also the fact that
some of the light is removed from the main waveguide at each coupler.
Note in these examples the sampler cannot distinguish between
positive and negative voltage.
This is due to the fact that the
couplers used in the sampler were symmetric couplers where both the
main optical waveguide and the output optical waveguide have equal
width and refractive indices.
Another consideration in deriving the
equations for output power is the effect of asymmetric couplers on the
sampler.
It was shown in Chapter 2 that if a coupler was fabricated
with asymmetric waveguides, (in other words, waveguides with different
indices), then the coupling curves could be made to be asymmetric
about zero, as shown back in Figure 20.
The difference in propagation
constants for the two waveguides was given in Equation 45 as
Ap =
-
2n
(83)
02
X
where n2Q is the effective index in the main channel and n2 o is the
effective index in the output waveguide.
instead of Equation
68
This equation can be used
in deriving the asymmetric version of the
average A0, which can then be substituted into Equations 76 and 77 to
determine the output optical signals.
Figure 27 shows the output signals of that sampler with asymmetric
couplers.
Note that under this condition the sampler can distinguish
between positive and negative voltages.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
81
A(t)
fO
3)
v(t)
c
o
o.
-o
66. 7
133.4
T 1m e
200.1
266. 8
333. 5 ^
(picoseconds)
o
o
CO
3)
U1
o
o
C
u
C
66. 7
133. 4
T
1m e
200 . 1
to
266. 6
333.5 '
( p 1 c o s e c o n d s ))
>>=0. 8 4 0 0 m
Nl=2.207974
N2=2.208285
Nl=4. 0 0 m
H2=5. 0 0 m
LEN=1.00mm
d=5. 0 0 m
r=30. B 0 E -12
KRP=219.00
FIGU R E 27.
I NPUT A N D O U T P U T S I G N A L S FOR A N I N T E G R A T E D O P T I C S A M P L E R
C O M P R I S E D O F T H R E E A S Y M M E T R I C COUPLE RS. A S H O R T O P T I C A L
P ULSE IS I N T E R A C T I N G W I T H AN E L E C T R I C A L SINE WAVE.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
82
CO
0. 5
U
0)
v(t)
0
0
0
66. 7
200 . 1
266. 6
(picoseconds)
133. 4
0. 050
Time
333. 5*?
o
<o
0.025
,0. 000
Intensity
o
>
_0.0
Intensity
Alt)
66. 7
266. 8
200 . 1
i
c
o
s
e
c
o
n
d
s
)
(c
133. 4
Time
333. 5°?
X=0. 8400m
N 1=2.207974
N 2=2.208285
W1 =4. 00m
H2=5. 00m
LEN=1. 00mm
d=5. 00 m
r=30. 80E-12
KRP=219. 00
FIGURE 27 (Continued)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
33
CO
Intensity
A(t)
U
O)
LO
d
0
y(t)
O
>
o
d.
0 .0
66. 7
133. 4
Time
200 . 1
m
266. 8
333. 5 '
(picoseconds)
o
in
m
o
o
O)
- in
o
0
o
>
o
<r>
66. 7
133. 4
T im e
200.1
266.8
333.5 '
(c i c o s e c o n d s )
X.=0. 8 4 0 0 m
N l =2.207974
N 2 =2.208285
Hl=4. 0 0 m
N2=5. 0 0 m
LEN=1.00mm
d=5. 0 0 m
r=30.80E-12
KflP=219.00
FIGURE 27 (Continued)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
84
Case 2: Sampler with Electrical Pulse Input
The second case is also considered a sampling example since,
again, the optical signal is a square pulse.
The electrical signal in
this case is also a square pulse, which will demonstrate the device's
capability of sampling transient electrical signals.
The electrical
signal can be represented by the pulse function
v(x,t) = V e p ^ [ tve + x - xe ] *
(84)
2
where V e is the amplitude, b is the physical length of the electrical
pulse in meters, and xe corresponds to the physical position of the
electrical pulse when the optical pulse arrives at the device, as
shown in Figure 28.
As in case 1, the optical pulse is assumed to arrive at the left
side of the device at t=t0 and propagate from left to right.
The
optical pulse can be described by the pulse function
A(x,t) = A q p fi
[ x - tVo + a/2 ]
,
(85)
2
where again A Q is the amplitude of the optical signal, v Q is the
velocity of the optical pulse in the waveguide, and a is the physical
length of the pulse in meters.
Assuming that the electrical signal is a square pulse, a photon
that propagates down the waveguide encounters one of two possible
voltages, 0 or V 0 , and therefore one of two propagation constants.
For a symmetric coupler, the difference in propagation constant at any
instant in time is either given by
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
H
ELECTRICAL PULSE
I
TRAVELING
WAVE
ELECTRODE
INPUT OPTICAL
PULSE
GROUND
STRIP
X = 0
F I GURE 28.
X = D
S A M P L E R E X A M P L E - CASE
00
cn
86
(86)
Ap = 0
for v=0 , or
o
Ap =
(87)
for v=V0 .
In order to determine tlie amount of light in the output
waveguides, one must calculate the average Ap that a photon
experiences as it propagates down the main optical channel.
This
again can be approximated by integrating the Ap over the interaction
length, L.
For the first coupler
L
Apx (t)
PQ
= 1
Pb [ tve + x + xe ] dx *
L
(88)
2
o
where P0 is given in Equation 75.
Similarly, for the second coupler
D + L
Ap,(t) - i p
2
_
o
L
Pb [ tve + * + xe ] dx
r2
(89)
D''
Using the discussion from chapter 2, one can show that for an
asymmetric coupler these average Ap are given by
L
Pfe. ttve + x + xel
o
dx , (90)
2
and
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Substituting these equations into the solution of the coupling
equations gives an expression for the optical intensities out of the
couplers.
The light out of the first coupler is given by
1
■
2
*
2
APl(to>
sin
Pl2 (t)
lAc l
Pa
[
2
X<
tv
°
1 4
X
T-
EL
2
K
(92)
+ - ]
2 J
5 F i (to)
1
+
2
K
The light remaining in the main channel waveguide after the first
coupler is given by
Pll(to> = ,Ao |2 Pa t x " tvo + a/2 ] " P12(V
2
(93)
The light out of the second coupler is given by
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The light remaining in the main channel after the second coupler is
given by
P21(to> * PU <to, - P22('„> '
(>5>
Figure 29 shows some examples of the input and output signals.
Case 3: Intensity Modulated Optical Signal and a Square Electrical
Pulse
In this third case, the optical signal is an intensity modulated
signal and the electrical signal is a short pulse, as shown in Figure
30.
This is an example of an sampler that samples optical signals
with an electrical pulse.
In this case the optical signal is
represented by an intensity modulated signal given by
1
A(x,t) = A 0 [l + f(x,t)]’
where A Q is the magnitude,
modulation function.
sinewave with
100%
0>o
e
jw t
° ,
(96)
is the optical frequency and f(t) is the
If the modulation function is given by a simple
modulation, then the amplitude is given by
R eproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
89
O
A(t)
m
v(t)
3)
in
c
V
o.
-i
66. 7
133. 4
200 . 1
266. 8
Time
(c ic o s e c o n d s )
■o
.
ro
333. 5 '
o
in
o
o
ro
o d
<D °
o
>
66. 7
.
266. 8
133. 4
200 1
Time
(c ic o se co n d s)
CO
333.5 i
>.=0. 8 4 0 0 m
N1= 2 .2 07 97 4
N 2 = 2. 208285
Wl=4.0 0 m
W2=5. 0 0 m
LEN=1. 00mm
d=5. 0 0 m
r=30.80E-12
KRP=219.00
FI GURE 29.
I NPUT A N D O U T P U T S I G N A L S FOR T H E S A M P L E R - CASE 2.
A S H O R T O P T I C A L P U LSE I N T E R A C T S W I T H A S Q U A R E
E L E C T R I C A L WAVEF O R M .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
90
A(t)
CO
v(t)
•h
c
I-I
— i
66. 7
133.4
Time
200.1
266. 6
-o
.
CO
333.5 '
(picoseconds)
o
m
o
r>
u
4-<
- in
in™
U)
d
o
o
o
>
o
o.
66. 7
133. 4
Time
266. 8
333.5 '
(picoseconds)
X=0. 8 4 0 0 m
Nl=2.207974
N 2=2.208285
Wl = 4. 0 0 m
W2=5. 0 0 m
LEN=1. 00mm
d=5.00 m
r=30. 80E-12
KRP=219.00
FIGURE 29 (Continued)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
H
INTENSITY MODULATED
OPTIC SIGNAL
ELECTRICAL PULSE
TRAVELING
WAVE
ELECTRODE
H— T°— H
GROUND
STRIP
X = 0
F I G U R E 30.
X = D
SAMPLER EXAMPLE - CASE 3
ID
92
A(x,t) = A o
1
+ s i n j ^ t + x_ ) + d ] I
e
(97)
vo
where TQ is the period of the modulation function, v 0 is the optical
velocity, and
1> is the relative phase of the modulation.
Everything
can again he referenced to the time that the photon enters the
waveguide, tQ .
The optical signal can then be given as only a
function of time tc since, by definition, x=0 at t=t0 .
The intensity
of the optical signal into the main waveguide is then given by
Another consideration is how much of the light will be coupled into
the output waveguides.
Since the electrical signal is a pulse
function the discussion from Case 2 applies and the average A{) is
given by
L
AfljU) =
Pfe. [tve+ * + xe]d x * (99)
.
o
2
Substituting this into the solution of the coupling equations, along
with Equation 98 gives
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
93
.2
sin
1 +
KL
AW
2K
(100)
P 1 2 (t)=lAo |2[1 + sin( — 11 + * } ]
+
1
2K
and
P 1 1 (t) = IA0
|2
[ 1 + sin<
t +
] ~ p1 2 (t) '
(lOD
Pe
For the second coupler the difference in propagation constant is given
by
D + L
V
ad t*■ \
2it,
. ,it<
3
3. o
^2 o = ~ (n10” n20 7 10 + n20 )rA
pb [tove + x " xe]dx* (102)
La
A
2
D
The power coupled out of the second coupler is given by
i
. 2 KL
1
sin
P 2 2 (to> "
+
A P2 (to )
2K
(103)
P11(V
1
+
AP2 (to>
2K
and the light remaining in the main waveguide after the second coupler
is given by
P21(to> - ?11<V - ■ W V •
<104)
Figure 31 shows some examples of this case.
R eproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
94
CO
A (t )
u
0)
o o
o
o
>
133.4
Time
200.1
266. 8
333.5 •
( p i c o s e c o n d s ))
o
u
O)
o
d
<U °
o.
66. 7
266. 8
200 . 1
( p ii c o s e c o n d s
133. 4
Time
333.5 '
X=0. 8400m
Nl=2.207974
N2=2.208285
W1 = 4 . 0 0 m
W2=5.00m
LEN=1.00mm
d=2. 0 0 m
r=30.80E-12
KflP=1432.00
FIGURE 31.
I NPUT A N D O U T P U T S I G N A L S FOR T H E S A M P L E - C A S E 3.
AN INTENSITY MODULATED OPTICAL SIGNAL BEING SAMPLED
BY A S H O R T E L E C T R I C A L PULSE.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
95
A(t)
<n
v(t)
4->
u
O)
a
o
o
o
>
o
■o
—
o.
66. 7
133. 4
Time
200 . 1
266. 8
I
•
CO
333.5
'
(c i c o s e c o n d s ))
o
o
o
to
u
O
-
CD
o a
+J
o —<
4->
0
>
o
o
o
66. 7
133. 4
Time
200.1
266.8
333.5
'
(c i c o s e c o n d s )
X=0. 8 4 0 0 m
N1 =2.207974
N2=2. 208285
H l=4. 0 0 m
H2=5. 0 0 m
LEN=1. 00mm
d=2. 0 0 m
r=30. 80E-12
KflP=1432.00
FIGURE 31 (Continued)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
96
Case 4; Arbitrary Optical and Electrical Signals
The fourth case is the most general case.
It assumes an arbitrary
electrical signal on the traveling wave electrode and an arbitrary
intensity modulated optical signal in the main optical waveguide, as
shown in Figure 32.
The main electrical signal traveling on the electrode structure
can be described as
v(x,t) = V 0 g(x ,t) ,
(105)
where V Q is the amplitude and g(x,t) is the arbitrary function of time
t and position z.
The optical signal can be described as
A(x,t) = Ao[l +
where AQ is the amplitude and f(x,t)
function.
i
jw t
f(x,t)]a e ° ,
(106)
is an arbitrary modulation
If the equations are again referenced back to when the
photons enter the waveguide, then the intensity is given by
A(t )A*(t ) =
o
o
|A |2 (1 + f(t ))
o
o
.
(107)
For this general case the average difference in propagation constant
through the first coupler is given by
R eproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ELECTICAL SIGNAL
ON ELECTRODE
TRAVELING WAVE
ELECTRODE
INTENSITY MODULATED
OPTIC SIGNAL
GROUND
STRIP
X= 0
F I G U R E 32.
X= D
SAMPLER EXAMPLE - CASE 4
VO
-vj
98
ao /a.
^1
o
\
^
‘
X
/
—
v
<B1 0 ' W
, Ji/
*X
3
3X
o
g(x,to )dx .
(n 10 + “ 2 0 >1 —
(108)
Ld
The optical signal out of the first optical coupler is given by
“
1
2
*2
1
1
sin2 KL
AW
J.
+
2K
(109)
P 1 2 <‘o> * lAo |2|> + « ‘o>]
1
+
A Pl(to )
2
K
The optical signal remaining in the main optical vaveguide after the
first coupler is given by
,2
p l l (to> - IA„I
[
1
+ « ‘o>] ‘ P 1 2 (to ’ •
(110)
The average difference in propagation constant through the second
coupler is given by
D + L
^2^0* = “ (n10" n20* + ~ (nl03+ n203^r
I
dx *
(HD
U
The optical signal out of the second optical coupler is given by
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The optical signal remaining in the main optical waveguide after the
second coupler is given by
P 2 1 (to> * Pl l (to> - P22<*0> •
(113>
Figure 33 shows some examples of the sampler with arbitrary electrical
and optical signals.
In this example the couplers have been designed
to couple all of the light when the voltage is about
of the light when the voltage is -2 volts.
2
volts and none
Since the intensity is
sinusoidally modulated at a frequency identical to the voltage
waveform, the output of the first coupler is maximum when the two
waveforms are in phase physically at a precise instant in time.
The
two waveforms cannot really be in phase since they are propagating in
the opposite directions.
the first coupler is
+2
However, if the voltage on the electrodes of
volts at the same time that the intensity of
the optical signal is high, then all of light couples to the output
waveguide.
If the velocity of the optical signal is equal to the
velocity of the electrical signal, then the maximum signals will
continue to occur simultaneously at a period equal to the period of
the optical and electrical signals.
Figure 33c demonstrates that for
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
o
A(t)
cn
o
66. 7
133. 4
Time
2 0 0 .1
266. 6
333.5 i
(pi c o s e c o n d s )
o
o
o
D)
o
C
.
<u °
4■>
c
o
o
o
° 0 .0
66. 7
200 . 1
266. 8
(picoseconds)
133. 4
T im e
333. 5
V=0. 8 4 0 0 m
Nl=2.207974
N2=2.208285
Wl = 4. 0 0 m
H2=5. 0 0 m
L E N = 1. 00mm
d=2. 0 0 m
r=30. 80E-12
KflP=l432. 00
FIGU R E 33.
I NPUT A N D O U T P U T S I G N A L S FOR T H E S A M P L E R - C A S E 4.
AN I N T E N S I T Y M O D U L A T E D O P T I C A L S I G N A L IS I N T E R A C T I N G
WITH A SINE ELECTRICAL WAVEFORM TO PRODUCE THREE
O P T I C A L O U T P U T SIGNAL S.
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101
A(t)
<n
Vv(t)
in
c
ft)
c
■o
o
o.
66. 7
266. 8
200 . 1
(picoseconds)
133. 4
Time
— r— - .
co
333.5 '
o
o
o
o
o.
66. 7
133. 4
Time
.
200 1
266. 6
333. 5
(c i c o s e c o n d s )
>.=0. 8 4 0 0 m
Nl=2.207974
N2=2.208285
Wl = 4. 0 0 m
W2=5. 0 0 m
LEN=1.00mm
d=2. 0 0 m
r=30. 80E-12
KflP=1432.00
FIGURE 33 (Continued)
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102
A(t)
o
0 .5
4-»
V(t)
0.0
Intensity
CO
66. 7
133. 4
(c
2 6 6 .8
tn
333. 5 i
i coseconds)
0.500
0.000
Intensity
1.000
Time
200. 1
0
66. 7
.
200 1
266. 8
(picoseconds)
133. 4
Time
333. 5
>•=0. 8 4 0 0 m
Nl =2.207974
N2=2.208285
Nl = 4. 0 0 m
W2=5. 0 0 m
LE N = 1. 00mm
d=2. 0 0 m
r=30.80E-12
KflP=l432.00
FIGURE 33 (Continued)
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103
A (t)
0 .5
v(t)
0.0
Intensity
CO
CO
66. 7
133. 4
266. 6
333.5 i
266. 6
333. 5
(n i c o s e c o n d s )
0.500
.000
Intensity
1.000
Time
200. 1
0 .0
66. 7
133. 4
Time
.
2 00 1
(picoseconds)
> •= 0 . 8 4 0 0 m
Nl=2.207974
N 2 =2.208285
W1 =4. 0 0 m
M2=5. 0 0 m
LE N=1.00mm
d=2. 0 0 m
r=30. 80E-12
KRP=1432.00
FIGURE 33 (Continued)
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104
this example the intensity of the second coupler is maxiinum if the
two signals are 180 degrees out of phase.
The reason for this is that
the maximum signals occur at the second coupler.
This demonstrates an
interesting application of the integrated-optic sampler.
Sampling Rate and Aperture
Two parameters of interest in a sampler are the rate at which the
electrical signal is sampled and the aperture, or the duration of the
sample.
The sampling rate can be determined by the velocity of both
the optical pulse and the RF signal, and the distance between the
electrooptic couplers.
in Figure 25.
To show this consider the example shown back
If the electrical signal propagates at a velocity v.
and the optical signal propagates at a velocity vQ and the distance
between the couplers is D, then the sampling rate is given by
v
f
=
+ v
____ t
D
.
(114)
In an ideal sampler, the sampling function consists of a series of
impulses which generate instantaneous sample points of the waveform,
as shown in Figure 34.
In the integrated optic sampler, as with all
realistic samplers, the sampling function consists of a series of
pulses with finite aperture.
The aperture of the sampler, which is the length of time that the
sampler is "looking" at the signal, is dependent on the interaction
length of the two waveguides (i.e. the length of the coupler), the
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105
SAMPLED WAVEFORM
INPUT WAVEFORM
x(t)
S(t) • x(t)
S(t)
SAMPLING FUNCTION
FIGURE 3 4 o IDEAL SAMPLER
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106
duration of the optical pulse, and the velocities of the the optical
and electrical signals.
As an example, consider an electrooptic coupler that has an
interaction region that is L meters in length, and an optical pulse
that is
x seconds in duration and is propagating at a velocity of vQ
meters per second while the electrical signal is traveling at a
velocity of v e meters per second.
Throughout this work it has been
assumed that the amount of coupling between the input and output
waveguides was determined by the average propagation constant that a
photon, or group of photons, experienced as they propagated along the
coupler.
With this in mind, the sampling function can be determined
by considering how long the photons remain in the interaction region
and how far the electrical signal propagates during that time.
The
length of time that a photon remains in the waveguide is given by
(115)
o
where L is the interaction length and vQ is the velocity of the
optical signal.
During that time the electrical signal propagates a
distance
(116)
where v e is the velocity of the electrical signal.
The total length
of electrical signal that the photon sees is given by the sum
(117)
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107
which can be rewritten as
v
L . = L (1 + -1 )
Pho
v
o
.
(118)
Since the electrical signal is propagating at a velocity, ve, the time
aperture of a single photon is given by
t
"pho
,
v.
V
V
,
V
e
e
(119)
o
which can be rewritten as,
W
- L [
] •
<120>
e o
The optical pulse, which is a collection of photons, is
duration.
x seconds in
Therefore, the total aperture of the sample pulse is given
by
t,.
= x + t . .
tot
pho
(1 2 1 )
Substituting in Equation 120 gives
v
[
e
+ v
o i
j •
(122)
vevo
Note that the aperture of the sampler can be reduced by (1) reducing
the optical pulse width, (2 ) reducing the interaction region of the
coupler, or (3) increasing either the electrical or optical velocity,
i.e. changing the dielectric constant or the index of refraction of
the integrated optic device.
The finite aperture of the sampler tends to distort the spectrum
of the sampled signal by what is known as the aperture effect1 .
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108
However, most or all of the distortion from the aperture effect can
be removed using equalization or signal processing.
Electronics Considerations
The two electrical components that will have a significant impact
on the sampler's speed and sensitivity are the laser diode and the
optical detector.
The laser diode is required to produce the short
optical pulse which indirectly determines the aperture of the
sampler.
The optical detector must determine how much optical energy
is coupled to the output waveguide and is therefore a major
contributor to the sampler's sensitivity.
The short optical pulse can be generated by direct modulation or
through an external modulator.
A laser diode can be used to generate
a short optical pulse by biasing the laser just below threshold and
using a current pulse to push the laser into its lasing region.
One
problem with direct modulation is that it is hard to maintain single
mode operation of the laser diode.
Researchers at NTT in Japan have
shown that gigabit-rate optical pulses can be generated with a single
longitudinal mode by means of harmonic frequency sinusoidal injection
current modulation, where the modulation frequency is twice as high as
the pulse frequency3 .
They have demonstrated the modulation of a
laser diode with 200 picosecond pulses at a 1.5 GHz repetition rate.
Researchers at Bell Laboratories 3 have used direct modulation of
injection current to generate optical pulses that are 42 picoseconds
in duration at a repetition rate of 500 MHz.
The technique uses a
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109
comb generator to generate large electrical pulses 50 picoseconds in
duration and 25 Volts in amplitude.
The electrical pulses are fed
through a bias tee so that the laser diode can be biased just below
threshold.
Their experiment results again verify that the pulses
required for this sampler are obtainable through direct modulation.
One can also consider generating the optical pulses through
external modulation using a CW diode laser.
One such device is a
directional coupler similar to that considered for the sampler.
Marcatili of Bell Laboratories showed that a directional coupler with
traveling wave electrodes could be used to generate optical pulses
from a CW laser source4 .
In his device the directional coupler
was designed so that all of the light would couple to the output
waveguide only if the voltage on the electrodes was zero.
The
traveling wave electrical signal was a simple sine wave which
propagated on the electrodes at a velocity equal to the velocity of
the optical signal propagating in the channel waveguides.
Since the
velocities were both equal and in the same direction, any photon or
group of photons which entered the waveguide coupler would see
essentially a constant voltage throughout the propagation down the
waveguide.
Any photon that entered the waveguide when the voltage was
zero would couple totally to the output waveguide.
If a large
amplitude sine wave is used, then it is predicted that sub-picosecond
pulses can be generated.
The optical detector will most likely be the component that limits
the sensitivity of the sampler.
response time and sensitivity.
There is always a tradeoff between
Devices that have fast rise times.
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110
like PIN photodiodes, are usually not very sensitive.
Detecting
devices that are sensitive, such as Avalanche Photodiodes, APD, have
slower response times.
The conventional photodiode circuit, shown in Figure 35, consists
of a photodetector connected to a load resistor R and an amplifier
with gain G.
The light received by the photodiode produces a current
i-L in the load resistor.
The magnitude of the current for a given
incident optical power is defined in terms of the responsivity in
units of amperes per watt.
A typical responsivity for a silicon PIN
photodiode is about 0.5 amperes per watt at 0.84 microns.
In other
words, for every watt of incident optical power, the photodiode will
produce 0.5 amperes of current.
the photodiode saturates.
Obviously there is a point at which
This is typically between 10 and 100 mW of
incident power for a PIN photodiode.
An alternate way to describe this relationship is the quantum
efficiency, i), which is by definition the ratio of the photo-generated
current i^ to the incident optical flux in photons per second.
This
makes the quantum efficiency a unitless parameter with a value less
than unity.
Another important parameter in selecting the detector is the dark
current, Ig, which is the current that flows even without incident
radiation.
The dark current tends to increase with temperature, and
is usually large for devices with a large active area.
The signal-to-noise ratio for a simple optical detector is given
by:
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BIAS
INCIDENT
OPTICAL
SIGNAL
7 \ PHOTODIODE
AMPLIFIER
FIGURE 35.
CONVENTIONAL PHOTODIODE CIRCUIT
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112
fu -hfn « l J
S
(123)
N
3e [ 2 1 <P + Pb )] + 2Id.
B
hi
where
P
= incident optical (mean) power on the photodiode
q
= quantum efficiency
h
= Planck's constant
f
= optical frequency
= dark current
M
= avalanche gain
k
= Boltzmann's constant
R
= effective load resistance
B
= bandwidth
Pj, = background optical power (unwanted)
n
= noise factor for avalanche multiplication
F
= noise figure of amplifier
There are two terms in the denominator that represent sources of
noise.
The first represents shot noise which is associated with the
random generation of carriers.
The term depends on the incident
optical power, P, the unwanted optical power, Pg, and the dark
current, 1^.
The second term represents thermal noise generated by
the output load resistor.
The load resistor of the detector is often made to be large in
order to reduce the effect of thermal noise and operate in what is
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113
referred to as shot-noise limited detection.
However, when the load
resistor becomes large, the RC time constant of the load resistor and
the junction capacitance of the photodiode will severely limit the
bandwidth of the detector.
The parameter H in Equation 123 is the avalanche gain of the
detector.
For PIN photodiodes M = 1.
However, an avalanche
photodiode, APD, can offer values of H between 10 and 100.
operates with
An APD
large reverse bias which accelerates the carriers
across the depletion region of the PN junction with enough energy to
force new electrons from the valence band to the conduction band5.
The multiplication factor increases the current by M and therefore
the signal power by
over the ordinary photodiode.
shot noise is increased by M 11 where 2 < n < 3 ^ * .
However, the
At high
multiplication rates, the shot noise has been observed to be
proportional to M^*l.
Typical parameters for commercially available photodetectors is
shown in Table 2.
Figure 36 graphically shows the relationship
between bandwidth and the minimum detectable signal (S/N = 1) for
these two detectors.
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114
TABLE 2.
TYPICAL PARAMETERS FOR COMMERCIAL PHOTODIODES
Manufacturer
Ortel
Mitsubishi
Part
PD050
PD1302
Type
PIN
APD
Quantum Efficiency
U = .84)
.65
.77
Avalanche Gain
1
100
Avalanche Noise Factor
0
2.25
Dark Current (nA)
.2
.3
Capacitance (pf)
.5
1.5
Bandwidth (GHz)
7
2
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115
Minimum Detectable Signal (dBm)
-20
-30
TJFEe Frn
-40
-50
-60
itsubi shi
-70
-80
-90
-100
-no
7
,8
9
Frequency (Hz)
FIGURE 36. MINIMUM DETECTABLE SIGNAL AS A FUNCTION OF
FREQUENCY
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116
Integrating Detector
It is clear from Figure 36 that, a relatively large amount of
optical power will be required to operate the detector at high
frequencies (> GHz).
However, it isn't important that the detector
reproduce the received optical pulse.
Instead, it is only important
that the detector has the capability of determining the total energy
of the optical pulse.
An integrating optical detector may have the capability of
measuring the total power at a bandwidth that is significantly reduced
over the typical optical detector.
schematically in Figure 37.
One such detector is shown
The photodetector is reverse biased
between V^£as and the virtual ground at the operational amplifier
input.
The output of the ideal integrator is given by
(124)
With the proper selection of a low bias current operation amplifier
and capacitor, this circuit can measure the energy in extremely small
optical pulses.
The signal power generated at the photodiode is proportional to
the mean square value of the current 7 which is given by
where P is the incident optical power, i) is the quantum efficiency, M
is the avalanche gain, if applicable, f is the optical frequency, and
h is Planck's constant.
The two sources of noise, as described
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717
BIAS
INCIDENT
OPTICAL
SIGNAL
FIGURE 37.
7 \
photodiode
INTEGRATING OPTICAL DETECTOR
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
118
earlier in this section, are shot noise and thermal noise.
The shot
noise term is given by:
i ,
nl
3e2 (P + P.JtjBM11
_____ + 2el. BM
hf
d
=
,
(126)
where P^ is the nndesired background optical signal, B is the
bandwidth,
1^
is the dark current, and n is a noise factor associated
with the avalanche process.
The thermal noise term is given by
in 2 2 = *kF B
,
(127)
where R is the load resistance, T is the temperature and F is the
noise figure of the amplifier.
An ideal integration supplies an output voltage that is the
integral of the input current, assuming that the operation amplifier
has infinite open-loop gain8.
In a realistic operational amplifier
the open loop gain is finite, Ayo, and there is a dominant pole at
some frequency f1# as shown in Figure 38.
The voltage gain for a
realistic operational amplifier is then given by
Ay = ___ 1° _
1
.
(128)
- JL
2^
The capacitor will add a pole at
f = -------------f„
1---Z
2 jtRC |A I
vo
,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(129)
119
20 LOG | A’
IDEAL
INTEGRATOR
20 LOG |Av(
OP-AMP FREQUENCY
RESPONSE
-20 dB/DECADE
LOG f
REAL
INTEGRATOR
FIGURE 38.
-40 dB/DECADE
FREQUENCY RESPONSE OF REAL INTEGRATOR
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120
where R is the source resistance in combination with the internal
resistances of the operational amplifier.
the detector is very large.
current source.
The source resistance for
This is why it is usually modeled as a
The pole due to the capacitor is therefore at a very
low frequency.
Since both the shot noise and thermal noise processes can be
considered white noise sources, particularly in the frequency range of
the integrator, a noise bandwidth can be defined for the integrator
where the noise bandwidth is the bandwidth of an ideal rectangular
filter that passes the same amount of noise power as the real filter.
It can be shown that the noise bandwidth for a simple RC low pass
filter is*
Bm = —
N
f
2
>
(130)
c
where fc is the 3 dB bandwidth of the low pass filter.
The noise
bandwidth for the integrator is then
B m = ----- ----N
4RC |A I
vo
.
(131)
This can be substituted into the equation for the noise.
Now the signal to noise of the detection system can be estimated.
Assume that the optical pulse propagating to the detector is a perfect
pulse with peak power P Q and duration
integrator is reset every t^ seconds.
t
.
Also assume that the
This reset time could
correspond to the repetition frequency of the laser diode.
The RMS
current from the detector produced by the received optical pulse is
given by
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121
_
i
=
8
1.414 P er)H
l _ p
hf
(132)
(t- t )
1
2
where tj is the tine the pulse arrives at the detector.
The
integrator produces a signal voltage given by
1
1.414 P eqM
o '
1
sig
C
PT(t
hf
(133)
t2)dt
If the pulse arrives before the integration time t^, the integral is
simply
^
1.414 PoenMT
(134)
v . =
sig
C
hf
The signal power is proportional to the mean square voltage, which is
given by
2
Vsi* =
r 'o'**!
~Zir
•*
(135)
’
From Equation 125 and 126 the RMS noise current is given by
36
x =
n
V
<P *
*BM
. ,.T
hf
RM0 . 4W
d
(136)
R
The integrated noise voltage is given by
*1
v
1
= _
*
C
3e2 (P + Pb ) gBM°
dt .
hf
d
(137)
R
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122
The only term that depends on time is the input power P,' which is
equal to zero except when the optical pulse is present.
can be broken into two parts.
The first term is integrated over the
time that the pulse is present.
The second term is integrated over
the rest of the repetition time tj.
The integral is given by
3e (P * ?t)
V” “ E
1
C
The integral
♦ 2ei„
hf
bm ”
♦ 122
d
3e (Pfe) qBM
4kTFB
+ ----R
+ 2eid BM
hf
The bracketed terms are now constant.
dt
+
R
dt .
(138)
The integrals are given by
2
3e (P + Pb ) ^BM A , . ^ n x 4kTFB
____ + 2eid BM + -----------------R
hf
(tj-r)
3e <Pb> ^
hf
.
! + 2eid BM
n
4kTFB
+ ----R
(139)
The noise power is again proportional to the mean square voltage
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123
2
-
v
n
3e (F *
=
nBM
+
hf
(tj-t)
^
d
R
3e2 (P. ) rjBM
*----- + 2ei. BM n+
f
d
.
4™
B
(140)
R
The signal to noise ratio after the integrator is given by
2
where
S
"
N
lout
v ,
_ ,fsig
(141)
_ 2
v
n
given by Equation 135 and vn^ is given by Equation 140.
As an example, consider the values shown in Table 3.
From
Equation 131 the effective noise bandwidth of the integrator is equal
to 25 Hertz.
Figure 39 shows the signal to noise of the system as a
function of optical power of the signal pulse.
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124
TABLE 3.
INTEGRATING DETECTOR EXAMPLE.
Integrator Capacitance
C = 10 picofarads
Effective Resistance
R = 1 M ohm
:
Avo =
Avalanche Gain
:
M = 1
Avalanche Noise
:
C4
Pnlse Duration
:
x = 500 picoseconds
Integration Time
:
tj =
Quantum Efficiency
:
H = .5
Noise Figure of Op Amp
:
N = 5 dB
1
microsecond
n
ig = 0.3 nanoamps
o
Background Optical Signal
1000
ts
Dark Current
II
Open-Loop Gain
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Signal-to-Noisc
( dB)
20 .
40 .
60 .
80 . 100.
120.
125
B = 100 Hz
0
-7 0 .0
-6 0 .0
-50.0
■
4 0 .0
Incident Optical Power
FIGURE 39.
-30 .0
(dBm)
SIGNAL-TO-NOISE RATIO FOR AN INTEGRATING
OPTICAL DETECTOR AS A FUNCTION OF INCIDENT
OPTICAL POWER.
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126
Coupler Considerations
The maximum amount of coupling at any given coupler will have to
be small in order to save some light for the last sample points.
This
maximum coupling requirement is dependent on how many sample points
there are in the sampler.
The amount of light that is available at
the Mth detector will depend on the percent of coupling Cmaz at the
maximum coupling point.
As a worst case example, consider an input
waveform that forces all the couplers to couple the maximum percentage
of light.
The power received at the Mth coupler is then given by
Preo.M * P in
where
[
1
' C„.x ]
<M 2 >
is the optical power into the sampler, Cmaz is the maximum
coupling percentage, and M is the number of couplers in the sampler.
This equation can be normalized by dividing the received power by the
input power.
The normalized relationship is shown graphically in
Figure 40.
The amount of energy that is detected at any output waveguide is
determined not only from the local voltage at the associated coupler,
but also from the local optical intensity at the coupler.
Therefore,
to reconstruct the electrical waveform the sampler must start at the
first coupler and determine the instantaneous local voltage from the
detected energy at the first detector.
From this, the sampler must
determine the amount of light that is remaining in the main optical
waveguide for the subsequent couplers.
This information, along with
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.
0
FIGURE 40.
.
.
.
.
40
80
120
160
200
N u m b e r of S a m p l e P o i n t s
.
NORMALIZED OUTPUT POWER OF THE LAST COUPLER
AS A FUNCTION OF THE NUMBER OF SAMPLE POINTS.
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128
the output from the second optical detector, can be used to determine
the instantaneous local voltage at the second coupler.
The sampler
can then proceed, using the same procedure, to the remaining detectors
and determine the sample points.
All of the sampler outputs can be
used to reconstruct the original electrical signal taking into
consideration the physical placement of the couplers and the
velocities of counter-propagating optical and electrical signals.
Sampler Design Procedure
This section presents the design strategy for the integrated-optic
sampler based on the theoretical work discussed thus far and published
experimental data.
This section will describe how the various
equations and models can be incorporated together to predict the
functionality of the integrated-optic sampler.
The design procedure
will determine the fabrication parameters required to achieve the
proper waveguide indices and the physical layout required to achieve
the proper optical coupling.
The five steps required to design the
sampler are discussed in the following sections.
Step 1: Optical Waveguide Design
The optical waveguides in the integrated-optic sampler are
fabricated by diffusing titanium into the surface of the lithium
niobate crystal.
This forms a graded index region that has a slightly
higher index than the bulk crystal.
The fabrication of the
waveguides, which is described in more detail in Chapter 4, consists
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129
of laying down titanium on the surface of the crystal, using
photolithography to delineate the channel waveguide structure, and
diffusing the titanium onto the crystal by placing it in a high
temperature (~1000° C) oven for a period of time (typically 3 to 7
hours).
There are four major fabrication variables with which one can
select the desired propagation characteristics of the channel
waveguide, including (1) titanium thickness, (2) oven temperature,
diffusion time, and (4) width of the titanium strip.
(3)
The first step
is to use past experimental data to determine the total index change,
An, and the diffusion depth, Y, for a given titanium thickness, oven
temperature and diffusion time.
The effective index method can then
be applied to obtain the effective indices of the various modes of the
channel waveguides.
Sten 2:
Coupling Coefficient
The coupling coefficient is a constant that determines how much
light couples between the two optical waveguides of a coupler.
It is
dependent on the material parameters, such as the refractive index,
and the waveguide separation.
The improved expression for coupling
coefficient is given in Equation 55 of Chapter 2.
This expression is
often written as
K = K
exp
0
where
£5
1
r
55
(143)
is the field penetration depth as described if Chapter 2, and
K 0 is a constant comprised of all the other terms in Equation 55.
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The
130
parameters KQ and
£5
can be experimentally determined for a given set
of fabrication parameters, as shown in Reference10.
Once these
two parameters are determined one can calculate the coupling
coefficient as a function of waveguide separation d.
Step 3:
Coupler Layout
The couplers must be designed to give the required
voltage-to-coupling response.
Once the waveguide parameters and
coupling coefficient are determined, the coupler layout can be
initiated.
This includes the interaction length, L, and the waveguide
separation, d.
Equation 45 of Chapter 2, which defines the difference
in propagation constant, A0, as a function of electrode voltage, and
Equations 32 and 33, which define the optical intensity out of the two
waveguides as a function of A0, can be used to determine the
voltage-to-coupling response for a given set of fabrication and
dimensional parameters.
evaluation.
The response can then be graphed for
The sampler requires that the couplers have a response
that is asymmetric about zero in order to differentiate between
positive and negative voltages.
Furthermore, the couplers must be
designed to have a maximum coupling of only a few percent of the
initial light in order to insure that there is light available for the
later couplers.
Step 4:
Sampler Parameters
Once the basic coupler configuration has been determined the
sampler parameters must be determined.
These parameters include the
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131
distance between the couplers. D, the length of the input optical
pulse a. and the magnitude of the optical pulse. A Q .
These parameters
are chosen to provide the sampler with the required sampling rate and
to insure that there will be enough light out of the output waveguides
for the detectors to operate.
It will be assumed at this time that the voltage on the traveling
wave electrode is a sinewave. as discussed in Case 1.
One must first
determine the average propagation constant that a photon experiences
as it travels in an optical coupler under a coplanar traveling wave
electrode as described earlier in this chapter.
The input variables
required for this calculation include the magnitude. V Q , and period
Te of the sine wave, the velocity of both the optical and electrical
signals in their respective media, the interaction length of the
optical and electrical signals, L, and the appropriate refractive
indices and electrooptic coefficients.
Equation 74 of this chapter
can be used to calculate the average propagation constant for the
configuration shown back in Figure 25.
The optical power out of the couplers can then be determined using
the average propagation constant A0, the coupling coefficient K and
the expression for the input optical signal given in Equation
65.
The
expressions for the optical signals out of the couplers is given by
Equations
76, 77 for coupler 1 and Equations 81 and 82 for coupler 2.
Step 5: Detector Requirements
The final step in the sampler design is to calculate the detector
requirements and determine if the sampler is feasible as designed.
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It
132
is assumed that the detectors integrate the power over the entire
received pulse and use the integrated power or energy to determine the
voltage on the electrode above the coupler.
The total energy received at the first detector is given by
(144)
E
where a is with length of the optical pulse in seconds and tQ is again
the time that the light arrives the first coupler.
Using the
expression for the initial optical power in Equation 65, and
substituting in Equation 76 gives
l'
a
*
.2
sin
E=
1
KL
2
0
+
1
m
til).
flA I2 p (!L - t J o
a
o
2
O
A0(t )
.
2K
,
dt
o
(145)
Ap(tQ )
O
1
+
2K
The pulse function from the optical signal can be taken out of the
equation since the time is covered in the limits of integration.
Therefore, Equation 125 can be rewritten as
■
1
a
r ip(t )
.a
sin
KL
,
•
1
+
[ A M t °>
1
2K
-12
■
dt.
(146)
f
2K
Expressions for the output light at the other couplers can be derived
in a similar manner.
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133
Sampler Design Example
This section develops an example of the sampler.
the overall device parameters.
Table 4 outlines
The first step is to determine the
effective index of the channel waveguides.
Using the published
experimental data from Naval Research Labs 1 1 , 1 3 one can determine the
total index change. An, and the diffusion depth, 7, as a function of
titanium thickness, diffusion time and diffusion temperature.
The
waveguide fabrication parameters considered in this design are shown
in Table 5.
The total index change and diffusion depth for the fabrication
parameters shown in Table
reference13.
6
can be estimated using the results of
These are given by
An = 0.015
Y 0 = 2.35
Using these two values along with the device parameters one can use
the effective index method outlined in Chapter 2 to determine the
effective index for a planar optical waveguide and for the channel
waveguides.
The results of the effective index method for the above
parameters are shown in Table
6.
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134
Table 4.
Device Parameters
Electrooptic Material
.
Lithium Niobate
Crystal Cut
•
•
Z-cut
Optical Polarization
•
Transverse Magnetic (TM)
Refractive Index
: Extraordinary (n0) = 2.204
Optical Wavelength
:
Electrooptic Coefficient
: r3 3 = 30.8 X10" 1 2
Table 5.
X = 0.84 microns
Waveguide Fabrication Parameters
Titanium Thickness
: 270 Angstroms
Diffusion Time
• 6 Hours
Diffusion Temperature
1020°C
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135
Table
6
.
Results of Effective Index Method
Effective Index of Planar Waveguide
: 2.209141
Effective Indices of Channel Waveguides
Width
Effective Index
3 microns
2.207468
3.5 microns
2.207759
4 microns
2.207974
4.5 microns
2.208149
5 microns
2.208285
5.5 microns
2.208395
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136
Once the effective indices of the waveguides has been determined
the coupler layout can be initiated.
A symmetric coupler can be used
to get a feel for the effect of the two layout parameters on the
voltage-to-coupling curves.
Figure 41 shows the voltage-to-coupling
curves for symmetric couplers with two 4 micron waveguides and a
interaction length of 2.25 millimeters.
In this figure the waveguide
separation is varied from 2 microns to 5 microns.
Figure 42 shows a
similar coupler except this time the waveguide separation is kept at 3
microns and the interaction length is varied from 0.5 millimeters to 2
millimeters.
Figures 43 and 44 consider asymmetric couplers in which the input
waveguide is 4 microns wide and the output waveguide is 5 microns
wide.
In Figure 43 the interaction length is kept constant at 1
millimeter and the waveguide separation is varied from 2 microns to 5
microns.
In Figure 44 the waveguide separation is kept at 3 microns
and the interaction length is varied from 0.5 millimeters to 2
millimeters.
The couplers required for the sampler should have the following
characteristics.
(1) A voltage-to-coupling curve that is asymmetric about zero.
(2) A maximum coupling of 5%.
(3) A monotonic curve over the voltages of interest.
With these characteristics in mind the asymmetric coupler with an
interaction length of 1 millimeter and a waveguide separation of 5
microns was chosen as the initial design.
In this coupler the width
of the input waveguide was chosen to be 4 microns and the width of the
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137
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v«o. 6 < c »
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i
n
c
V
C
•20.0 -15.0 >10.0
>5.0
0.0
VoltaQe
(c)
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)
0 .0
!
Voltage
(d)
VOLTAGE-TO-COUPLING CURVES FOR A SYMMETRIC OPTICAL COUPLER.
THE DISTANCE BETWEEN THE WAVEGUIDES IS VARIED FROM
2 MICRONS TO 5 MICRONS.
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138
— 0.740.
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ni.a.ao7.7«
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FI GURE 42.
S.O
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•20.0 -IS.O -10.0
-5.0
O.C
S.O
10.0
IS.O
20.0
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(d)
V O L T A G E - T O - C O U P L I N G C U R V E S FOR A S Y M M E T R I C O P T I C A L
COU PLE R. T H E I N T E R A C T I O N L E NGTH IS V A R I E D FROM
2 M I L L I M E T E R S TO 1/2 M I L L I M E T E R S .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
139
MO, 840**
Nl-2.207974
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Ml-4.00M2-5. 00-
MO. 840Nl-l.207974
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•20.0 *15.0 >10.0
-5.0
0.0
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5.0
20.0
•20.0 -15.0 -10.0
-5.0
20.0
0.0
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(b)
(a)
MO. 840Nl-2.207974
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T
•20.0 -15.0 -10.0
-5.0
0.0
Volt age
(c)
FIGURE 43.
«
l
•20.0 -IS.O -10.0
-5.0
0.0
i
5.0
10.0
15.0
20.0
Voltoge
(d)
VOLTAGE-TO-COUPLING CURVE FOR AN ASYMMETRIC OPTICAL COUPLER.
THE DISTANCE BETWEEN WAVEGUIDES IS VARIED FROM 2 MICRONS
TO 5 MICRONS.
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140
>■0.840NM2. 207974
N2-2.208285
M O . 840W*2. 2079*4
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C
•20.0 >15.0 *10.0
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0.0
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•20.0 *15.0 *10.0
!
*5.0
0.0
Voltage
(a)
S.O
(b )
MO. 840NI-2. 207974
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c
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FIGURE 44.
!
•20.0 *15.0 *10.0
*5.0
Voltage
(d)
VOLTAGE-TO-COUPLING CURVES FOR AN ASYMMETRIC COUPLER.
THE INTERACTION LENGTH IS VARIED FROM 2 MILLIMETERS
TO 1/2 MILLIMETERS.
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141
output waveguide was chosen to be 5 microns.
This led to a curve that
was monotonic between -5 and +5 volts, as shown in Figure 43d.
The distance between the couplers, D, was chosen to be 10
millimeters.
per second.
Using Equation 114, the sampling rate is 30 Giga-samples
Finally, in this example the optical pulse duration was
chosen to be 5 picoseconds.
The sampler aperture can be determined
using Equation 122 along with the previous defined parameters.
In
this example the aperture was 18.3 picoseconds.
This example demonstrates the potential sampling rate and aperture
of the sampler.
However, there are still many technical issues that
need to be addressed before the sampler can be realized.
The next
chapter discusses the experimental work completed during this
project.
Although the experiments were far from optimal they do offer
some interesting insight.
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142
References
1.
Taub, H., and Schilling, D.L., Principles of Cominicstion
Systems.
(McGraw-Hill Book Company, New York), 1971.
2.
Kawaguchi, H., and Otsuka, K . , "Generation of
Single-Longitudinal-Mode Gigabit-Rate Optical Pulses From
Semiconductor Lasers Through Harmonic-Frequency Sinusoidal
Modulation", Electronics Letters, Vol. 19, No. 17, June 28th,
1983.
3.
Lin, C.L., Liu, P.L., Damen, T.C., and Eilenberger, D.J.,
"Simple Picosecond Pulse Generation Scheme for Injection
Lasers", Electronics Letters, June 25, 1980.
4.
Marcatili, E.A.J., "Optical Subpicosecond Gate", Applied
Optics, Vol. 19, No. 9, May 1, 1980.
5.
Yariv, Amnon, Introduction to Optical Electronics, 2nd ed.,
(Holt, Rinehart and Winston, New York), 1971, p. 328.
.
Yariv, Amnon, Introduction to Optical Electronics, 2nd ed.,
(Holt, Rinehart and Winston, New York), 1971, p. 330.
7.
Yariv, Amnon, Introduction to Optical Electronics, 2nd ed.,
(Holt, Rinehart and Winston, New York), 1971, p. 326.
8.
Hillman, J., and Halkias, C.C., Integrated Electronics:
Analog and Digital Circuits and Systems, (McGraw-Hill Book
Company, New York), 1972, p. 545.
9.
Taub, H. and Schilling, D.L., Principles of Communication
Systems, (McGraw-Hill Book Company, New York), 1971, p. 254.
6
10. Bulmer, C.H., and Burns, W.K., "Polarization Characteristics
of LiNbOg Channel Waveguide Directional Couplers", Journal of
Lightwave Technology, Vol. LT-1, No. 1, March, 1983.
11. Bulmer, C.H. and Burns, W.K., "Polarization Characteristics of
LiNbOg Channel Waveguide Directional Couplers", Journal of
Lightwave Technology, Vol. LT-1, No. 1, March, 1983.
12. Burns, W.K., Klein, P.H., and West, E.J., "Ti Diffusion in
Ti: LiNbOg Planar and Channel Optical Waveguides", J. Applied
Physics, Vol. 50, No. 10, October, 1979.
13. Bulmer, C.H. and Burns, W.K., "Polarization Characteristics of
LiNbOg Channel Waveguide Directional Couplers", Journal of
Lightwave Technology, Vol. LT-1, No. 1, March 1983.
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER IV
EXPERIMENTAL PROCEDURES AND RESULTS
This chapter describes the procedures and results of the
experimental work completed during this investigation.
The first
section presents the fabrication of the integrated optic devices
I
including the optical waveguides and the electrode structures.
The
second part describes the experiments that were used to measure device
parameters and to test their operation.
The third section is a
discussion of the electronic components that make up the sampler
including the laser diode and the detectors.
The fourth part
describes the experiments that were completed to verify the operation
of the integrated optical sampler.
The final section summarizes the
experimental results.
It is important to note at this point that the devices considered
in this chapter are by no means optimal.
However, these experiments
offered some much needed laboratory experience in integrated channel
waveguide devices and high speed optical generation and detection.
Furthermore, these experimental results will provide an excellent
starting point for designing the next generation sampler.
Integrated Optic Device Fabrication
The heart of the sampler is the integrated optic directional
coupler.
Because of its small feature size (~1 micron) the device
143
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144
must be fabricated in an ultra clean room.
The devices were
fabricated in a Class 100 facility with the capability of submicron
photolithography and an evaporation chamber for sputtering of various
metals (i.e. aluminum, titanium, chrome, and gold).
In addition, the
facility has a diffusion furnace for optical waveguide fabrication.
Lithium niobate was chosen for the electrooptic substrate due to
its high electrooptic effect and its dominant historical role in
passive integrated optic devices.
The crystals were cut perpendicular
to the z axis (z-cut) in order to use the
coefficient, as described in Chapter 2.
^ 3
electrooptic
The following discussion
summarizes the integrated optic fabrication procedures.
Optical Waveguide Fabrication
The fabrication of integrated optical waveguides is by no means an
exact science.
Although much has been written about the procedures
there is a great deal of "black magic" that must be performed during
the process.
The main reason for this is that integrated optic
devices have not yet been considered for high production.
They are
usually made in small quantities in an ultra-clean room using a recipe
that has been collected with years of experience.
Other labs can use
the same recipe but most likely with different results due to
differences in equipment and materials.
Even within the same clean
room devices differ due to materials variations and slight changes in
process conditions.
There are two principal methods for fabricating optical waveguides
in lithium niobate, namely, the in-diffusion of a transition metal,
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145
such as titanium, and the out-diffusion of lithium oxide.
To
capitalize on past experiences, the titanium in-diffusion method was
chosen.
The following outline describes the procedure for fabricating
the waveguides.
1)
Surface Preparation.
Surface preparation is an important part of
fabrication due to the dimensions of the device (order of
1
micron).
The lithium niobate was ordered from the crystal manufacture (Crystal
Technology, Palo Alto, California) with an optical grade polish on one
side.
The crystals were then ultrasonically cleaned in a soap
solution.
This was followed by five minutes of light scrubbing with
an ultra-clean soft cloth and a thorough rinse with distilled water.
Once the crystal has been thoroughly rinsed, the surface was dried
with compressed nitrogen.
2)
Titanium Evaporation.
The second step is to coat the surface of
the crystal with titanium using a vacuum deposition process.
The
crystals were placed in a vacuum chamber which was taken to a pressure
of 2 x 10~** Torr.
An electron gun was then used to heat up the
titanium and induce evaporation onto the surface of the crystal.
thickness was monitored using a crystal monitor.
The
Once the desired
Titanium thickness was obtained, the electron gun was turned off and
the evaporation ceases.
The desired thickness of the titanium was
nominally between 270 and 300 angstroms.
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146
3)
Titanium Photolithography.
The optical waveguide pattern oust be
formed in the titanium using photolithography.
coated with a thin coat (<
1
The titanium was
micron) of photoresist using a spinner
to spin the crystals at 4000 rpm.
The time and rotation rate of the
spinning determine the photoresist thickness.
Once the desired
thickness was obtained, the photoresist was baked for 45 minutes at
80°C to ensure proper drying.
The mask of the waveguide pattern was
placed above the coated crystal and exposed to collimated ultraviolet
light.
Since positive photoresist was used, the mask blocked the
waveguide pattern so it was not exposed to the ultraviolet light.
The
photoresist was then developed in a developer which leaves only the
unexposed photoresist on the device.
A microscope was then used to
inspect the unexposed photoresist in the waveguide pattern.
The crystal was then placed in a titanium etchant to etch off the
exposed titanium which then leaves only the titanium in the waveguide
pattern.
After using a microscope to verify that the pattern was
good, the crystal was placed in a methanol bath to clean off the
photoresist that was covering the titanium pattern.
The photoresist that was used was P-05 which was spun for 30
seconds at 4000 rpm and baked at 80°C for 45 minutes.
It was then
exposed for 4 seconds to ultraviolet light, developed for 35 seconds
in the P-05 developer and the titanium was etched for 5 seconds.
4)
Diffusion.
The titanium was diffused into the crystal by placing
it in a diffusion furnace at 1000°C.
To reduce the chance of cracking
the crystal with an abrupt change in temperatures, the crystal was
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147
placed in the furnace before the heat was turned on.
The crystals
were left in the furnace for 5.5 hours after the furnace reached
1000°C and then placed in a cooling zone to slow the cooling process.
Oxygen was bubbled through water and forced over the crystals in the
furnace to suppress the out-diffusion of lithium.
5)
Polishing.
The ends of the crystals were polished to facilitate
end-fire coupling of the laser light to the optical waveguides.
samples were mounted to a
flake shellac.
1 /2
The
" glass fixture with low temperature
Three fixtures were then placed in a brass jig which
weighs 861.1 grams.
Once the devices were mounted in the jig, the ends were polished
in the following procedure:
First, the samples were rough polished by
lapping the jig on a glass plate with
samples were grayed evenly.
12
micron alumina until all
The jig was then placed on the lapmaster,
which automatically rotates and circulates the jig, using a 5 micron
alumina on glass for 1 hour.
The jig was then placed on a solder
wheel for one hour with 3 micron diamond paste.
chemical polish for 2-3 hours.
The final step was a
In this case Nalcoag 1040 colloidal
silica on expanded polyeorathene was used.
Once the polishing was completed the devices were inspected under
a microscope and removed from the fixtures by heating the devices and
melting the shellac.
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148
Buffer Laver Fabrication
When TM polarized light is required to propagate beneath the metal
electrodes, as in the push-pull configuration discussed back in
Chapter 2, a buffer layer between the waveguides and electrodes is
required to reduce optical attenuation.
These buffer layers are
often fabricated by evaporating a thin (1000 Angstroms) layer of glass
on the substrate after the waveguides have been diffused.
Although
this technique has been used for some time, there are still many
unknowns.
The thin layer of glass does reduce the optical attenuation
but it also tends to change the coupling characteristics of the
electrooptic couplers.
This is in part due to the change in
dielectric constant which changes the electric field lines between the
electrodes.
Electrode Fabrication
The next step in fabricating the integrated optic directional
coupler was to place the electrodes on the surface.
This was done
using a procedure similar to that used to define the optical waveguide
structure.
This time, however, the metal was not diffused into
the crystal.
Instead, the metal pattern, which was again defined
using photolithography, remained on the surface of the crystal.
Integrated optic electrodes are usually fabricated with either
aluminum or a combination of chrome and gold.
Aluminum is often used
because it permits a single step procedure and is adequate for many
applications.
However, aluminum is not very durable and is therefore
easily scratched. Furthermore, electroplating cannot be used to
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149
increase the thickness of the electrode in order to reduce its
resistance, as explained in Chapter 2.
Instead a two step evaporation process of chrome and gold is often
used to make the electrode more durable and enable electroplating.
The chrome layer makes a very durable bond with the lithium niobate
and provides the strength of the electrode.
The gold layer provides
a low resistance path and enables electroplating to further reduce the
DC resistance of the electrode.
The fabrication of a chrome-gold
electrode requires the following three step process.
1)
Chrome-Gold Evaporation.
The first step in fabricating the
electrode is to evaporate the metal onto the surface of the crystal
using a vacuum deposition process.
As with the titanium evaporation,
the crystals were placed in a vacuum chamber which was taken to a
pressure of 2 x 10“^ torr.
The electron gun was positioned to
heat the chrome target which stimulated the evaporation of chrome onto
the buffer layer.
Again, the thickness was monitored using a crystal
monitor.
Once the desired chrome thickness was obtained the electron gun
was positioned to heat the gold target which stimulated the
evaporation of gold onto the chrome layer.
The electron gun was
turned off once the desired gold thickness was obtained.
2)
Chrome-Gold Photolithography.
The electrode pattern must be
formed in the chrome-gold layer using a two step photolithography
process.
As with the titanium, the gold was coated with a thin layer
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
150
of photoresist using a spinner to spin the crystals at 4000 rpm.
After spinning, the resist was dried in a fnrnace at 80°C for 45
minutes.
A mask of the electrode pattern was placed above the coated
crystal and exposed to collimated ultraviolet light.
The mask blocks
the ultraviolet light from exposing the photoresist which defines the
electrode pattern.
The photoresist was then developed which left
only the unexposed photoresist on the device.
The device was then placed in gold etchant which etched all of the
exposed gold and left only the gold which made up the electrode
structure.
The device was then placed in a chrome etchant which
etched all of the exposed chrome, again leaving only the electrode
pattern.
After verifying that the pattern was good, the crystal was
cleaned in a methanol bath to remove the photoresist.
The device used fox the fundamental experiments is shown
schematically in Figure 45.
It consists of an input horn to assist in
coupling the light into the device, main channel waveguide that is 4
microns in width, and an output waveguide that is 5 microns in width.
Ihe distance between the two waveguides is 4 microns and the
interaction length is 2 millimeters.
At the output face of the
crystal the waveguides were placed 40 microns apart.
were
6 microns wide and placed
8
microns apart.
The electrodes
The output optical
wave was placed in the center of the electrodes, leaving the main
optical waveguide completely covered by one of the electrodes.
The
electrode structure was divided into two
1
millimeter segments which
could be used individually or together.
A glass buffer layer was
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
POLISHED
CRYSTAL
EDGE
''iigsii
5
6 iim WIDE
I
HORN
COUPLER
6 |im WIDE
TS,
**<■><*
BUFFER L A Y E R \
S4#**vj •/' x-rvfe. Kr'4r*3&Hf&pi
POLISHED
CRYSTAL
EDGE
FIGURE 45.
SCHEMATIC DRAWING OF EXPERIMENTAL DEVICE
152
placed betveen the waveguides and electrodes to reduce optical
attenuation of TM polarized light propagating down the optical
waveguides.
Figures 46 and 47 photographically show the devices used
in the fundamental and proof-of-principle experiments.
Fundamental Experiments
Mode Structure
This purpose of the first experiment was to verify the mode
structure of the channel waveguides.
This was done using prisms to
couple the light in and out of the waveguide as shown in Figure 48.
The input light was focused into the channel to not only increase the
amount of light into the channel but also to excite all of the
waveguide modes.
The output prism sent each of the output modes out
of the device at a different angle due to the different effective
index of refraction of each of the modes.
A ground glass screen was
used to observe the output modes of the channel waveguides.
For
visible light the modes were observed on the ground screen with the
naked eye.
For the infrared light of the diode laser, an infrared
viewer was required.
The waveguides were tested using a visible HeNe laser (k = .6328
microns) and an infrared diode laser (k = .84 microns).
The
waveguides had two modes in the visible light range but appeared to be
single mode for the laser diode.
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153
FIGURE 46(a). PHOTOGRAPH OF TITANINUM IN-DIFFUSED OPTICAL WAVEGUIDES
IN DIRECTIONAL COUPLER CONFIGURATION.
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FIGURE 46(b).
PHOTOGRAPH OF CHROME-GOLD ELECTRODES OVER OPTICAL
WAVEGUIDES.
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155
M
FIGURE 47.
M
i
PHOTOGRAPH OF INTEGRATED-OPTIC DIRECTIONAL COUPLER
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
156
LASER
RUTILE
PRISM
/
LITHIUM
NIOBATE
CRYSTAL
FIGURE 48.
GROUND GLASS
SCREEN
CHANNEL
WAVEGUIDE
COUPLER
EXPERIMENTAL ARRANGEMENT FOR DETERMINING THE MODE
STRUCTURE OF OPTICAL WAVEGUIDES
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157
Endfire Coupling
The goal of this experiment vas to develop a procedure for
coupling light in and out of the waveguide using the polished ends.
The initial experimental arrangement is shown in Figure 49.
visible HeNe laser was used to aid in the initial set-up.
The
The device
was mounted in a fixture with x and z translation capability, the
input lens had y translation capability, and the output objective had
x, y, and z translation capability.
The laser was rotated so that its
light was polarized 45 degrees off the x and z axes, in order to
stimulate both TE and 'EM light in the channel waveguides.
A linear
polarizer was used to select either the TE (parallel to x) or TM
(parallel to z) light.
The detector used for evaluating the integrated optic devices was
a 12 mm by 12 mm optical detector array of an EG G/Princeton Applied
Research Optical Multi-Channel Analyzer (OMA-2).
The detector output
could be observed on an oscilloscope in real time or observed on a
computer screen after some signal processing.
The computer output
that was used repeatedly in this work was essentially an integration
of the light in the y direction as a function of position x.
In other
words, the computer summed up all the light in a column in the y
direction and displayed it as a function of x.
The endpoints of
the integration were user selectable, and were usually specified to
eliminate as much of the background light as possible.
The output microscope objective was used to image the end of the
waveguide onto the optical detector array.
To initially position the
output lens an intense white light (tensor light) was positioned just
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LINEAR
POLARIZER
INTEGRATED
OPTIC
DEVICE
SILICON
DETECTOR
ARRAY
HeNe LASER
40X
MICROSCOPE
OBJECTIVE
PAR 1216
DETECTOR
CONTROLLER
10X
MICROSCOPE
OBJECTIVE
COMPUTER
PAR 1215
FIGURE 49. LABORATORY ARRANGEMENT FOR ENDFIRE COUPLING
159
above the
output edge of the device.
front of the detector
A white screen was placed in
array in order to view the image of the crystal
edge produced by the white light.
Once the output lens was positioned
correctly, the edge of the crystal was clearly visible, on the screen.
The first samples that were tested appeared to have a planar
waveguide on the surface of the crystal in addition to the channel
waveguide.
This was probably due to the out-diffusion of lithium
while the samples were in the diffusion furnace.
predominantly guided
T M polarized light.
The planar modes
Although it usually
desirable to suppress the outdiffused modes during the fabrication
process, in this case it gave a precise indication of the crystal
surface and aided in imaging the output edge of the crystal on the
detector array.
Figure 50 shows the image of the crystal edge on the
detector for TM polarized light.
The bright line is the surface of
the crystal illuminated by the planar outdiffused modes.
Once the surface of the crystal was clearly visible on the
detector array output, the input lens was adjusted.
The input lens
was visually lined up and positioned by taking into consideration the
focal length and working distance of the microscope objectives.
The x
and z translation stages on the device were used to position the
spot of the laser onto the input edge of the channel waveguide.
The
y-translation of the input lens was used to adjust the spot size of
the input light on the device.
It is important to remember that the
optical waveguides were 4 microns in width.
Even with the highly
polished edges, it was very difficult to get the laser light into the
channel waveguide.
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160
.
FIGURE 50.
- - IfK ( |
OSCILLOSCOPE PHOTOGRAPH OF DETECTED TM LIGHT FROM
THE END OF THE CRYSTAL.
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161
It was hard to identify the output waveguides on the detector
array with TM polarized light due to the planar modes.
However, using
TE polarized light the two channels were easily identified.
Figure
51a shows the output light of the channels as viewed on the
oscilloscope and Figure 51b shows the integrated output of the optical
multichannel analyzer (OMA -2).
The HeNe laser was replaced by the infrared laser diode (Ortel
SL-310).
Now the lenses and devices had to be lined up with an
infrared viewer.
This added a new challenge to the procedure.
52 shows the arrangement for the laser diode experiments.
input lens was replaced by a 6Ox microscope objective.
Figure
The 40x
The 60x lens
reduced the size of the focused spot thereby increasing the amount of
light that got into the channels.
Furthermore, the 60x lens reduced
the effect of the planar modes by spreading out the planar light.
Again the laser diode was mounted with its output polarization 45
degrees from the x and z axis to facilitate both TE and TM
polarizations.
polarization.
A prism polarizer was used to select optical
Figure 53 shows the results of the laser diode coupling
tests.
Coupler Characterization
Once the techniques for coupling light in and out of the channel
waveguides had been established, the DC characterization of the
coupler could proceed.
During these tests a DC voltage was applied to
the electrode structure and the coupling between the two waveguides
was monitored.
Figure 54 shows the measured voltage-to-coupling curve
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162
FIGURE 51 .
DETECTED LIGHT OUT OF THE OPTICAL WAVEGUIDES USING TE
POLARIZED LIGHT, (a) REAL-TIME OSCILLOSCOPE OUTPUT,
(b> INTEGRATED OUTPUT USING MULTICHANNEL ANALYZER.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ORTEL
SL-310
LASER DIODE
INTEGRATED
OPTIC
\ = 0.84nm
----- - - - - -
‘=- V - - - - -
10X
vt-ft- - - - - - - - - - - - - - - - - - -
—
SILICON
DETECTOR
ARRAY
DETECTOR
CONTROLLER
PAR 1216
COMPUTER
PAR 1215
Z
X
FIGURE 52. LABORATORY ARRANGEMENT FOR ENDFIRE COUPLING EXPERIMENTS USING LASER DIODE
164
FIGURE 53.
DETECTED LIGHT OUT OF THE OPTICAL WAVEGUIDES
USING TM POLARIZED LIGHT IN LASER DIODE COUPLING
EXPERIMENTS.
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0 .25
Normalized
0 .50
Output
Power
0.75
165
T 1— 1---- 1---- 1--- 1— I----- 1---- IT -]---- 1---- 1---- 1---- 1---- 1---- i---- 1---- 1---- 1---- 1
-20.0
0 .0
20.0
40.0
Voltage
FIGURE 54 . MEASURED VOLTAGE-TO-COUPLING CURVE FOR
OPTICAL COUPLER.
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
166
for the electrooptic coupler.
voltage controlled coupler.
This device clearly functions as a
However, it required a great deal of
voltage to achieve an appreciable change.
There were three major
reasons for this large voltage requirement.
were not positioned optimally.
First, the electrodes
As shown back in Figure 47, one of the
waveguides was beneath the electrode while the other was half way
between the two electrodes.
This reduced the effectiveness of the
electrodes since only one of the waveguides was affected by the
z-oriented electric field.
Furthermore, since the electrodes were
further apart, the electric field was smaller for a given voltage.
The second problem with this coupler was that only part of the
electrode was operational after fabrication.
A short formed across
part of the electrode which made it inoperable.
The other half of the
electrode was still functional and could be used in the evaluation.
The final reason for this coupler requiring the large voltage was
that a glass buffer layer was added between the electrodes and the
waveguides.
Although this is not completely understood, the buffer
layer is known to increase the voltage requirements by as much as
300%.
Part of this is probably due to the dielectric constant of the
glass affecting the electric field lines between the electrodes.
Annealing of the buffer layer has been used to reduce the voltage
requirements.
However, this was not considered for the purpose of the
present investigation.
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167
S n n n le r- Electronics
The laser diode and fast optical detector are the two fundamental
components of the sampler electronics.
The laser diode that was used
in the experiment (Ortel SL-310) had a 3 dB bandwidth of 3 GHz, a
maximum output power of 5 milliwatts, and an optical wavelength of
0.84 microns.
A bias tee was used to combine the pulse input with the
bias current.
The bias current was delivered from a laser diode power
supply (Ortel LDPS-1).
The laser diode had a monitor photodiode to
monitor the laser output.
This was fed back to the power supply for
automatic stabilization of the CW output power.
A variety of detectors were considered for detecting the optical
pulse out of the integrated optic device.
The fastest detector was a
high speed GaAlAs/GaAs pin photodiode (Ortel PD050-0M) which had a 3
dB bandwidth of 7 GHz.
However, it did not appear to have the
sensitivity required for the first experiments.
The most sensitive
detector was a silicon avalanche photodiode (Mitsubishi PD-1002) which
had a 3 dB bandwidth of 2 GHz and a gain bandwidth product approaching
800 GHz.
A preamplifier was used to amplify the photodiode output.
The preamplifier contained a built-in bias tee for decoupling the
photodiode bias current from the signal output.
The preamplifier had
a 3 dB bandwidth of 600 MHz and a gain of 20 dB.
The electronics were initially tested using a network analyzer (HP
8410) as shown in Figure 55.
The A port was connected through the
bias tee to the laser diode.
A lOx microscope objective was used to
focus the diverging light from the laser diode onto the face of the
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
NETWORK ANALYZER
HEWLETT PACKARD
8410
BIAS TEE
10X
II
11
T
■
LASER
DIODE
ORTEL
SL-310
PD-1002
APD
DETECTOR
>
P REAMP
LASER
POWER
SUPPLY
FIGURE 55. NETWORK ANALYZER CONFIGURATION FOR TESTING FREQUENCY RESPONSE OF THE LASER DIODE
AND OPTICAL DETECTOR
169
avalanche photodiode.
The jtho^odiode was biased just under the
avalanche breakdown voltage of 150 volts.
between the APD and the B port.
The preamplifier was placed
Figure 56 shows the Sj j response of
the electronics from 500 HHz to 1.5 GHz.
The overall 3 dB bandwidth
of the electronics was approximately 600 MHz. which was governed by
the preamplifier's response.
The pulse response of the electronics was then tested using an
Avtech pulse generator (AVM-1P).
The experimental arrangement is
shown in Figure 57.
The pulse generator was fed through the bias tee
to the laser diode.
The lOx microscope objective again focused the
diverging laser light onto the APD.
The photodiode output was fed
through the preamplifier to the sampling oscilloscope (Tektronix 7854
with the S-6 sampling head).
The photodiode was again biased just
below the avalanche breakdown voltage of 150 volts.
Figure 58a shows
the input pulse from the pulse generator and Figure 58b shows the
received pulse out of the preamplifier.
Proof-of-Principle Demonstration
The experimental arrangement for the proof of principle
demonstration is shown in Figure 59.
The experiment centers around
the integrated optic device described in the previous sections.
As
pointed out earlier, the electrodes were not traveling wave devices
but were instead in a lumped configuration.
This means that the
voltage across the electrode was essentially constant for any group of
photons.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
with,out
no.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APD
SUPPLY
AVM-
BIAS
TEE
AVTECH
PULSE
GENERATOR
10X
MICROSCOPE
OBJECTIVE
SL-310
LASER
DIODE
APD
DETECTOR
MITSUBISHI
PD-1002
SAMPLING
OSCILLOSCOPE
TEKTRONIX
7854 WITH
S-6 SAMPLING
HEAD
LASER
POWER
SUPPLY
FIGURE 57.
LABORATORY ARRANGEMENT FOR TIME DOMAIN TESTING OF LASER DIODE AND OPTICAL DETECTOR
FIGURE 58.
TIME DOMAIN RESPONSE OF LASER DIODE AND OPTICAL DETECTOR.
(a) PULSE INTO LASER DIODE, (b) ELECTRICAL SIGNAL FROM APD
PHOTODETECTOR.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LASER
POWER
SUPPLY
INTEGRATED
...........
HP
RATE GEHERATOR
8091A
AVTECH
PULSE
GENERATOR
____
™X
60X
/—
OPTIC
0PT,C
DEVICE
M
m
w u ^ in o u
ADJUSTABLE
20X
APERATURE
APERATURE
I
10X
nrrcrTno
DETECTOR
PD-1002
n y s = = ^ ^ ^ n= = ^ = = =S ^ — |
DIODE
SL-310
*— 1
WAVETEK
164 FUNCTION
GENERATOR
OSCILLOSCOPE
TEKTRONIX
FIGURE 59. LABORATORY ARRANGEMENT FOR PROOF-OF-PRINCIPLE EXPERIMENT
^sl
CO
174
The first experiment demonstrated that a 1.5 nano-second optical
pulse could he focused into the optical waveguide* partially coupled
across to the output waveguide and detected with a fast optical
detector.
The silicon detector array was used to initially align the
system with the laser diode emitting CV light.
The two output
optical spots were imaged onto the oscilloscope output of the detector
to verify that the light from the laser diode was getting into the
coupler.
An adjustable aperture was placed between the integrated
optic device and the detector array to eliminate all of the substrate
light and the light from the main optical waveguide.
This left only
the light from the coupled output waveguide.
The detector array was then removed from the experiment and
replaced with the fast avalanche photodiode (APD) described in the
last section.
The preamplifier after the APD did not pass low
frequencies so the laser diode had to be modulated in order to
position the APD.
Figure 60 photographically shows the laser diode*
the integrated-optic device, and the APD photodetector.
The laser diode was biased just above threshold and pulsed using
the Avtech pulse generator.
The electrical pulses were 1.5
nano-seconds in duration and 0.4 volts in amplitude with a repetition
rate of 10 MHz.
The APD was positioned while observing the output of
the preamplifier with a fast oscilloscope (Tektronix 7104) with a
real-time bandwidth of 1 GHz.
The lOx microscope objective after the
adjustable aperture focused the light onto the small (0.003 mm?)
active area of the APD.
The magnitude of the output pulses varied
with the DC voltage applied to the electrodes.
Figure 61 shows the
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FIGURE 60.
PHOTOGRAPH OF PRGOF-OF-PRINCIPLE EXPERIMENT.
LEFT: LASER DIODE, CENTER: INTEGRATED-OPTIC
DEVICE, RIGHT: APD AND PREAMPLIFIER.
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176
FIGURE 61.
DETECTED OPTICAL PULSES FROM PROOF-OF-PRINCIPLE
EXPERIMENTS WITH DC VOLTAGE ON ELECTRODES.
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
177
detected optical pulses out of the integrated optic device for two DC
voltages.
The change in amplitude was not very large
however, it is
similar to that depicted in the voltage-to-coupling curve back in
Figure 55.
One other reason for the limited change in amplitude was
that the fast detector was detecting some substrate light which
didn't vary with electrode voltage.
There was also a small amount of CW light since the laser diode is
biased above threshold.
However, the signal detected by the APD from
the CW light did not propagate through the preamplifier due to the
coupling capacitance that made up part of the bias tee.
Once the fast detector was in place and the DC characterization of
the integrated optic device was completed, the DC supply used to
control the coupler was replaced with a function generator (Wavetek
164).
The function generator was synchronized with the 10 MHz clock
in order to observe the varying output on the fast oscilloscope.
Figure 62 shows the results of the proof-of-principle demonstration of
the sampler.
The sine wave is a 1.5 MHz signal which is being sampled
with a series of 1.5 nanosecond pulses.
At this point the sampler consists of only a single electrooptic
coupler.
The sampling rate was not determined by the distance between
any two electrooptic couplers but instead by the repetition rate of
the laser diode.
The goal here was not necessarily to demonstrate a
sampler but to instead show that the amplitude of the short output
pulse changed with the applied electrode voltage.
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178
FIGURE 62.
DETECTED OPTICAL PULSES FROM PROOF-OF-PRINCIPLE
EXPERIMENTS WITH SINUSOIDAL SIGNAL ON ELECTRODES.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
179
Experimental Results
Although the experimental resnlts of the sampler did not verify
many of the theoretical discussions presented in this work, they did
offer some valuable insight.
It was the first time that a pulse of
light has been used to determine the instantaneous voltage on an
electrooptic coupler.
And, although the voltage was only a 1.5 MHz
sine wave, it is being sampled with a 1.5 nanosecond optical pulse
which should have the ability to sample frequencies in excess of
500MHz.
There are many fundamental limitations of the overall experimental
arrangement discussed in the last section.
The lumped electrode
structure severely limited the frequency that could be applied to the
electrode structure, primarily due to the electrode capacitance.
This
limited the frequency of the signal that could be sampled.
Fabrication problems, which caused 8 short in part of the electrode
structure, further reduced the sensitivity of the sampler.
The laser diode and detector/preamplifier combination were also
not optimized for this sampler application.
The laser diode was one
of the fastest commercial laser diodes currently available.
its pulse width was limited to about 1 nanosecond.
However,
The pulse
generator which drove the laser diode had a maximum repetition
frequency of 10 MHz which dictated the sampling rate of this single
switch sampler.
The detector and preamplifier combination further
reduced the response of the electronics to a 1.5 nanosecond minimum
pulse width.
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CHAPTER V
CONCLUSIONS AND RECOBfMENDATIONS
This theoretical and experimental investigation has introduced a
novel integrated-optic sampler for transient RF and microwave signals.
The device consists of a series of optical directional couplers placed
beneath a traveling wave RF stripline on an electrooptic substrate.
It is shown theoretically that such a structure can be used to sample
a transient RF or microwave signal using a short optical pulse which
propagates in a direction opposite of the electrical signal.
Such a
device could provide a low cost method of detecting and analyzing high
frequency (up to 20 GHz) electrical signals for communication
systems.
The device could also provide a sampling technique with
extremely low variation in sampling rate, or sampling jitter.
Furthermore, it is shown the integrated-optic device can be used
to sample intensity modulated optical signals using a short electrical
pulse.
This optical sampler could be integrated into a fiber
communication system and provide a new means of detecting and
analyzing the optical signals.
During this investigation an attempt was made to address as many
of the sampler components and requirements as possible.
there is no total system design presented,
Although
it is hoped that the
180
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181
theoretical discussion and experimental results will provide an
interested researcher with the necessary basis for a complete design.
There are many areas that need particular attention in future
studies.
The microwave stripline on the crystal surface poses one of
the most serious system limitations.
The directional couplers require
that the stripline and ground plane be extremely close.
Also, in
order to maintain the stripline impedance, it is necessary that the
stripline be very thin, leading to a highly resistive and lossy
device.
Changes in system geometry could lead to a stripline
configuration that has both the proper RF impedance and low DC
resistance.
The optical detection technology is another area that needs
additional attention.
Optical damage considerations1^
integrated
optical waveguides limit the amount of optical power that can be
propagated down the couplers.
This limitation along with the system
requirement that the maximum coupling be only a small percentage
(based on the number of samples required) of the light in the main
channel, seriously limits the amount of light that finally propagates
to the detectors.
In order to maintain a large dynamic range, a
detector that is very sensitive is necessary.
However, due to system
requirements, the detector must be fast in order to detect the short
pulses.
The design and testing of the integrating optical detector
discussed in Chapter 3, which is not necessarily fast but can
accurately measure the energy in a fast pulse could provide the
sampler with its detection requirements.
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
There is also a great deal of additional experimental work that
conld provide additional insight into the sampling device.
Although
the experimental work presented in Chapter 4 may be significant and
nsefnl in its own right, it is by no means completed.
Further
fabrication advances and experimental measurements are necessary to
Y
take the integrated optic sampler from the theoretical and proof of
principle stage to a full system demonstration.
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183
References
1.
Holman, R.L. and Cressman, P.J., "Optical Damage Resistance of
Lithium Niobate Waveguides", Optical Engineering, Vol. 21,
No. 6, November/December, 1982.
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BIBLIOGRAPHY
Adams, M.J., "Three-Layer Dielectric Slab Waveguides", in An
Introduction to Optical Waveguides, (Wiley, New York), 1981.
Auston, D.H., Johnson, A.H., Smith, P.R., and Bean, J.C., "Picosecond
optoelectronic detection, sampling, and correlation measurements in
amorphous semiconductors", Appl. Phys. Lett., Vol. 37, No. 4, August
15, 1980.
Becker, R.A., Johnson, L.M., "Low-loss multiple-branching circuit in
Ti-indiffused LiNbO channel waveguides". Optics Letters, Vol. 9,
No. 6, June, 1984.
Bulmer, C.H. and Burns, W.K., "Polarization Characteristics of LiNbOg
Channel Waveguide Directional Couplers", Journal of Lightwave
Technology, Vol. LT-1, No. 1, March, 1983.
Burns, W.K., Klein, P.H., and West, E.J., "Ti Diffusion in Ti: LiNbOg
Planar and Channel Optical Waveguides", J. Applied Physics, Vol. 50,
No. 10, October, 1979.
Dokhikyan, R.G., Zolotov, E.M., Karinskii, S.S., Maksimov, V.F.,
Popkov, V.T., Prokhorov, A.M., Sisakyan, I.N., Shcherbakov, E.A.,
"Prototype of an integrated-optics four-digit analog-to-digital
converter", Sov. J. Quantum Electron., Vol. 12, No. 6, p. 806, June
1982.
Hocker, G. Benjamin, Burns, William K., "Modes in Diffused Optical
Waveguides of Arbitrary Index Profile", IEEE J. Quantum Electron.,
Vol. QE-11, No. 6, June 1975.
Hocker, G. Benjamin, Burns, William K., "Mode dispersion in diffused
channel waveguides by the effective index method", Applied Optics,
Vol. 16, No. 1, January 1977.
Holman, R.L. and Cressman, P.J., "Optical Damage Resistance of Lithium
Niobate Waveguides", Optical Engineering, Vol. 21, No. 6,
November/December, 1982.
Hunsberger, R.G., Integrated Optics: Theory and Technology, Springer
Series in Optical Sciences, (Springer, Berlin, Heidelberg, New York),
1982.
184
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