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Nonlinear dynamics of semiconductor lasers for microwave photonics applications

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UNIVERSITY OF CALIFORNIA
Los Angeles
Nonlinear Dynamics of Semiconductor Lasers for
Microwave Photonics Applications
A dissertation submitted in partial satisfaction
of the requirements for the degree
Doctor of Philosophy in Electrical Engineering
by
Sze-Chun Chan
2007
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UMI Number: 3299527
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© Copyright by
Sze-Chun Chan
2007
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The dissertation of Sze-Chun Chan is approved.
Harold R. F<
xman
Tatsuo Itoh
Shantanu Sinha
Jia-Ming Liu, Committee Chair
University of California, Los Angeles
2007
ii
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“Thy word is a lamp unto m y feet,
and a light unto m y path. ”
Psalms 119:105
This dissertation is dedicated to my parents and sister
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T
1
2
3
a b l e
o f
C
o n t e n t s
In tr o d u c tio n ...................................................................................................
1
1.1
M otivation................................................................................................
1
1.2
B a c k g ro u n d .............................................................................................
2
1.3
Objective
................................................................................................
3
1.4
Outline of the D issertatio n ...................................................................
4
P h oton ic M icrowave G eneration by P eriodic O scillations . . .
5
2.1
In tro d u c tio n .............................................................................................
5
2.2
Optical Injection S e tu p .........................................................................
6
2.3
S im u la tio n s .............................................................................................
8
2.3.1 Rate Equation M o d el..................................................................
8
2.3.2 Dynamical P a ra m e te rs ...............................................................
10
2.3.3 Dynamical S t a t e s ........................................................................
10
2.3.4 Microwave G e n e ra tio n ...............................................................
12
2.4
Experimental R e s u lts .............................................................................
18
2.5
C o m p a riso n .............................................................................................
22
2.6
Summary
23
................................................................................................
Single-Sideband R adio-over-Fiber Transm ission
.........................
25
3.1
In tro d u ctio n .............................................................................................
25
3.2
Chromatic Dispersion-Induced Power P e n a l t y ................................
26
3.2.1 F o rm alism .....................................................................................
26
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3.2.2
Representative S ta te s .................................................................
27
3.3
Single Sideband (SSB) Characteristics
.............................................
32
3.4
Operating C onditions.............................................................................
37
3.5
Summary
................................................................................................
40
4 Frequency M od u lation on Period-O ne O s c il la t io n .......................
41
4.1
In tro d u c tio n .............................................................................................
41
4.2
Frequency Modulation (FM) C h a ra c te ristic s...................................
42
4.2.1
Setup
..........................................................................................
42
4.2.2
FM Modulation C h a ra c te ristic s.............................................
44
4.2.3
FM Frequency R e sp o n se ..........................................................
48
4.3
AM-to-FM Upconverter
4.4
Summary
......................................................................
52
................................................................................................
58
5 M icrowave Frequency Conversion by Period-T w o O scillation .
59
5.1
In tro d u c tio n .............................................................................................
59
5.2
Period-Two O scillatio n .........................................................................
61
5.3
Frequency D iv is io n ................................................................................
63
5.4
Frequency M ultiplication......................................................................
70
5.5
D iscu ssio n ................................................................................................
72
5.6
Summary
73
................................................................................................
6 M icrowave Frequency Com b G eneration by Frequency Locking 75
6.1
In tro d u c tio n .............................................................................................
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75
6.2 Frequency Locking S t a t e ........................................................................
77
6.3 Microwave Injection L ocking .................................................................
79
6.4 C o m p a riso n ..............................................................................................
82
6.5 Summary
..................................................................................................
84
C o n c lu sio n .......................................................................................................
86
R e fe r e n c e s ..............................................................................................................
88
7
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L
is t
o f
F
ig u r e s
2.1 Schematic of the optical injection setup.......................................
7
2.2 Evolution of the optical injection dynamics.................................
11
2.3 Fundamental microwave frequency /o ...........................................
13
2.4 Mapping of the fundamental frequency / 0...................................
15
2.5 Fundamental and second harmonic microwave power................
16
2.6 Mapping of the fundamental microwave power P/0....................
17
2.7 Tuning characteristics for generating microwave frequency / 0 un­
der injection at zero detuning
19
2.8 Tuning characteristics for generating microwave frequency /o un­
der a constant injection of & = 0.082
19
2.9 Experimental spectra of the slave laser under period-one oscillation
at /o = 40 GHz.................................................................................
20
3.1 Optical spectrum under optical injection.....................................
28
3.2 Power spectra obtained before and after fiber propagation......
30
3.3 Microwave power received after propagation in fiber.................
31
3.4 Relative magnitudes of the optical frequency components under
different injections............................................................................
33
3.5 Mapping of the sideband rejection ratio R ..................................
35
3.6 Relative frequency difference A / / / 0.............................................
36
3.7 Mapping of the worst case
Pfo
after power penalty.
........................
3.8 Same as the previous figure except th at yp is increased............
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39
38
4.1 Schematics of the setup for modulating the period-one state. . . .
43
4.2 Behavior of the modulated period-one oscillation under a slowlymodulated injection..................................................................................
45
4.3 Behavior of the modulated period-one oscillation at different mod­
ulation frequencies....................................................................................
47
4.4 FM frequency response of the period-one state....................................
49
4.5 AM frequency response of the period-one state...................................
51
4.6 Schematic of the AM-to-FM setup.........................................................
53
4.7 Power spectrum of the slave laser under FM period-one oscillation.
54
4.8 Eye diagrams for AM-to-FM conversion................................................
56
4.9 BER for AM-to-FM conversion...............................................................
57
5.1 O utput of the slave laser under optical injection into period-two
oscillation....................................................................................................
62
5.2 Period-two power spectrum under modulation at / m = /o ................
65
5.3 Phase variance versus Pm when / m = / 0................................................
66
5.4 Period-two power spectrum under modulation at f m near / 0. . . .
67
5.5 Phase variance versus detuning for frequency division.......................
69
5.6 Locking ranges for frequency division....................................................
69
5.7 Phase variance versus Pm when / m = / 0/2 ...........................................
71
5.8 Phase variance versus detuning for frequency multiplication. . . .
71
5.9 Locking ranges for frequency multiplication.........................................
72
5.10 Phase variance versus the modulation power on the master laser. .
73
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6.1 Schematic of the optoelectronic feedback setup...................................
78
6.2 Optoelectronic feedback states................................................................
79
6.3 Stabilization of the frequency locking state..........................................
80
6.4 Phase noise suppressions of the frequency comb components. . . .
82
6.5 Comparison of frequency locking and gain switching.........................
84
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ACKNOWLEDGMENTS
I would first like to express my gratitude to Professor Jia-Ming Liu. My Ph.D.
study would not have been possible without his insightful guidance and encour­
agement.
I would also like to thank Professors Harold R. Fetterman, Tatsuo Itoh, and
Shantanu Sinha for their service on my Ph.D. dissertation committee.
I wish to thank the members of the Photonics Research Laboratory.
My
gratitude goes to Sheng-Kwang Hwang, How-Foo Chen, Shuo Tang, and Fan-Yi
Lin for kindly teaching me about semiconductor lasers dynamics. I would also
like to express my appreciation to Juan C. Garcia and Andrew K. Newman for
teaching me on solid-state laser experiments. I would also like to thank Margaret
C. Chiang, who is always there to lend a helping hand. I also thank Rosemary
Diaz, who is always very patient and helpful. I wish also to thank Tyan-Lin Wang,
Chieh-Feng Chang, Ting-Hsiang Wu, and Pei-Chi Jiang for their friendship and
support. I would also like to thank Professor Guang-Qiong Xia for her support.
My gratitude goes to Professor Claudio R. Mirasso and Raul Vicente for their
friendship. I am sincerely grateful to Mrs. Vida Liu for her encouragement.
My deep gratitude goes to my family. I would like to thank Aunt Barbara and
Uncle Alfred for their hospitality during my stay at Los Angeles. I am especially
indebted to my parents and my sister for their love.
Glory be to God for He is my strength, my shield, and my light.
x
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VITA
1998-2001
B.Eng., Department of Electrical and Electronic Engineering,
University of Hong Kong, Hong Kong
2001-2004
M.S., Department of Electrical Engineering, University of Cal­
ifornia, Los Angeles
2004-2007
Research and Teaching Assistant, Department of Electrical En­
gineering, University of California, Los Angeles
P
u b l ic a t io n s
S. C. Chan, S. K. Hwang, and J. M. Liu, “Period-One Oscillation for Photonic
Microwave Transmission Using an Optically Injected Semiconductor Laser” , sub­
mitted to Opt. Express.
S. C. Chan, G. Q. Xia, and J. M. Liu, “Optical Generation of a Precise Microwave
Frequency Comb by Harmonic Frequency Locking” , accepted by Opt. Lett..
G. Q. Xia, S. C. Chan, and J. M. Liu, “Multistability in a Semiconductor Laser
with Optoelectronic Feedback” , Opt. Express, vol. 15, pp. 572-576, 2007.
R. Diaz, S. C. Chan, and J. M. Liu, “Lidar Detection Using a Dual-Frequency
Source” , Opt. Lett., vol. 31, pp. 3600-3602, 2006.
xi
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S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-Fiber AM-to-FM Upconversion Using an Optically Injected Semiconductor Laser” , Opt. Lett., vol. 31,
pp. 2254-2256, 2006.
S. C. Chan and J. M. Liu, “Frequency Modulation on Single Sideband Using
Controlled Dynamics of an Optically Injected Semiconductor Laser” , IEEE J.
Quantum Electron., vol. 42, pp. 699-705 , 2006.
S. C. Chan and J. M. Liu, “Microwave Frequency Division and Multiplication
Using an Optically Injected Semiconductor Laser” , IEEE J. Quantum Electron.,
vol. 41, pp. 1142-1147, 2005.
S. C. Chan and J. M. Liu, “Tunable Narrow-Linewidth Photonic Microwave Gen­
eration Using Semiconductor Laser Dynamics” , IEEE J. Select. Topics Quantum
Electron., vol. 10, pp. 1025-1032, 2004.
S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-Fiber Transmission from
an Optically Injected Semiconductor Laser in Period-One State” , Proc. of SPIE,
vol. 6468, p. 646811, 2007.
R. Diaz, S. C. Chan, and J. M. Liu, “Dual-Frequency Multifunction Lidar”, Proc.
of SPIE, vol. 6457, p. 645700, 2007.
S. C. Chan and J. M. Liu, “Microwave Frequency Switching of an Optically
Injected Semiconductor Laser” , Opt. Soc. Am. Annual Meeting, FTuA5, 2005.
xii
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ABSTRACT OF THE DISSERTATION
Nonlinear Dynamics of Semiconductor Lasers for
Microwave Photonics Applications
by
Sze-Chun Chan
Doctor of Philosophy in Electrical Engineering
University of California, Los Angeles, 2007
Professor Jia-Ming Liu, Chair
Semiconductor lasers are high-speed devices th at can be modulated at microwave
frequencies. They are also intrinsically nonlinear devices because of the funda­
mental dependence of the optical gain on the electron and photon densities. By
introducing proper perturbations to an ordinary semiconductor laser, a variety
of high-speed nonlinear dynamics can be obtained. While these dynamics are
often avoided or neglected in practical applications, the goal of this dissertation
is to examine the feasibility of taming these dynamics for microwave photon­
ics applications. Two types of perturbation schemes are considered: the optical
injection scheme and the optoelectronic feedback scheme. In the optical injec­
tion scheme, the laser generally exhibits oscillatory dynamics, which include the
period-one and period-two oscillation states. The period-one oscillation is a state
obtained by exciting the instabilities of the injected laser so th at it undergoes pe­
riodic motion at a single frequency. The laser thus emits an optical carrier with a
single-cycle microwave modulation. This state is applied for tunable photonic mi­
crowave generation. The microwave frequency generated can exceed the original
modulation bandwidth of the laser. The photonic microwave is also analyzed for
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radio-over-fiber (RoF) transmission. The effect of chromatic dispersion-induced
power penalty is reduced by the single sideband (SSB) property of the period-one
state. Communication using frequency modulation (FM) is also demonstrated by
optically controlling the microwave frequency. In addition, the period-two state
is investigated using the optical injection scheme. The period-two state is a state
where the laser oscillates at twice the period of the period-one state. The periodtwo state is obtained from the period-one state through a nonlinear dynamical
period-doubling bifurcation, which generates the half-frequency from the original
fundamental microwave frequency. Microwave frequency division and multipli­
cation are demonstrated through microwave injection locking. Besides optical
injection, the optoelectronic feedback scheme is also investigated. The laser is
operated under the frequency locking state, where a microwave frequency comb is
generated on the optical carrier. The stability is improved by adding an external
microwave injection in obtaining a precise frequency comb. The overall results of
this dissertation illustrate th at the laser dynamics can be properly controlled for
a variety of microwave photonics applications.
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C H A PT E R 1
Introduction
1.1
M otivation
Semiconductor lasers have inevitably gained much attention since the early demon­
strations in 1962 [1, 2]. W ith the progress in semiconductor fabrication technol­
ogy, semiconductor lasers have been developed into compact, reliable, and efficient
coherent light sources. A wide optical spectrum from infrared to ultraviolet can
now be covered by semiconductor lasers [3]. The modulation bandwidth is also
significantly improved. A relaxation resonance frequency as high as 20 GHz has
been demonstrated recently [4]. As a result of these advantages, semiconductor
lasers are applied in many areas such as optical communication systems, data
storage, and medical applications.
Semiconductor lasers are also inherently nonlinear devices [5]. From the dy­
namical point of view, the state of a semiconductor laser is completely described
by the intra-cavity optical field and the population inversion. They are intrinsi­
cally coupled through the optical gain [6, 7]. The existence of nonlinearity stems
from the fact th at the optical gain is itself a function of the optical field and the
population inversion. Therefore, such nonlinearity is common to all semiconduc­
tor lasers. In fact, it is the reason for the well-known clamping of the population
inversion above threshold. Although the nonlinear dynamics are usually not ob­
served in a solitary semiconductor laser, they can be invoked by using different
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perturbation schemes such as optical injection [8, 9, 10, 11, 12, 13, 14, 15, 16],
optoelectronic feedback [17, 18, 19, 20, 21, 22, 23], optical feedback [24, 25], mu­
tual optical coupling [26, 27, 28], mutual optoelectronic coupling [29, 30, 31], and
strong current modulation [32].
A number of nonlinear dynamics can be obtained by properly adjusting the
perturbations. The dynamical states include stable locking [33], periodic oscilla­
tion [34, 35, 36, 37], regular pulsation [38], quasi-periodic pulsation [39], frequency
locking [40, 41], chaotic oscillation [42, 43, 44, 45, 46, 47, 48], and chaotic pulsa­
tion [49]. Because the dynamical parameters, such as the photon decay rate and
the electron decay rate, are typically in the range between 109 s-1 and 1011 s-1,
the nonlinear dynamics cause the light to vary at microwave frequencies. The
dynamics thus provide a convenient way of generating different microwave wave­
forms. While the nonlinear dynamics are often avoided or neglected in most
practical applications, the goal of this dissertation is to explore the feasibility of
taming these dynamics for microwave photonics applications.
1.2
Background
Microwave photonics generally refers to the technology of using optoelectronic
devices in handling microwave signals [50, 51]. It includes high-speed capabilities
such as the generation of light with microwave modulation [52], optical transmis­
sion of microwave [53], microwave frequency conversion [54], and signal conver­
sion [55]. Although there are several applications of semiconductor laser dynamics
reported in the area of microwave photonics, only the simplest dynamical states
and the most complicated dynamical states have been considered. On one hand,
the simplest dynamical state of stable locking has been applied to improve the
microwave modulation characteristics. The locking has been shown to enhance
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the laser modulation bandwidth [56, 57] and to reduce the laser chirping [58].
Stable locking from sideband injection also provides a method to improve the
signal purity when two lasers are heterodyned [59, 60]. On the other hand, the
most complicated dynamical states of chaotic oscillation and chaotic pulsation
are used in special applications. They are used for secure chaotic communication
because of the broadband and deterministic nature [61, 62, 63, 64, 65, 66, 67].
In the studies of chaos control, the knowledge about the chaotic state is used to
suppress its occurrence [68, 69]. Chaos is also used simply as a source of broad­
band signal [70], which can be applied for lidar and radar applications [71, 72].
However, besides the well-understood stable locking and chaotic states, there are
more nonlinear dynamical states to be explored.
1.3
O bjective
In this dissertation, we consider the photonics microwave applications of the rich
nonlinear dynamical states.
By considering the optical injection scheme, the
period-one oscillation state is generated. The single-cycle oscillation is applied
for photonic microwave generation. The generated frequency can be well beyond
the limit of the laser bandwidth. It is shown to possess a single sideband prop­
erty, which is desirable for microwave transmission over fiber. The state is also
optically controlled and modulated. The result is used for the transformation
of amplitude-modulated signal to frequency-modulated signal. The period-two
oscillation state is also generated by allowing the laser to undergo a perioddoubling bifurcation. The double-cycle oscillation is obtained and can be applied
for microwave frequency conversion. Besides the optical injection scheme, the
optoelectronic feedback scheme is also considered. The laser is operated under
the frequency locking state, where a microwave frequency comb is generated on
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the optical carrier. The stability of the comb is improved by adding an external
microwave injection. The overall results of this dissertation illustrate that the
laser dynamics can be properly controlled for a variety of microwave photonics
applications.
1.4
O utline o f th e D issertation
The outline of the dissertation is as follows. The main focus is put on the opti­
cal injection scheme under the period-one oscillation state. The simulation and
experimental results for using the state for photonic microwave generation are
presented in Chapter 2. It is followed by the analysis on the fiber transmission
characteristics in Chapter 3. The modulation characteristics of the period-one
state is considered in Chapter 4. Then the attention is turned towards the periodtwo state th at is obtained from the same optical injection system. The period-two
state is applied for microwave frequency conversion in Chapter 5. The optoelec­
tronic feedback scheme is investigated for microwave frequency comb generation
in Chapter 6. Finally, the conclusion and future directions are addressed in
Chapter 7.
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C H A PT E R 2
P hotonic M icrowave Generation by Periodic
Oscillations
The investigation on the application of laser nonlinear dynamics begins with the
generation of photonic microwave. In particular, the optical injection scheme is
considered because it is known to generate oscillatory dynamics at microwave
frequencies. The laser is first injection-locked and is subsequently driven into in­
stability. The dynamical state is referred to as the period-one oscillation, where
an optical wave with a microwave modulation is obtained. The microwave fre­
quency is broadly tunable by varying the injection conditions. Microwave fre­
quency several times the natural relaxation resonance frequency of the laser is
obtained [73, 74, 75].
2.1
Introduction
An im portant driving force behind the microwave photonic technology is the need
for transm itting microwave signals through optical fibers. In a radio-over-fiber
(RoF) system, a central office is connected to remote base stations by optical
fibers, through which light carrying microwave subcarriers is transm itted. At
the base stations, photodetectors recover the microwave signals, which are then
radiated to the wireless customer units [76]. RoF has the advantages of central-
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izing the high-speed electronics in the central office and allowing long-distance
microwave transmission. The capability of modulating up to about 60 GHz is
often desirable for wireless communication [77].
Semiconductor lasers have been applied as the source for RoF systems [78].
The simplest approach is to directly modulate a semiconductor laser with a mi­
crowave current source. However, due to intrinsic and parasitic constraints, both
modulation frequency and modulation amplitude of direct modulation are very
limited. The microwave frequency is limited by the relaxation resonance of the
laser to typically below 10 GHz.
The bandwidth limitation can be circumvented by applying an optical in­
jection to the laser. By invoking the period-one nonlinear dynamics, the laser
behaves as a widely tunable photonic microwave oscillator. In this chapter, the
properties of the microwave generation are presented. The setup of the optical
injection is described in Section 2.2. The simulation model and results are pre­
sented in Section 2.3, which explain the generation of the period-one state. The
experimental results are presented in Section 2.4. A brief comparison with other
available photonic microwave sources is discussed in Section 2.5, which is followed
by a summary in Section 2.6.
2.2
O ptical Injection Setup
A simplified schematic of the experimental setup is shown in Fig. 2.1. All semi­
conductor lasers are at 1.3 //m throughout this dissertation, but the principles
of nonlinear dynamics described in this dissertation are also applicable to lasers
at other wavelengths.
The lasers are single-mode distributed feedback lasers
(Bookham Technology LC131). The slave laser (SL) is biased at 2.22 times its
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ML
VA
FC
Of
SL
HWP
PD -
PSA
PBS
^
Optional
Figure 2.1: Schematic of the optical injection setup. ML: master laser; SL:
slave laser; M: mirror; VA: variable attenuator; PBS: polarizing beam splitter;
FR: Faraday rotator; HWP: half-wave plate; F: fiber; FC: fiber coupler; PD:
photodiode; A: microwave amplifier; PSA: power spectrum analyzer; OSA: optical
spectrum analyzer; and MFS: microwave frequency synthesizer. Thin and thick
lines correspond to optical and microwave paths, respectively.
18-mA threshold and tem perature stabilized at 18.00 °C. The output power is
about 4.5 mW, and it has a relaxation resonance frequency / r of 10.25 GHz. The
linewidth enhancement factor b is about 3.2. Light is injected into the slave laser
from a master laser (ML) through a free-space circulator arrangement that con­
sists of a polarizing beam splitter (PBS), a Faraday rotator (FR), and a half-wave
plate (HWP). Light is injected from the master laser to the slave laser, while the
output of the slave laser is transm itted through the PBS into an optical fiber (F).
It is then split by a 3-dB fiber coupler (FC). The optical spectrum of the electric
field is monitored by an optical spectrum analyzer (OSA) (Newport SR-260-C).
The power spectrum of the intensity is monitored by a power spectrum analyzer
(PSA) (HP E4407B) after detection by a 35-GHz photodiode (PD) (Discovery
Semiconductors DSC 20S-3-FC) and amplified by a 26.5-GHz 20-dB amplifier
(A) (HP 83006A).
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The injection power of about 5 mW impinges on the front facet of the slave
laser.
Much of the power is lost because of imperfect alignment and spatial
mode mismatch. It is estimated, by comparison with simulations, th at the actual
power injected into the slave laser is on the order of 10 [AN. In the experiment,
the injection power can be adjusted using a variable attenuator (VA). The optical
frequency of the injection can be carefully tuned by adjusting the temperature
and the bias of the master laser. The optical injection is sufficient to drive the
slave laser into the period-one state for microwave generation. However, as an
option, a microwave frequency synthesizer (MFS) (HP 83620A) can be used to
apply a weak current modulation for the purpose of frequency stabilization.
2.3
Sim ulations
The experimental setup of optical injection is first simulated based on the rateequation model. The equations have been verified by many numerical and exper­
imental studies of laser nonlinear dynamics [79, 6].
2.3.1
R a te E quation M odel
The slave laser is described by the following rate equations of a single-mode
semiconductor laser under optical injection [79]:
r
dL4
dt
di
2
=
+ \(u0 - 1uc) A + ^-(1 - \b)gA + 77A e m
2
(2.1)
^
7d - ^ N - * s
where A is the complex intracavity field amplitude at the free-running angular
frequency
uiq
of the slave laser, yc is the cavity decay rate, u c is the cold cavity
angular frequency, T is the confinement factor of the optical mode inside the gain
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medium, b is again the linewidth enhancement factor, g is the optical gain, r) is
the injection coupling rate, A\ is the injection field amplitude, /; = 0 ; / 27t is the
detuning frequency of the master laser with respect to
luq/2 tt,
N is the charge
carrier density, J is the injection current density, e is the electronic charge, d is
the active layer thickness, ys is the spontaneous carrier relaxation rate, and S
is the active region photon density. The photon density is related to the field
by [80]:
S = ^ -\A \2
h(j0
(2.3)
where eo is the free-space permittivity, n is the refractive index, and fi is the
reduced Planck’s constant. The gain is a function of N and S. It is given by [3]:
N —N0
7c ,
S -S 0
( 2 ' 4 )
where yn is the differential carrier relaxation rate, yp is the nonlinear carrier
relaxation rate, and No and So are respectively the steady-state values of N and
S when the slave laser is free-running.
The rate equations (2.1) and (2.2) can be normalized using or + ia, = T /|T 0|
and 1 + n = N/N o, where To is the free-running A. The equations become:
dUr
l r7 c 7 n ^
dt
777
dt
dn
dt
2 7SJ
.
/
2
,
2
n - 7P(ar + af - l)](ar + 6aj) +
=
7 [ - ^ - y ^ - 7 P(Or + o f - l ) ] ( - 6 or + a i ) - ^ 7 c S m f i i i
=
~[7s + 7n(ar + Oj )]n - 7SJ ( a r + as - 1)
I 7s J
-I-TVT^j(q2 -1- a 2 )( Q2 -1- a 2 _
1
)
(2.5)
(2.6)
^2.7)
7c
where J = (J/ ed —^sNo)/%No is the normalized bias above the threshold current
and
= 771A;[/7C|^401 is the dimensionless injection strength [79].
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2.3.2
D ynam ical Param eters
The values of the dynamical parameters can be experimentally extracted from the
slave laser using a well established four-wave mixing technique [81]. Their values
are as follows [56]: yc = 5.36 x 1011 s_1, % = 5.96 x 109 s_1, yn = 7.53 x 109 s_1,
7P = 1.91 x 1010 s-1 , b = 3.2, and J = 1.222. The relaxation resonance frequency
is given by / r = (27r)_1(7c7n + 7S7P)1//2 ~ 10.25 GHz [3]. Numerically, we conduct
a second-order Runge-Kutta integration for a duration longer than 1 ps. The
injection strength & is varied between 0 and 0.4, while the frequency detuning f\
is varied between —10 and 60 GHz. We consider mainly positive f\ because the
period-one state is usually seen at positive detunings. Negative
leads to stable
locking and mode hopping dynamics [82]. The optical and the power spectra are
obtained from the Fourier transforms of or + ioj and |ar -I- iaj|2, respectively.
2.3.3
D ynam ical S tates
The evolution of the dynamics of the slave laser is shown in Fig. 2.2. The injection
strength £; is increased, while the injection detuning is kept constant at f\ —
5 GHz. The left column shows the optical spectra with the frequency axis offset
to the free-running frequency of the slave laser. The arrows indicate the position
of the optical injection. The right column shows the trajectories of the electric
field phasor, which is presented in the frame of the injected optical frequency.
When £ = 0.016, shown in Fig. 2.2(a), the slave laser is stably locked by the
master laser into the injected frequency as shown in the optical spectrum. The
phasor is fixed at a point, and the slave laser is under the stable locking state [80].
When
= 0.026, shown in Fig. 2.2(b), sideband emerges in the optical spectrum
as instabilities develop through a Hopf bifurcation. The corresponding phasor
traces a closed loop periodically at a microwave frequency / 0. This is called the
10
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Optical Spectrum (20 dB/div.)
Phasor, (a+'\a) eP*
^ = 0.016
(a)
Stable locking
L
Hopf
bifurcation
= 0.026
< ?
Period-one
Perioddoubling
bifurcation
t =
0.039
**?.
Period-two
Perioddoubling
bifurcations...
L = 0.050
traos
Frequency Offset (GHz)
Figure 2.2: Evolution of the optical injection dynamics. The injection strength &
varies, while the detuning is kept constant at /; = 5 GHz. Left column: the optical
spectrum with the arrows indicating the injected component. Right column:
trajectory of the electric field phasor in reference to the injection frequency.
11
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period-one oscillation state [79, 83]. When & = 0.039, shown in Fig. 2.2(c), the
frequency spacing in the spectrum is reduced by half through a period-doubling
bifurcation. The corresponding trajectory becomes a connected double-loop such
that it takes twice as long to complete a full period. The laser is said to be in
the period-two state [15]. As the injection strength £ continues to increase, the
laser undergoes more cascaded period-doubling bifurcations so th at the frequency
spacing decreases monotonically while the spectrum broadens. At £, = 0.050
in Fig. 2.2(d), a continuous spectrum is obtained. The trajectory becomes a
complicated structure and the motion is aperiodic. The laser has followed the
period-doubling route into chaos [45]. However, if £ is further increased beyond
0.053, the laser will soon return to the period-one state through a reverse perioddoubling route.
Among the four states presented, the stable locking state has been throughly
studied because of its improved modulation characteristics [80, 56, 84]. The
chaotic state has also received much attention for its usefulness in chaotic se­
cure communication [61, 62, 63, 64]. Therefore, this dissertation does not focus
on those two states, but instead investigates the remaining periodic states. In
particular, the microwave generation characteristics of the period-one state are
analyzed throughly as follows.
2.3.4
M icrow ave G eneration
When the slave laser is in the period-one state, the beating of the optical com­
ponents (Fig. 2.2(b)) at the photodiode generates a microwave signal with a
fundamental frequency of /o . Period-one states exist within a large region of the
injection param eter space defined by (&, /;). The dependence of / 0 as a function
of £; is shown in Fig. 2.3 for different values of /;. When £ is very small, the slave
12
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30 GHz
20 GHz
::—10 GHz
: —
*a
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Injection Strength, ^
Figure 2.3: Fundamental microwave frequency folaser emits at its undisturbed free-running optical frequency. The regenerated
injection beats with the slave laser and generates fo & f\- This is the case for
all the curves in Fig. 2.3 at & ~ 0. When & is gradually increased for the cases
of /; — 40, 30, and 20 GHz, Fig. 2.3 shows that fo also increases accordingly.
It can be qualitatively understood as a result of the red-shifting of the cavity
resonance. When & increases, the optical gain deficit increases [80, 85]. Because
of the antiguidance effect, the refractive index increases and thus the cavity reso­
nance shifts red. Hence, / 0 generally increases with £ for a fixed positive f . This
is observed in many related studies [79, 73, 86, 37].
However, exceptions to the general trend are found when the cavity redshifting effect is opposed by another effect, the injection pulling effect. The pulling
effect is explained by the Adler’s equation that governs the phase dynamics of
the laser [87]. As a weak injection progressively locks the optical phase of the
slave laser, the injected field pulls the frequency of the intracavity field oscillation
away from the cavity resonance towards the injected frequency. Hence, the pulling
13
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effect tends to reduce the frequency separation f 0.
The dependence of f 0 on & is determined by whether the red-shifting effect or
the injection pulling effect dominates. The competition between these two effects
is illustrated by the curve of /; =10 GHz in Fig. 2.3. For £, < 0.02, fo decreases
with £ as a result of the progressive injection pulling en route to locking. For
> 0.04, f 0 obeys the general trend of increasing with £ as the cavity redshifting dominates. For 0.02 < 6 < 0-04, fo changes abruptly because the laser
enters the chaotic state. Since it is impossible to define a fundamental frequency
for the broadband chaotic spectrum in a conventional sense, fo is numerically
defined such th at integrating the power spectrum from 0 to / 0 contains 1% of the
steady-state power.
The dependence of / 0 on £ and f is more clearly presented as a mapping
in Fig. 2.4. A large region of period-one states is identified above the stable
locking region across the Hopf bifurcation line. Period-two and chaotic regions are
embedded within the period-one region when /; is near the free-running relaxation
resonance frequency, / r [79, 88, 11]. The injection pulling effect dominates only
when /j is small enough for the progressive pulling into locking to be significant
(Fig. 2.4). The slopes of the contour lines indicate th at fo decreases with
Other
than these small and isolated regions in Fig. 2.4, the contour lines of constant / 0
reveal th at / 0 increases with £ in nearly the whole period-one region. The optical
injection system is capable of generating widely tunable microwave signals of over
60 GHz, which is almost 6 times the free-running relaxation resonance frequency
of the laser. Even higher frequencies can be obtained by increasing the detuning
frequency until / 0 reaches the free-spectral range of the laser, where the single­
mode model of the laser no longer applies. The free-spectral range is on the order
of 100 GHz for a typical edge-emitting laser.
14
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Frequency Detuning,^ (GHz)
Fundamental Frequency,^, (GHz)
Period-one
Stable locking
Period-two/chaos
Injection pulling
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Injection Strength, £,;
Figure 2.4: Mapping of the fundamental frequency / q.
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0.40
10
<5 —10
-20
o -30
-40
_JQ
0.00
1
0.05
0.10
■
1
1
1
1
0.15
0.20
0.25
0.30
0.35
0.40
Injection Strength, ^
Figure 2.5: Fundamental and second harmonic microwave power Pfo (closed sym­
bols) and P^fo (open symbols) at /; = 40 GHz (circles), 30 GHz (triangles), and
20 GHz (squares).
The optical frequency components in Fig. 2.2(b) separated by / 0 are converted
into microwave signals at the photodiode. For RoF applications, it is important
to understand how the generated microwave power varies with & and f\. The
powers at the fundamental / 0 and the second harmonic 2 /0 are denoted as
Pfo
and P2fo, respectively. The fiber length is assumed to be zero here to illustrate
the power variation before suffering from the chromatic dispersion power penalty.
Figure 2.5 shows the variations of P/0 and P2f0 with respect to
The circles,
triangles, and squares correspond to /; = 40, 30, and 20 GHz, respectively. The
powers level off soon after the period-one region is entered (Fig. 2.4).
Also,
the second harmonic is significantly weaker than the fundamental. The ratio
Pfo/Pzfo
always larger than 20 dB. The mapping of Pf0 is shown in Fig. 2.6.
Since the absolute microwave power generated depends on the responsivity of the
photodiode, all microwave power measurements are normalized to the peak value
of Pf0, which is shown in Fig. 2.6 as the 0-dB point at £ = 0.095 and /i =5 GHz.
16
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Fundamental Microwave Power,
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Injection Strength, ^
Figure 2.6: Mapping of the fundamental microwave power P fo generated before
transm itting over fiber. All microwave powers are normalized to the maximum
power obtained at (£, /j) = (0 .0 9 5 ,5 GHz).
17
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Using a laser output of 1 mW, the microwave power at the 0-dB point is about
—22 dBm when a typical 0.5-A/W detector is employed.
2.4
E xperim ental R esults
Experiments are performed to verify the simulations. Optical injection alone in
Fig. 2.1 is used to generate the signal without using the microwave synthesizer.
When the frequency detuning of the injection is set at zero, a range of fo can
be obtained by varying the injection strength. Figure 2.7(a) shows the nearly
linear dependence of the required injection strength on the desired frequency of
the microwave signal, while Fig. 2.7(b) shows the corresponding microwave power
obtained. The microwave power emerges at about fo = 11.3 GHz, close to the
original relaxation resonance frequency of the slave laser, and it stays almost
constant as the frequency increases. The microwave signal can also be tuned
by varying the frequency detuning of the injection. Figure 2.8(a) shows the re­
quired detuning as a function of the desired fo under a fixed injection strength of
£i = 0.082, which corresponds to the injection power of 7.3 mW. The generated fo
increases as the detuning increases. The corresponding microwave power gener­
ated is shown in Fig. 2.8(b). The power stays nearly constant as long as the slave
laser is in the period-one state, which occurs for fo > 14.8 GHz. Due to errors
in the measurements of the dynamical parameters, there are small quantitative
discrepancies between experiments and simulations. Nevertheless, these results
show th at the system can be used as an optically controlled microwave source of
large tunability.
The stability of the generated microwave is demonstrated in Fig. 2.9. By
adjusting the bias current of the master laser, the optical frequency of the master
laser is detuned from the free-running optical frequency of the slave laser by
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0.16
. 0.12
0.08
0.04
0.00
11
Microwave Frequency,/, (GHz)
12
13
14
15
16
17
Microwave Frequency,/, (GHz)
Figure 2.7: Tuning characteristics for generating microwave frequency / 0 under
injection at zero detuning, (a) The injection strength required, (b) The relative
microwave power generated.
11
12
13
14
15
16
17
18
12
Microwave Frequency,/, (GHz)
13
14
15
16
17
Microwave Frequency,/, (GHz)
Figure 2.8: Tuning characteristics for generating microwave frequency / 0 under
a constant injection of & = 0.082. (a) The injection frequency detuning required,
(b) The relative microwave power generated.
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0.2
Injection
(a)
fi
3
/ 0 = 40G H z
<3
&
o
~
o.l
o
*£3
&
o
0.0
-1 0
-5
0
5
10
15
20
25
30
35
Optical Frequency Offset (GHz)
?
-3 0
Span = 50 MHz
(b) Not locked
§ , -4 0
uiiuiid
<3
1
-5 0
P*
£
-6 0
£
2
-7 0
40.000
Microwave Frequency (GHz)
-4 0
(c) Locked
Span = 100 Hz
-6 0
-8 0
| -loo » V
H - 1 2 0 _____
39.99999995
40.00000000
40.00000005
Microwave Frequency (GHz)
Figure 2.9: Experimental spectra of the slave laser under period-one oscillation
at fo = 40 GHz. The injection strength is £ = 0.328 and the injection detuning
is /j = 30.7 GHz. (a) Optical spectrum offset to the free-running frequency of the
slave laser, (b) Power spectrum revealing the fluctuation between the two optical
lines, (c) Power spectrum stabilized by current modulation at the subharmonic
frequency / 0/2.
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/i = 30.7 GHz. The injection strength is adjusted to & = 0.328. The injection
drives the slave laser into period-one oscillation with a fundamental frequency
of / 0 = 40 GHz. In this particular detection, the original photodetector and
amplifier do not have enough bandwidth; therefore, they are replaced by a faster
45-GHz photodiode (New Focus 1011). The power spectrum analyzer is also
replaced by a faster model (Agilent 8565EC).
Figure 2.9 shows the spectra obtained in the period-one state. The optical
spectrum in Fig. 2.9(a) is again offset to the free-running frequency of the slave
laser and only the two strongest lines are shown in this span. Unlike a freerunning laser th at emits only a single line at the zero offset, the slave laser emits
two lines of approximately equal magnitudes, which cannot be obtained by direct
current modulation. The line at the frequency offset of f = 30.7 GHz is caused
by the injection from the master laser, whereas the line at fi — fo — —9.3 GHz
is caused by the period-one oscillation at / 0 = 40 GHz. The beating of the two
lines results in the power spectrum as shown in Fig. 2.9(b). The signal is quite
noisy because of the intrinsic fluctuations of the system, such as the spontaneous
emission noise of the slave laser and the power variation from the master laser
injection.
In order to improve the signal purity, the microwave synthesizer is switched
on to apply a stable microwave current modulation.
In this experiment, we
demonstrate subharmonic microwave locking by applying an external microwave
at / 0/2 to lock the fundamental at fo [89]. W ith a modest modulation strength
of 5 dBm, the signal can be drastically improved. The stabilized signal is shown
in Fig. 2.9(c) at a much reduced span. The full width at half-maximum is mea­
sured to be less than 1 Hz, which is limited by the measurement equipments.
The signal can also be stabilized if the modulation is applied at fo [90]. How-
21
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ever, the subharmonic locking technique allows us to use an external source at
a reduced frequency. It is particularly useful for generating high frequency mi­
crowave beyond the usual bandwidth of electronic components. The microwave
frequency can also be stabilized through various microwave locking techniques,
such as self-injection locking [91, 73] and phase locking [92], These techniques
cannot be directly applied if the microwave is instead generated by heterodyning
two independent lasers.
2.5
Com parison
Generation of an optical wave that carries a tunable microwave modulation is de­
scribed in the previous sections using the period-one dynamics. However, there
are other sources commonly employed for the same purpose. Most of these meth­
ods can be categorized into four groups: direct current modulation, mode locking,
external modulation, and optical phase-lock loop. These methods are briefly de­
scribed as follows.
Direct current modulation refers to applying a microwave signal on the bias
current of a semiconductor laser. It is the simplest method of photonic microwave
generation, but it cannot be used beyond about 10 GHz because of the modulation
bandwidth limitation [56], This limitation can be slightly alleviated by applying
an optical injection while operating the slave laser in the stable locking state [93],
but the complexity of the setup is then the same as th at described in this chapter.
Furthermore, when direct current modulation is used for microwave generation,
the modulation depth is limited. The laser has to stay in the small-signal regime
so as to avoid other nonlinear dynamics.
Mode-locked semiconductor lasers using a multi-section cavity design can gen-
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erate microwave at the reciprocal of the cavity round-trip time. Frequencies of
tens of gigahertz have been demonstrated [94, 95]. However, the physical con­
straint of having a fixed cavity causes difficulties to tune the frequency. Therefore,
this method is not very flexible.
External modulators, including electro-optic and electro-absorption modula­
tors, are im portant devices for high frequency photonics. Modulation frequencies
of up to 165 GHz have been demonstrated [96]. However, these devices are rela­
tively lossy and require a strong pump laser as input [97].
Optical phase-lock loop can be used to stabilize the beating between two in­
dependent semiconductor lasers. Beating of over 36 GHz has been demonstrated
using a fast loop [77], but this method has very stringent requirement on the
bandwidth of the phase-lock electronics and frequency control of the lasers.
Therefore, photonic microwave generation using the period-one dynamics
compares favorably to the other methods. The wide tunability beyond 6 times the
relaxation resonance frequency is illustrated in Fig. 2.4. It is also easily stabilized
by various microwave locking techniques. The drawback of the method is the rel­
ative complexity of the setup, but the setup can be simplified into fiber-based
system in practice.
2.6
Sum m ary
In summary, this chapter presents a method of photonic microwave generation.
By controlling the operating condition of an optically injected semiconductor
laser, the period-one oscillation is obtained as part of the nonlinear dynamics.
The microwave frequency and power are described in detailed using a simulation
model, which shows th a t a microwave frequency of more than 6 times the relax-
23
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ation resonance frequency can be generated. The frequency generated generally
increases with both the injection strength and detuning. Experiments are also
performed to verify the microwave characteristics. As an example, a 40-GHz sig­
nal is generated from a period-one state. The optical spectrum consists of two
lines of nearly equal amplitudes. The two lines can be locked so th at the beating
fluctuates within less than 1 Hz, which is limited by the measurement equipment.
Such widely tunable photonic microwave cannot be easily generated with other
methods.
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C H A PT E R 3
Single-Sideband Radio-over-Fiber Transmission
This chapter investigates the transmission of the period-one microwave modula­
tion over an optical fiber. Through controlling the optical injection, the generated
optical spectrum can be adjusted to be nearly single sideband (SSB). The SSB
spectrum is advantageous for minimizing the chromatic dispersion-induced power
penalty. A map is obtained for optimized operation [74, 75].
3.1
Introduction
In an RoF system, microwave signals are transm itted over long distances through
optical fibers [98, 99, 76]. The effect of dispersion becomes im portant as the
distance increases. Most RoF systems uses double sideband (DSB) modulated
light for simplicity. However, when the dispersion introduces a phase difference
between the sidebands from the optical carrier, the generated beat signals be­
tween the sidebands and the carrier may add up destructively depending on
their phase relationship. This results in a reduction of the generated microwave
power. The effect is referred to as the chromatic dispersion-induced microwave
power penalty [95, 100].
The power penalty can be avoided by using the SSB modulation scheme. A
number of SSB optical microwave sources have been reported, including phaselocked heterodyne lasers [101, 77, 102], SSB external modulators [76, 52, 100],
25
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dual-mode or multisection semiconductor lasers [103, 95, 104, 105, 106], and
filtering directly modulated semiconductor lasers [107].
When properly controlled, the period-one states give SSB spectra as well.
These properties enable the optical injection system to be a useful RoF source.
The SSB characteristics and the associated immunity to the power penalty are
addressed in this chapter. Comprehensive numerical simulations of the system
are conducted over a range of injection strengths and frequency detunings. Un­
der different injection conditions, DSB and SSB are found for the period-one
state. The results serve as a guideline for optimizing the systems for practical
RoF applications. The origin of the chromatic dispersion-induced power penalty
is discussed in Section 3.2. The SSB characteristics are presented in Section 3.3.
The optimal operating conditions are presented in Section 3.4. The RoF perfor­
mance is summarized in Section 3.5.
3.2
Chrom atic D ispersion-Induced Power P enalty
3.2.1
Form alism
In order to investigate the effect of fiber dispersion on the period-one microwave
transmission, we first simulate the slave laser dynamics using the rate equations
(2.1) and (2.2) to obtain the complex optical spectrum. The fiber dispersion is
then modeled by introducing a frequency-dependent phase into the spectrum.
The phase is simply given by [3]:
0(o;) - - *
- u j 0)2
(3.1)
47TC
where
uj
is the optical angular frequency, A is the wavelength, I is the fiber
length, D \ is the group-velocity dispersion, and c is the speed of light in freespace. In the simulation of dispersion, we adopt typical values th at A = 1.55 /xm
26
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and D \ = 17 ps/km-nm, as in a Corning SMF-28 fiber. Fiber attenuation is
neglected here. The modified optical spectrum is Fourier-transformed into the
time-domain optical field. The field is squared into intensity, which is transformed
back to the frequency domain. The result is the power spectrum detected after
the propagation through the fiber.
3.2.2
R ep resen tative S tates
The significance of dispersion-induced power penalty depends on the optical spec­
trum of the period-one state. Figure 3.1 shows the detailed evolution of the op­
tical spectra. The frequency axis is again offset to the free-running slave laser
frequency. The injection frequency detuning is kept constant at /, = 20 GHz,
while the injection strength & is varied. When & = 0.35, shown in Fig. 3.1(a), the
injection is strong enough to pull the slave laser to the injected frequency. The
laser is stably locked at f . When £; is decreased to 0.29, shown in Fig. 3.1(b),
the laser undergoes a Hopf bifurcation into period-one oscillation at frequency
fo. The spectrum consists of components separated from f by multiples of / 0.
The main components are at f c = f\ — fo and f . The next strongest component
is at / c —fo, but it is over 20 dB weaker than the two main components. There­
fore, the signal is approximately SSB, which is desirable for RoF transmission.
However, when & is reduced to 0.06, shown in Fig. 3.1(c), the period-one spec­
trum becomes nearly DSB. The carrier frequency at /; —/ 0 is surrounded by two
equally strong sidebands. Also, the frequency separation / 0 is reduced. When
£ is further decreased to 0.01, shown in Fig. 3.1(d), the spectrum continues to
be double-sided. The microwave frequency fo is further decreased such that the
carrier is now at f — f 0 ~ 0, which corresponds to the free-running frequency of
the slave laser. The period-one state has gradually become a four-wave mixing
27
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-1 0 0
f.
(a) ^ = 0.35
-150
-200
50
^10
-3 0
-2 0
-1 0
10
0
i
20
.
.
30
40
5
-100
(b) 6 , - 0.29
fi
fo
PQ
w
!
fo
-150
-
.
.
-200
o<D
-50 -40 -30
a -100
CZ5
(c) S; = 0.06
13
o
,
,
J1
.
.
-20
-10
0
10
20
30
40
50
-20
-10
0
10
20
30
40
50
-20
-10
0
10
20
30
40
50
,
J,
•^
a,
O
-50
(d)
-200
-50
-40
-30
= 0.01
-40
-30
Frequency Offset (GHz)
Figure 3.1: Optical spectrum with the frequency offset to the free-running slave
laser frequency. The injection frequency detuning is kept constant at f\ = 20 GHz
as indicated by the arrows. The injection strength & is varied to obtain different
states: (a) stable locking (& = 0.35); (b) SSB period-one (& = 0.29); (c) DSB
period-one (& = 0.06); and (d) four-wave mixing (£; = 0.01).
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state between the free-running slave laser and the optical injection [81]. Regions
of complicated dynamics are absent under this value of injection detuning.
In order to illustrate the effect of dispersion on the period-one states, we con­
sider the representative SSB and DSB period-one states presented in Fig. 3.1(b)
and (c), respectively. Their power spectra before and after propagating in the
fiber are shown in Fig. 3.2. The SSB period-one state is obtained at & = 0.29
and /i = 20 GHz. Figure 3.2(a-i) shows its power spectrum before propagating in
the fiber, where a strong fundamental microwave signal at / 0 is obtained. From
the corresponding optical spectrum of Fig. 3.1(b), it is apparent th at the mi­
crowave power
Pf0
is generated mainly from the beating of the optical frequency
components at /; and f\ — fo- When propagated through the fiber, the phase
difference between the two optical components changes. However, the phase dif­
ference does not strongly affect the magnitude of the beat signal. Therefore, the
power spectrum after propagating through the fiber, shown in Fig. 3.2(a-ii), re­
veals no significant changes in
Pfo-
The penalty varies with the distance, but the
value of I = 1.5 km shown is already the worst for this frequency.
On the other hand, the DSB period-one state obtained at £ = 0.06 and
/i = 20 GHz behaves differently.
The power spectrum in Fig. 3.2(b-i) before
the fiber propagation corresponds to the optical spectrum in Fig. 3.1(c). In this
case, fo is generated from the beating between f x and f\ —fo and th at between
f\ —fo and /j — 2 /0. Because the optical components at f\ and /j — 2 /0 are of
comparable magnitudes, both of their beat signals with the common /, —f 0 are
important to the microwave generated. The microwave is a coherent sum of the
beat signals; therefore,
Pfo
depends critically on their phase difference. As a
result, when extra phases are acquired during the fiber propagation, the value
of Pf0 varies significantly. It is shown in Fig. 3.1(b-ii) th at Pf0 is significantly
29
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(a-i)
(a-ii)
<u o
0
20
40
60
80
100
0
20
Frequency (GHz)
40
60
80
100
80
100
Frequency (GHz)
(b-ii)
Si= 0.06
20
40
60
0
80
Frequency (GHz)
20
40
60
Frequency (GHz)
Figure 3.2: Power spectra obtained (i) before, and (ii) after fiber propagation of
length I. The input period-one states are obtained at (&, f ) : (a) (0.29, 20 GHz),
and (b) (0.06, 20 GHz).
reduced at I — 5.5 km. The power penalty A Pf0 is about 13.1 dB in this case.
The effect is more clearly shown in Fig. 3.3. The fundamental microwave
power Pf0 at fo is plotted against the fiber length for both the SSB and the DSB
period-one states. The second-harmonic microwave power P2/0 at 2/o is also plot­
ted. For the DSB period-one state in Fig. 3.3(b), a repetitive and deep variation
of APf0 — 13.1 dB in the fundamental microwave power Pf0 is observed as the
fiber length increases. The periodicity in I corresponds to a 27r-increment of the
dispersive phase difference. By contrast, the SSB period-one state in Fig. 3.3(a)
experiences only a small power variation of A Pf0 = 1.6 dB. The improvement is
expected because the microwave power is generated predominantly by the beat­
ing of two optical lines and there is no phase issue for the SSB case. For a fair
comparison, the spectra in Figs. 3.2(a-ii) and (b-ii) are calculated at different val-
30
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30
(a) SSB
<3
£ 20
o
Ph
<L)
£
£
2o 10
u
•>
^
0
P4
5
0
10
15
20
25
30
25
30
Fiber Length (km)
30
(b) DSB
<3
£ 20
o
put
<D
£
£
oIH 10
o
<D
>
lia
0
p4
0
5
10
15
20
Fiber Length (km)
Figure 3.3: Microwave power at the fundamental fo and the second-harmonic 2/o
received after propagation in fiber, (a) SSB period-one generated at (&, /,) =
(0.29, 20 GHz), (b) DSB period-one generated at (£;, /,) = (0.06, 20 GHz).
31
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ues of I, which are obtained from the first minima of P/0 in Figs. 3.3(a) and (b),
respectively. From Fig. 3.3, it is clear th at a desirable optical injection should
drive the slave laser into an SSB period-one state so as to mitigate the fluctua­
tion of Pf0 over I. We thus turn our attention to the dependence of the optical
spectrum on the injection parameters & and f\.
3.3
Single Sideband (SSB) C haracteristics
Referring to the optical spectra in Figs. 3.1(b) and (c), the main optical com­
ponents of the period-one state are situated at the frequency offsets of f\ —2 /0,
/i —fo, f , and /j + fo- In order to quantify the study of the optical spectrum,
the field components are denoted here as
A f^fo,
Afc-/o> A f v and Afi+/o> respec­
tively. Figure 3.4 shows the magnitudes of these components as & varies while
fi is kept constant at 40, 30, and 20 GHz. We notice th at A j.^fo, A /W o and
Afi+fo vanish when £ > 0.33 in Fig. 3.4(c) because the laser is stably locked by
the master laser. The same transition happens for Figs. 3.4(a) and (b) at large
values of £ beyond the presented range. For the rest of Fig. 3.4, the laser is under
period-one oscillation. A few general characteristics are observed:
• The magnitude of A ^ increases with £; because it is the direct regeneration
of the optical injection.
• The magnitude of Af{- f 0 gradually decreases as & increases because the
gain is increasingly saturated and reduced by Afr In the limit of £ = 0,
= A 0. In fact, Fig. 3.4 is normalized to
the laser is free-running and
|A 0|.
• The strongest components are Af.t and
Because they have opposite
dependencies on &, their beat microwave signal Pf0 has a weaker dependence
32
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(a)/: = 40 GHz
2 -20
-6 0
OjOO
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.15
0.20
0.25
0.30
0.35
0.40
13 -20
-6 0
000
(c)f{ = 20 GHz
ok
—60
0.00
0.05
0.10
Injection Strength, ^
Figure 3.4: Relative magnitudes of the optical frequency components when f\ =
(a) 40 GHz, (b) 30 GHz, and (c) 20 GHz.
33
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on £j. (See Fig. 2.5.)
• The Af.+f0 component is usually the weakest among the four components
shown. Thus, it can be neglected along with the other components not
considered in Fig. 3.4, which are even weaker.
Therefore, the period-one state consists mainly of a central carrier A/._/0, which
is surrounded by the sidebands A fx- 2f0 and A fr A true SSB would consist of
only the
A
and Af. components, whereas a balanced DSB has equal
and
components. The SSB characteristics can be quantified by the sideband
rejection ratio th at is defined here as R = 20log |A/i/ J4/._2/0|.
The dependence of R on (&, /j) is presented as a mapping in Fig. 3.5. The
period-one oscillation is exactly DSB along the 0-dB contour line. However, as
the operation point moves away from the region enclosed by the 0-dB line, there is
a large region of increasingly SSB states. At the proximity of the Hopf bifurcation
line, states with A/; over 20 dB stronger than A/;_2/0 can be easily found, which
can be practically regarded as an SSB signals [95]. It is desirable to operate the
laser in this region such th at the dispersion-induced power penalty is small.
The reason th at most period-one states possess nearly SSB spectra can be
qualitatively explained as follows. Due to optical injection, the time-averaged
gain of the slave laser (g) is reduced from its free-running value 7c/ r . Through
the coupling to the refractive index, the optical resonance of the cavity is shifted
by
/*= S ',(g- T >
(3'2)
which can be obtained by inspecting (2.1) and (2.2). The frequency difference be­
tween the existing period-one component A/j_/0 and the shifted cavity resonance
34
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Frequency Detuning,^ (GHz)
Sideband Rejection Ratio, R (dB)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Injection Strength, ^
Figure 3.5: Mapping of the sideband rejection ratio R.
35
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0.40
0.8
0.4
0.2
0.0
20 GHz
0.00
0.05
0.10
0.15
0.20
0.25
0.30
• • • • • <
A
AA▲.
30 GHz
0.35
0.40
Injection Strength, ^
Figure 3.6: Relative frequency difference A / / / 0. A / is the frequency difference
between the period-one component /; —/ 0 and the shifted cavity resonance / s.
is given by:
A / = /i - / 0 - / s.
(3.3)
By applying (2.4) and the simulation results of (N , S) from (2.1) and (2.2), A /
is obtained as shown in Fig. 3.6, which shows th at | A / / / 0| <C 1. Thus
/t—/0
receives the strongest enhancement from the frequency-shifted cavity among the
other components of the optical spectrum. In addition, the other component, Af.,
is strong because it is the direct regeneration of the injection. Therefore, there
are two dominating optical components, namely,and Af., which constitute
an SSB spectrum.
This qualitatively explains the immunity to the power penalty
for a large region of the period-one oscillations in the maps.
36
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3.4
O perating C onditions
The main focus of this chapter is to study the immunity of the SSB periodone states to the RoF power penalty. From the practical point of view, we are
interested in knowing the minimum microwave power Pf0 th at is guaranteed to a
user at an arbitrary distance. The minimum power equals the power generated
immediately after the laser (Fig. 2.6) minus the maximum power penalty. In
other words, we are interested in finding the values of Pf0 at the minima of the
curves similar to th at of Fig. 3.3. The minimum power is shown as the mapping
in Fig. 3.7. A peak of —3 dB is attained at & = 0.25 and /, = 20 GHz. The
high-power region around it is compared to the high-power region of Fig. 2.6. It
is shifted towards the direction of increasing & because R, and the corresponding
immunity to the power penalty, generally increases with & according to Fig. 3.5.
Comparison to Fig. 2.4 shows that / 0 is still broadly tunable between 12 and
62 GHz when the injection condition is limited to within the —6-dB contour line
of Fig. 3.7. It is also interesting to note th at a remanent of the contour line
of R — 0 dB in Fig. 3.5 is clearly visible in Fig. 3.7 because the corresponding
DSB states are very much prone to the power penalty. Therefore, from these
main features of the map, the laser is best operated under strong injection that
is detuned slightly above the Hopf bifurcation line.
The laser dynamical parameters are known to have a significant effect on
the nonlinear dynamics of the optical injection system [88]. In particular, the
nonlinear carrier relaxation rate 7P is known to have a stabilization effect on the
system. Increasing the value of 7P is expected to reduce the period-one region. As
a result, we are interested in investigating the effect of 7P on RoF transmission.
For comparison, the map of minimum power in Fig. 3.7 is reproduced in Fig. 3.8
with the 7P increased by 22% to 2.34 x 1010 s-1. The general structure of the
37
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Worst Case Pj-0 (dB) after Power Penalty
Frequency Detuning,^ (GHz)
7
-10
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Injection Strength, ^
Figure 3.7: Mapping of the worst case
penalty is considered.
Pfo
when the dispersion-induced power
38
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Worst Case
iO t
(dB) after Power Penalty
M O
7777
-16 -1 4 -1 2
-lO i -;rT
yn increased
-10
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Injection Strength, ^
Figure 3.8: Same as the previous figure except th at 7P is increased by 22% from
its original value.
39
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mapping is maintained, and the best region of operation is still located slightly
above the Hopf bifurcation line. However, the entire period-one region is reduced.
These observations are consistent with the stabilization nature of yp.
3.5
Sum m ary
In summary, the RoF transmission of the period-one oscillation is presented.
Depending on the injection conditions, the spectrum of the oscillation can be DSB
or SSB. The microwave power penalty induced by fiber chromatic dispersion is
considered. When properly adjusted into SSB period-one oscillation, the system
is shown to be quite immune to the power penalty. The system is least susceptible
to the penalty when operated in a region slightly above the Hopf bifurcation line
in the (£;, / j) mapping. The results suggest th at the period-one state of the
optically injected semiconductor laser is a useful source for delivering microwave
signals over fibers.
This chapter presents only the results of transm itting a microwave subcarrier,
without d ata modulation, on the optical carrier. This is already useful for some
special RoF systems [89]. In those systems, the baseband data and the pure
microwave subcarrier are sent separately over fibers. The microwave upconversion
is performed remotely by a mixer at the base station. However, it is often more
convenient to directly modulate the subcarrier when the photonic microwave is
generated. The modulation characteristics of the period-one state are discussed
in the next chapter.
40
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C H A PT E R 4
Frequency M odulation on Period-O ne
Oscillation
This chapter focuses on the transmission of data using a frequency-modulated
period-one oscillation. From Chapter 2, it is observed th at the period-one fre­
quency /o depends on the injection parameters
and /;.
If the injection is
modulated with data, the generated frequency will be modulated accordingly.
The modulation response of /o is considered in this chapter. The results are
applied for transforming amplitude modulation (AM) to frequency modulation
(FM) [108, 109].
4.1
Introduction
The period-one oscillation is controlled by the optical injection. When the optical
injection is modulated, the period-one oscillation is expected to be modulated as
well. Accordingly to Figs. 2.7(a) and 2.8(a), the frequency f 0 generated by the
period-one state varies nearly linearly with the injection strength £ and the fre­
quency detuning /,. At the same time, the microwave power generated remains
approximately constant once the period-one dynamics is entered. Therefore, it
is conceivable to apply this optical controllability of the period-one state to re­
alize FM on /o. The modulation bandwidth depends on how fast the period-one
41
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state can respond to the change of the injection. The bandwidth is measured bymonitoring the FM response as the modulation frequency is varied. The exper­
iment is discussed in Section 4.2. The application in AM-to-FM conversion is
demonstrated in Section 4.3.
4.2
Frequency M odulation (FM ) Characteristics
4.2.1
Setup
In order to examine the modulation characteristics of the period-one oscillation,
the setup in Fig. 4.1(a) is adopted. It is essentially the same as the previous setup
in Fig. 2.1. The only difference is that the injection now consists of light from the
master laser combined with a probe laser, which is operated at a slightly detuned
optical frequency from the master laser. The light from the strong master laser
is regarded as the central frequency of the injection, while the light from the
weak probe laser is regarded as a sideband of the injection. Thus, the combined
injection is SSB modulated with the modulation frequency / m, which is equivalent
to the frequency difference between the master laser and the probe laser. The
modulation depth and the modulation frequency can be respectively varied by
adjusting the power and the frequency of the probe laser.
In this chapter, the injection condition from the master laser is set at & =
0.082 and f\ = 0. The injection of the master laser is responsible for driving the
slave laser into a period-one state at /o = 15.24 GHz. This operating point is re­
garded as the bias point upon which modulation is to be applied. The probe laser
is responsible for realizing the modulated injection, and the period-one state is
modulated correspondingly. The modulated microwave oscillation of the periodone state is generally under both FM and AM. It is analyzed using a delayed
42
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PL
hf
ML
BS
VA
FR
SL
PSA
HWP
PBS
DSA
Delay x
SC
PD1
AT
MIX
Light from SL
PSA
PD2
BS
(b)
Figure 4.1: Schematics of the setup for modulating the period-one state, (a)
Optical injection system, (b) Microwave homodyne detection. ML: master laser;
SL: slave laser; PL: probe laser; M: mirror; BS: beam splitter; VA: variable
attenuator; PBS: polarizing beam splitter; FR: Faraday rotator; HWP: half-wave
plate; F: fiber; PD: photodiode; A: microwave amplifier; PSA: power spectrum
analyzer; OSA: optical spectrum analyzer; P: prism; MIX: mixer; PSA: power
spectrum analyzer; and OSC: oscilloscope. Thin and thick lines correspond to
optical and microwave paths, respectively.
43
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microwave (not optical) homodyne method as shown in Fig. 4.1(b). The optical
output of the slave laser is divided into two arms, each consisting of a photodiode
and an amplifier, which have a combined bandwidth of 6—18 GHz. The ampli­
fied signals, each of about —2.5 dBm, are sent into a mixer (W J MV50C) that
is monitored by the power spectrum analyzer or a 3-GHz real-time oscilloscope
(Tektronix TDS694C). By properly adjusting the relative delay time r using the
prism, the FM and the AM components of the modulated microwave signal can
be analyzed separately.
4.2.2
FM M od u lation C haracteristics
The dynamical characteristics of the period-one state are investigated in detail
by using the SSB modulated injection. Initially, the probe laser is tuned so as
to obtain a slow modulation of f m = 10 MHz. The relative power of the probe
laser to th at of the master laser is varied from 0 to 0.01, which corresponds to an
equivalent modulation depth on the injection electric field in the range of 0 to 0.10.
The subsequently modulated period-one state is monitored as shown in Fig. 4.2.
The optical spectra are shown in the left column for the modulation depths of
0.05, 0.08, and 0.10 in Figs. 4.2(a-i), (b-i), and (c-i), respectively. The signal at
—/o is generated by the period-one oscillation. Though the modulation sideband
of the injection itself is too weak to be observed directly, its effect shows as a
progressive broadening of the generated peak at —/ 0. In fact, the power spectrum
shown in the right column gives clear evidence of FM on / 0 around the center
frequency of 15.24 GHz. The maximum frequency deviation, denoted by A /,
increases with the injection modulation depth. It is measured to be 0.10 GHz,
0.35 GHz, and 0.60 GHz for Figs. 4.2(a-ii), (b-ii), and (c-ii), respectively.
44
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(a-ii)
-3 0
2A /
-6 0
-20
20
-10
13.24
15.24
17.24
15.24
17.24
15.24
17.24
(b-ii)
0
10
20
13.24
(c-ii)
w.
-3 0
-6 0
20
Optical Frequency Offset (GHz)
13.24
Microwave Frequency (GHz)
Figure 4.2: Behavior of the modulated period-one oscillation under a slowly mod­
ulated injection ( / m = 10 MHz), (i) Optical spectrum, (ii) Power spectrum. The
modulation depths of the injection field amplitude are: (a) 0.05, (b) 0.08, and (c)
0 . 10 .
45
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The behavior of the period-one state at a few different modulation frequencies
is then investigated. The modulation depth of the injection is kept constant at
0.10. By tuning the frequency of the probe laser, the optical and the power
spectra of the period-one state at different values of / m are obtained, as shown
in Fig. 4.3. Figure 4.3(a-i) shows the optical spectrum for f m — 80 MHz. The
peak at —/ 0 is again broadened as a result of the FM. The corresponding power
spectrum in Fig. 4.3(a-ii) shows a continuum of frequencies with a maximum
deviation of A / = 0.65 GHz. Because / m < A /, the state is said to be under
a wideband FM [110]. Although the spectrum under the periodic modulation
ought to contain discrete peaks separated by / m, the separation is too small to
be resolved in Fig. 4.3(a-ii).
As / m increases to 500 MHz, the discreteness becomes apparent. The optical
spectrum in Fig. 4.3(b-i) shows that a sharp peak at —/ 0 is now accompanied
by closely separated sidebands.
The sidebands are clearly seen in the power
spectrum of Fig. 4.3(b-ii) as peaks separated by multiples of f m from / 0. The
discreteness of the spectrum hinders an accurate determination of A / because it is
now comparable to / m. When f m is increased to 2 GHz, the modulation sidebands
of —/ 0 are too small to be recorded by the optical spectrum in Fig. 4.3(c-i), but
they are observed in the power spectrum in Fig. 4.3(c-ii). Because / m > A / in
this case, the spectrum belongs to th at of a narrowband FM. The determination
of A/ needs to rely on a time-domain method as outlined below.
46
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(a-ii)
-3 0
2A /
-6 0
-20
-10
‘* 0 = M==+Z
O -2 0
-1 0
20 'S'
13.24
15.24
17.24
20
13.24
15.24
17.24
13.24
15.24
17.24
-3 0
-6 0
-2 0
-10
20
Optical Frequency Offset (GHz)
Microwave Frequency (GHz)
Figure 4.3: Behavior of the period-one oscillation under a modulated injection
with a depth of 0.10. (i) Optical spectrum, (ii) Power spectrum. The modulation
frequency f m is (a) 80 MHz, (b) 500 MHz, and (c) 2 GHz.
47
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4.2.3
FM Frequency R esponse
In general, the modulated microwave signal generated after the photodiode can
be represented by
V(t) = (Vo +
+ c.c,
(4.1)
where V0 is the steady-state amplitude of the microwave generated, v(t) is the
AM part of the signal, and <p(t) is the time-varying phase accounting for the FM.
Under a modulation at / m, the instantaneous microwave frequency is given by
f° ~
Z7T at
=
+ A /cos(27r/mt).
(4-2)
The AM part can be written as
v(t) = m \ o cos(27r/mt + a),
(4.3)
where m and a are, respectively, the index and the phase of the AM.
In order to determine A / for the whole range of / m, a delayed microwave
homodyne method is applied (Fig. 4.1(b)). The mixer output is thus
M
= [(Vo + u (t))e-i27r/ot+iv«]
x[(Vo + v(t - r ))e~i27r^°it- T)+'l^ t~T)]* + c.c..
(4.4)
The delay is set to be r = (4/0)_1 so that
M w —47rU02rA /cos(27r/mt).
(4.5)
The mixer output is thus modulated at the modulation frequency / m, and its am­
plitude measures the maximum frequency deviation A / of the FM. Figure 4.4(a)
shows the mixer output at / m = (i) 80 MHz, (ii) 500 MHz, and (iii) 2 GHz,
respectively. The modulation depth of the injection is 0.10. The amplitudes of
48
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3
10
10
15
Time (ns)
^ 0 .9
>. 0.5
« 0.4
u 0.3
£ o.o
0.5
1.0
Modulation Frequency, f
1.5
(GHz)
Figure 4.4: (a) Mixer output with r = (4/0)_1 measuring the FM through a
conversion factor of —50 MHz/mV. The modulation frequency / m is (i) 80 MHz,
(ii) 500 MHz, and (iii) 2 GHz. (b) FM frequency response of the period-one state.
49
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these traces, after a conversion factor of —50 MHz/mV, gives A / of 0.65 GHz,
0.60 GHz, and 0.50 GHz, respectively. The variation of A / with respect to / m is
the frequency response of the FM. The FM frequency response under the injec­
tion modulation depth of 0.10 is shown in Fig. 4.4(b), where a broad modulation
bandwidth is observed. The maximum frequency deviation A f is about 0.6 GHz
at f m — 0, which agrees with the static measurement in Fig. 2.7(a) when the
injection amplitude changes by 10 % around the bias point.
The modulated period-one oscillation is predominantly under FM, but the
AM response is also measured for completeness. The delay is set at r = 0 so that
M w 2V02(1 + 2mcos(27r/mt + a)),
(4.6)
which undulates with an amplitude proportional to m. Figure 4.5(a) shows the
mixer output again at different modulation frequencies. From the very small un­
dulation amplitude, the AM index m is determined. The AM frequency response
is summarized in Fig. 4.5(b), which shows th at m is always smaller than 0.035
over the frequency range measured.
Although our dynamical characterization was done only on one period-one
state, similar results are observed for the other period-one states at different / 0
as well. The sensitivity of the microwave frequency to the injection modulation
is expected to vary slightly, according to the variation of the local slopes on the
tuning curves in Figs. 2.7(a) and 2.8(a). Therefore, using an optimal periodone state would result in an improved FM performance. All the experimental
data suggest th a t the period-one state can be easily frequency modulated. With
the broad frequency response and the small residual AM component, the optical
injection scheme is applicable to FM communication systems. The next section
demonstrates transmission of real data using this scheme.
50
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200
(a-i)
150
m
100
(a-ii)
100
m
10
15
Time (ns)
0.10
0.09
0.08
£ 0-07
* 0.06
E 0.05
2 0.04
0.03
0.02
0.01
0 . 00 ,
0
0.5
1.0
1.5
Modulation Frequency, f m (GHz)
2.0
Figure 4.5: (a) Mixer output with r = 0 measuring the AM. The modulation
frequency / m = (i) 80 MHz, (ii) 500 MHz, and (iii) 2 GHz. (b) AM frequency
response of the period-one state.
51
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4.3
A M -to-F M Upconverter
In an RoF system, d ata are usually carried by microwave through frequency
or phase modulation [111]. Because of the problem of wireless channel fading,
amplitude modulation is often not adopted. In contrast, a conventional optical
communication system usually employs baseband AM because of its simplicity.
When a conventional system is connected to an RoF system, an interface is
required for baseband-to-microwave upconversion with simultaneous AM-to-FM
conversion. Although the interface can be realized by electrically modulating an
RoF light source by using the photodetected signal of the baseband AM, a simple
all-optical method bypassing the electronics is preferred.
Such AM-to-FM upconversion is demonstrated as follows using the modula­
tion behavior of the period-one state. In this experiment, the injection detuning is
kept at fj = 3.7 GHz and the central period-one frequency is / 0 = 15.90 GHz. By
simply injecting the baseband AM optical signal into the slave laser, it generates
the corresponding FM microwave signal. The setup is modified to incorporate
data modulation as shown in Fig. 4.6. The master laser is current modulated by
a pattern generator with a 27 — 1 pseudorandom binary sequence at 622 Mbps
(megabits per second). It then emits light th at carries a baseband AM signal,
which represents a signal of a conventional optical communication system. The
modulation depth is about 12%. Although in our experiment an injection power
of about 5 mW impinges on the front facet of the slave laser, optimization of the
injection coupling and polarization can potentially reduce the injection power to
the order of 10 /xW, which is comparable to the received power levels used in
conventional optical communication systems [112]. The light is injected into the
slave laser and thus controls the microwave frequency of the period-one state.
Because the microwave frequency varies with the injection strength nearly lin-
52
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PG AM on baseband
i
ML
-o -
©
SL
[AM-to-FM
•upconversion
Microwave frequency
(_ discriminator^ _
M
VA
T ir
HWP
FM on RoF
D elay-i
|
L—
Imix<
PD1
§
\
PBS
|QSA
PSA
OSC
PD2
Figure 4.6: Schematic of the AM-to-FM setup. ML: master laser; SL: slave
laser; M: mirror; VA: variable attenuator; PBS: polarizing beam splitter; FR:
Faraday rotator; HWP: half-wave plate; F: fiber; PD: photodiode; MIX: mixer;
PG: pattern generator; PSA: power spectrum analyzer; OSC: digital sampling
oscilloscope; and OSA: optical spectrum analyzer.
early, the AM of the injection is transformed into FM of the microwave with
little distortion. The slave laser acts as an AM-to-FM upconverter. As in an
RoF system, the laser output is an optical wave th at carries an FM microwave
signal and is transm itted through an optical fiber with about 1.28 mW of power.
The modulation depth of the FM increases with th at of the AM, but the laser
has to remain in the period-one state.
The fiber shown in Fig. 4.6 represents the optical transmission channel. Al­
though the fiber length is only a few meters in our proof-of-concept experiment,
it can be extended to hundreds of kilometers in a real system. The output of
PD1 is a microwave signal with FM around the center frequency. It is to be
radiated by a base station to customer units in a real system. However, in our
demonstration, it is sent directly to a microwave frequency discriminator for FM
demodulation. The function of the discriminator is to electrically mix the mi-
53
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-1 0
m -2 0
w
^ -3 0
£
Ph -4 0
<u
o
£ -5 0
a
° -6 0
-7 0
14.50
15.00
15.50
16.00
16.50
17.00
Frequency (GHz)
Figure 4.7: Power spectrum of the slave laser. Dark curve: steady-state pe­
riod-one oscillation under constant injection. Gray curve: frequency modulated
period-one oscillation under AM injection. (Resolution bandwidth = 3 MHz.)
crowave signal with its delayed replica. The delay r is set at (4/0)_1 as before so
that the output is proportional to the instantaneous frequency deviation from the
central frequency. The mixer gives the demodulated signal, and it is monitored
by a digital sampling oscilloscope (Tektronix TDS8000). The result is compared
with the input AM baseband signal th at is detected by PD2.
When the AM of the injection is switched off, the unmodulated power spec­
trum is shown as the dark curve of Fig. 4.7, which is just a single peak at
15.90 GHz. W ith the AM switched on, the frequency of the period-one state
is modulated. The gray curve of Fig. 4.7 shows the correspondingly broadened
spectrum. The frequency is switched between 15.23 GHz and 16.40 GHz when
the injection strength is low and high, respectively. The frequency separation
increases if the modulation depth of the AM injection increases.
54
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The quality of the AM-to-FM upconversion is evaluated from the eye diagrams
in Fig. 4.8 recorded from the oscilloscope. The input baseband AM of the injec­
tion intensity as directly detected by PD2 is shown in Fig. 4.8(a). The output
microwave FM is demodulated by the discriminator and is shown in Fig. 4.8(b),
which shows only slight signal degradation. The degradation is examined by
measuring the bit-error rate (BER) as a function of the signal voltage in Fig. 4.9.
First ignoring the gray curves, the BER of the AM input is compared with that
of the demodulated FM output, which are respectively shown as closed and open
circles. Comparison of the BER shows a 1.5-times increase or a 3.5 dB penalty
on the signal voltage. An output BER of less than 10-9 can be obtained. The
generated microwave also contains a small AM component, but the modulation
depth of this AM component is less than 5%. The data for other period-one cen­
ter frequencies under various injection conditions are shown as the gray points in
Fig. 4.9, but the response of our discriminator is not optimized at these frequen­
cies. We also examine a period-one state at 100 GHz when the injection power
is doubled and the detuning is increased to 90 GHz. Although we are not able
to measure the power spectrum because of equipment bandwidth limitations, the
optical spectrum shows spectral broadening of the period-one oscillation under a
modulated injection.
Our system can be compared to the experiment by Kaszubowska et al. [93]
that also uses the period-one state for RoF communication. In their experiment,
the d ata modulation is first applied on an external microwave source, and the
data-carrying microwave is then used to injection-lock the slave laser. Injection
locking works by the pulling of the original period-one frequency. It forces the
laser to oscillate according to the external microwave. The maximum frequency
55
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
a
o
■j—i
4-»
o
<D
xn
a
<L>
£"-
y . ^ ' : ‘;-,
2
• . ; ^ f^ .
y-.n%v
3
Time (ns)
Figure 4.8: Eye diagrams of (a) the variation of the optical injection intensity
from the master laser under AM, and (b) the demodulated FM signal of the
microwave generated by the slave laser.
56
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,-2
3.5 dB
,-8
0.2
0.4
0.6
Voltage (V)
0.8
1.0
Figure 4.9: BER as a function of the signal peak-to-peak voltage. Closed circles:
input AM signal after PD2. Open circles: demodulated FM signal for the original
period-one state. Gray points: demodulated FM signal for other period-one
states. The injection conditions (&, /; (GHz),/0 (GHz)) are: open circles (1, 3.7,
15.9); dark triangles (1, 7.1, 17.2); light triangles (1, —0.8, 14.6); dark squares
(0.07, 3.7, 17.4); and light squares (0.04, 3.7, 12.8).
57
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deviation A / of such a system is thus limited by the locking range of the periodone state. In contrast, our system is based on the modulation of the periodone frequency by instead controlling the laser dynamics. Hence, our maximum
frequency deviation is limited only by the tuning range of the period-one state,
which we have shown to be rather broad (Fig. 2.3).
4.4
Sum m ary
In summary, we considered modulation on the period-one state generated from
optical injection. The state is frequency modulated because / 0 varies with both
the injection strength and detuning. As long as the laser is maintained in the
period-one state, the modulation depth of the output FM increases with that of
the input AM. A broad FM response is obtained and the transmission of 622-Mbps
data is demonstrated. It is used for all-optical conversion of an AM baseband
signal into an FM microwave signal for RoF applications. The period-one oscilla­
tion is not the only state th at is useful for photonic microwave applications. The
period-two oscillation is to be considered in the next chapter.
58
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C H A PT E R 5
M icrowave Frequency Conversion by
Period-Tw o Oscillation
We now turn our attention from the period-one oscillation to the period-two oscil­
lation. The period-two oscillation is obtained when a laser experiences a perioddoubling bifurcation from a period-one state. The resultant spectrum consists
not only of the original fundamental frequency / 0 but also its exact subharmonic
at /o/2. Because the two frequencies are related through the laser nonlinear dy­
namics, they can be utilized for photonic microwave frequency conversion [113].
5.1
Introduction
Microwave frequency division/multiplication is an im portant element in commu­
nication systems. In the optical time division multiplexing (OTDM) system, the
clock at the aggregated data rate must be divided in order to demultiplex an
individual channel. Photonic devices have been widely studied for such appli­
cation. In one approach, an optical pulse train is sent into a terahertz optical
asymmetric demultiplexer (TOAD), which is an optical loop mirror based on a
semiconductor optical amplifier (SOA) [54]. The output is amplified and fedback after a delay to control the switching of the loop mirror. Due to the slow
nonlinearity of the SOA, an output pulse train at half the original repetition
59
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rate is obtained. All-optical clock division from 20 GHz to 10 GHz has been
demonstrated [114], among some of its variants [115, 116]. Despite the advan­
tage of being integrable into a chip, the speed of this approach is limited by the
lifetime of the SOA. In another approach, one can use an optoelectronic oscil­
lator (OEO), which is essentially a microwave oscillator with its energy stored
as an optical wave inside a long fiber [117]. An OEO can generate high-quality
microwave oscillation and can be injection-locked to an externally applied mod­
ulation. When the free-running OEO frequency is close to the subharmonic of
the external modulation, it can be locked to the subharmonic frequency. Clock
division from 160 GHz to 40 GHz has been demonstrated [118], together with
some similar experiments [119, 120]. Injection locking into the subharmonic of
an external frequency has also been investigated in devices such as a passively
mode-locked external-cavity laser diode [121], a passively mode-locked fiber ring
laser [122], and a twin-section self-pulsating laser diode [123].
Direct generation of subharmonic frequency can also be realized by harness­
ing the nonlinear dynamics of semiconductor lasers. One simple approach uses
semiconductor lasers under strong microwave current modulation.
When the
modulation is strong enough to invoke period-doubling bifurcation, the subhar­
monic frequency at half of the modulation frequency is generated [32, 124]. The
process can be controlled optically [125, 126] and the modulation can be done
through optical injection [127, 128]. All-optical clock division has been demon­
strated at 19.6 GHz [129]. However, a deep modulation is often necessary to drive
the laser into the gain switching mode with a broad optical spectrum.
In this chapter, we study an alternative scheme for frequency division and
multiplication by the semiconductor laser nonlinear dynamics. We continue to
focus on the optical injection system. As the injection strength varies, the slave
60
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laser is first destabilized into the period-one state and oscillates at the funda­
mental microwave frequency /o as before. It then undergoes period-doubling
bifurcation to generate the subharmonic frequency at fo/2 [79, 11]. The fre­
quencies can be simultaneously injection-locked to a weak external current mod­
ulation. When the modulation matches the fundamental frequency, the locked
subharmonic becomes the frequency-divided signal. On the other hand, when the
modulation matches the subharmonic frequency, the locked fundamental becomes
the frequency-multiplied signal [92]. While the optical injection is responsible for
generating the microwave frequencies, the weak current modulation is only re­
sponsible for locking the microwave.
The route to the period-two state is described in relation to the period-one
state in Section 5.2. The experimental results for frequency division and multi­
plication are presented in Sections 5.3 and 5.4, respectively. They are followed
by the discussion and the summary in Sections 5.5 and 5.6, respectively.
5.2
Period-T w o O scillation
Using the same optical injection setup as in Fig. 2.1, the period-two oscilla­
tion is obtained experimentally as follows. The injection detuning is fixed at
/; = 13.91 GHz, and the injection strength & is varied from 0 to 0.150. Fig­
ure 5.1 shows, for different values of £;, the optical spectra on the left column
and the power spectra on the right column. In Fig. 5.1(a), & is 0; the optical
spectrum shows th at the slave laser is oscillating at its free-running frequency. No
modulation is observed in the corresponding power spectrum. In Fig. 5.1(b), & is
increased to 0.054; the slave laser is locked to the master injection frequency at an
offset of 13.91 GHz with respect to the free-running frequency, together with the
period-one oscillation peak at an offset of —2.92 GHz. The power spectrum shows
61
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-3 0
£
-2 0
-1 0
0
10
20
-20
-10
0
10
20
-6 0
0
~T
uu ii ^ < ~ * f
5
10
15
20
25
5
10
15
20
25
(c-ii) / 0/2
R -3 0
-2 0
-1 0
0
10
-60,0
20
5
10
15
20
25
5
10
15
20
25
-3 0
-20
-10
0
10
-60,
20
Optical Frequency Offset (GHz)
Microwave Frequency (GHz)
Figure 5.1: O utput of the slave laser under optical injection into period-two
oscillation, (i) Optical spectrum offset to the free-running frequency of the slave
laser, and (ii) power spectrum. The data for different & are plotted: (a) 0, (b)
0.054, (c) 0.087, and (d) 0.150. The arrows indicate the injection frequency.
62
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the beating of the optical lines at a fundamental frequency of /o = 16.83 GHz.
When £ is further increased to 0.087 in Fig. 5.1(c), / 0 is increased to 18.56 GHz.
Also, a period-doubling bifurcation into the period-two state has occured. The
subharmonic frequency / 0/2 = 9.28 GHz is generated, as seen in the power
spectrum in Fig. 5.1(c-ii). The optical spectrum in Fig. 5.1(c-i) also shows new
peaks at —13.93 GHz and 4.63 GHz around the main oscillation frequency of
—4.65 GHz. In Fig. 5.1(d), & is increased to 0.150; the slave laser returns to the
period-one state. While / 0 is increased to 22.46 GHz, / 0/2 disappears from the
spectrum.
This chapter focuses on applying the period-two state for frequency division
and multiplication. The existence of the state depends on the dynamical and
operational parameters in a complicated manner [88], but the period-two fre­
quencies are usually on the order of the relaxation resonance frequency. A faster
slave laser can be used if a higher operational frequency is desired. In the current
setup, the state exists when & = 0.055 to 0.101, which gives / 0 = 17.49 GHz to
19.61 GHz. The region is also shown in the simulation map of Fig. 2.4. In the
following discussions, & is fixed at 0.087 as in Fig. 5.1(c) unless specified other­
wise. The microwave frequency synthesizer in the setup of Fig. 2.1 is not needed
for the generation of the period-two state. However, it is used to apply a current
modulation of power Pm and frequency / m into the slave laser for stabilization.
5.3
Frequency D ivision
The linewidths of the microwave frequencies generated by the nonlinear dynamics
are rather broad due to noise. By applying an external microwave modulation, the
linewidths can be substantially narrowed and locked. In order to demonstrate
the frequency division, modulation at / m = f 0 = 18.56 GHz is applied to the
63
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slave laser while the modulation power Pm is varied. Figure 5.2 shows the power
spectra zoomed into a 1.6-GHz span, centered at / o / 2 and /o , respectively. When
Pm = —43 dBm, the modulation is too weak to have any observable effect on the
spectrum in Fig. 5.2(a). The fluctuating spectrum is essentially the same as
that generated by optical injection alone. As Pm is increased to —18 dBm, the
injected external microwave starts to lock the oscillation, as Fig. 5.2(b) shows. A
narrow peak appears at f m with a suppression of the sidebands in Fig. 5.2(b-ii).
Since the subharmonic is linked to the fundamental through nonlinear dynamics,
a narrow peak also appears at / m/2 as shown in Fig. 5.2(b-i).
The spectra
are shown in Figs. 5.2(c) and (d) as Pm is increased to —4 dBm and then to
10 dBm, respectively.
The locking improves as Pm increases, thus achieving
frequency division from 18.56 GHz to 9.28 GHz. However, there is an upper
limit for Pm, above which the modulation will severely affect the dynamics of
the laser [32, 124]. This is shown in Fig. 5.2(e) at Pm = 14 dBm, corresponding
roughly to 32 mA of current modulation.
The deep modulation is sufficient
to drive the slave laser below the threshold, hence modifying its dynamics and
grossly degrades the locking as Fig. 5.2(e) shows. Therefore, it is important to
choose an optimum Pm to suppress the frequency fluctuation while keeping the
laser in the period-two state.
In order to quantify the locking behavior, the phase noise is analyzed. Assum­
ing the noisy sidebands in Fig. 5.2 come mainly from small phase fluctuations, the
phase noise variance is estimated by integrating the normalized single sidebands
from 3 MHz to 1 GHz. The results are plotted as a function of Pm in Fig. 5.3.
The phase variances decrease for both the / m and the f m/2 components as Pm
increases, until the period-two state is disrupted at Pm > 10 dBm. Thus, the
highest quality frequency division occurs at Pm = 10 dBm, shown in Fig. 5.2(d),
where minimum phase variances of 0.019 rad2 and 0.007 rad2 are found for the
64
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(a-i)
(a-ii)
-25
-25
-50
-50
8.48
8.88
9.28
9.68
10.08
17.76
18.16
18.56
18.96
19.36
18.16
18.56
18.96
19.36
18.16
18.56
18.96
19.36
(b-ii)
-25
-25
-50
-50
IT
8.48
8.88
9.28
9.68
10.08
17.76
(c-i)
(c-ii)
£ -25
-25
9 -50
-50
8.48
8.88
9.28
9.68
10.08
17.76
(d-i)
(d-ii)
-25
-25
-50
-50
I
■
8.48
I .i
8.88
I
9.28
9.68
I
10.08
■
17.76
(e-i)
■
-
18.56
18.96
19.36
18.16
18.56
18.96
19.36
(e-ii)
-25
-25
-50
-50
8.48
■
18.16
8.88
9.28
9.68
10.08
Frequency (GHz)
17.76
Frequency (GHz)
Figure 5.2: Power spectrum under modulation at f m = / 0, (i) centered at
/m /2 = 9.28 GHz, and (ii) centered at / m = 18.56 GHz, while Pm is varied:
(a) —43 dBm, (b) —18 dBm, (c) —4 dBm, (d) 10 dBm, and (e) 14 dBm. (Span
= 1.6 GHz. Resolution bandwidth = 300 kHz.)
65
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101
'
-1 5
-1 0
1
I
I
I
-5
0
5
10
15
Modulation Power, Pm(dBm)
Figure 5.3: Phase variance versus Pm when / m = /o. Closed symbol: fundamental
at / m. Open symbol: subharmonic at f m/ 2.
components at / m and f m/ 2, respectively. When the period-two state is locked,
the subharmonic always has a lower phase variance than the fundamental. This
is also observed in systems involving period-doubling [127, 129] and is commonly
found in electrical regenerative frequency dividers.
The microwave injection locking tolerates a large frequency detuning. Fig­
ure 5.4 shows the spectrum at Pm = 4 dBm when / m is tuned across / 0. In
Fig. 5.4(a), / m is detuned far away from / 0 by 0.78 GHz. The fundamental os­
cillation is pulled away from / 0 towards / m in Fig. 5.4(a-ii) and it is about to
be locked. As the detuning is reduced to 0.54 GHz, Fig. 5.4(b-ii) shows that
the fundamental starts to be locked to / m. However, the locking is not strong
enough to enable locking at f m/ 2 in Fig. 5.4(b-i). When the detuning is reduced
to 0.42 GHz, narrow peaks are observed at both f m and / m/2 in Fig. 5.4(c), sup­
pressing the sidebands. The locking trend continues as the detuning decreases to
0.18 GHz in Fig. 5.4(d). Both / m and f m/2 are best locked when the detuning
66
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(a-ii)
(a-i)
-25
-25
/c /2
-50
-50
8.87
9.27
9.67
10.07
10.47
18.54
-25
-50
-50
9.15
9.55
9.95
10.35
18.30
(c-i)
S
-25
-50
-50
9.09
9.49
9.89
10.29
18.18
20.14
18.70
19.10
19.50
19.90
18.58
18.98
19.38
19.78
18.34
18.74
19.14
19.54
(d-ii)
(d-i)
g -25
-25
-50
-50
1.57
19.74
(c-ii)
-25
8.69
19.34
(b-ii)
(b-i)
-25
8.75
18.94
8.97
9.37
9.77
10.17
17.94
(e-i)
(e-ii)
-25
-25
-50
-50
8.42
8.82
9.22
9.62
10.02
17.64
18.04
18.44
18.84
19.24
8.38
8.78
9.18
9.58
9.98
17.56
17.96
18.36
18.76
19.16
17.56
17.96
18.36
18.76
(g-ii)
(g-0
-25
-25
-50
-50
8.18
8.58
8.98
9.38
9.78
Frequency (GHz)
17.16
Frequency (GHz)
Figure 5.4: Power spectrum under modulation at f m near / 0, (i) centered at f m/ 2,
and (ii) centered at f m, while Pm is fixed at 4 dBm. The detuning frequency,
fm ~ /o, is varied: (a) 0.78 GHz, (b) 0.54 GHz, (c) 0.42 GHz, (d) 0.18 GHz, (e)
—0.12 GHz, (f) —0.20 GHz, and (g) —0.60 GHz. (Span = 1.6 GHz. Resolution
bandwidth = 300 kHz.)
67
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becomes —0.12 GHz in Fig. 5.4(e), with the phase variances of 0.027 rad2 and
0.012 rad2, respectively. The best locking is not found at the zero detuning be­
cause the central fo is also shifted by the modulation. A similar shifting of the
intrinsic resonance frequency in a modulated self-pulsating semiconductor laser
has been reported [40]. Further reduction of the detuning degrades the locking,
as shown in Fig. 5.4(f) at —0.20 GHz. The slave laser eventually falls out of
locking at a detuning of about —0.60 GHz. It results in merely the frequency
mixing of / 0, fo/2, and / m, as shown in Fig. 5.4(g).
The phase variance is shown in Fig. 5.5 as a function of the frequency detun­
ing. Locking behavior is clearly observed as a sharp reduction of phase variance
within a locking range. The fundamental has a larger locking range than the
subharmonic because it is directly under modulation. However, a locked subhar­
monic is necessary for frequency division purposes. If we define the locking range
as the frequency detuning range where the phase variance is less than 0.5 rad2,
then the subharmonic has a locking range of 0.61 GHz (—0.21 GHz to 0.40 GHz).
This is consistent with the observations made in Fig. 5.4. The large locking range
of our system is inherent from the absence of any microwave feedback loop, thus
allowing a relatively broad oscillation spectrum th at is sustained by the optical
injection alone. In addition, the locking range increases with the strength of the
modulation. As shown in Fig. 5.6, the locking range expands linearly with the
modulation index, and it is asymmetric around the zero detuning.
We have experimentally demonstrated the frequency division by applying mi­
crowave injection locking to the fundamental of an optically injected semiconduc­
tor laser in a period-two state. Both the locking quality and the locking range
increase with the modulation power. In practice, extra tunability can be obtained
by electrically changing the operating conditions of the lasers, such as the bias
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TJ
S 10'
-
0.20
0.00
0.20
0.40
0.60
0.80
Detuning, / m- / 0 (GHz)
Figure 5.5: Phase variance versus detuning, f m — /o, at Pm = 4 dBm. Closed
symbol: fundamental at f m. Open symbol: subharmonic at f m/2.
1.0
Unlocked
■
0.05
0.10
■
'
0.15
0.20
■
0.25
0.30
Modulation Index
Figure 5.6: Locking ranges when / m is around / 0. Hatched region between closed
symbols: fundamental at / m. Shaded region between open symbols: subharmonic
at /m/2.
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current level, thereby adjusting the fundamental frequency / q.
5.4
Frequency M ultiplication
Frequency multiplication is realized by applying a modulation around the subhar­
monic frequency of the period-two state. The modulation is applied at / m ~ fo/2.
When the modulation is strong enough, both the subharmonic and the funda­
mental will be locked to the modulation. Thus, the fundamental at 2 /m can be
regarded as a frequency-multiplied signal. The power spectrum evolves in a way
similar to th at presented in Figs. 5.2 and 5.4 when the modulation power and the
detuning are respectively varied. At zero detuning, the change of the phase vari­
ance with respect to Pm is shown in Fig. 5.7. The locking quality is not as good
as th at in the frequency division experiment. It is because the slave laser exits
the period-two state when Pm is above —21 dBm, before the microwave locking is
established. However, when the detuning / m —/ 0/2 is varied, a high-quality lock­
ing can be obtained. Figure 5.8 shows the clear locking when the detuning falls
within the 0.22-GHz locking range (for a detuning from 0.21 GHz to 0.43 GHz)
at Pm = —5 dBm. The best result is obtained for the 9.65 GHz to 19.30 GHz
multiplication, with phase variances of 0.008 rad2 and 0.027 rad2 for the subhar­
monic and the fundamental, respectively. The locking range again increases with
the modulation index, as shown in Fig. 5.9. The asymmetry around the zero
detuning suggests a substantial modification of the period-two frequencies by the
modulation. In some region outside the locking range, a few frequency-locked
states are found. These states may also be utilized for frequency conversion of
different rational ratios.
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-5 0
-4 5
-4 0
-3 5
-3 0
-2 5
-2 0
-1 5
-1 0
-5
0
Modulation Power, Pm(dBm)
Figure 5.7: Phase variance versus Pm when / m = f 0/2. Closed symbol: funda­
mental at 2 /m. Open symbol: subharmonic at f m.
<N
2 10'
0.15
0.20
0.25
0.30
Detuning,
0.35
0.40
0.45
(G H z)
Figure 5.8: Phase variance versus detuning, f m — fo/2, at Pm = —5 dBm. Closed
symbol: fundamental at 2 /m. Open symbol: subharmonic at / m.
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1.0
Unlocked
O.QI
0.07
i
0.08
i
0.09
i
0.10
i
0.11
i
0.12
0.13
Modulation Index
Figure 5.9: Locking ranges when f m is around fo/2. Hatched region between
closed symbols: fundamental at 2 /m. Shaded region between open symbols:
subharmonic at f m.
5.5
D iscussion
In the previous experiments, the input microwave signal is carried into the slave
through current modulation. In fact, the microwave input can also be carried op­
tically as sidebands of the optical injection.
All-optical microwave frequency
division and multiplication can thus be achieved without the need for opti­
cal/electrical conversion. The approach is demonstrated on a period-two state of
/o = 18.73 GHz at an adjusted injection strength. The master laser, instead of
the slave laser, is current-modulated at f m = 18.56 GHz to generate microwave
sidebands. The microwave signal is carried by the optical injection. It enters into
the slave laser and locks the period-two oscillation. The resulting spectrum is
similar to th at in Fig. 5.2 and the phase variances reduce with the modulation
power as shown in Fig. 5.10. When the master laser is under a 10-dBm mod­
ulation, corresponding to relative sidebands power of less than 1%, we obtain
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-1 0
-5
0
5
10
Modulation Power (dBm)
Figure 5.10: Phase variance versus the modulation power on the master laser.
Closed symbol: fundamental at / m. Open symbol: subharmonic at f mf 2.
a divided frequency at f mf 2 = 9.28 GHz with a phase variance of 0.032 rad2.
Similar behavior is observed for frequency multiplication when the master laser
is modulated near fo/2. In the future, if the optical injection is replaced by an
optical data stream, the frequency component at the clock rate will be carried
into the slave laser for all-optical clock division and multiplication.
5.6
Sum m ary
In summary, microwave frequency division and multiplication are demonstrated
using semiconductor laser nonlinear dynamics. Optical injection to a slave laser
generates a period-two state that consists of both a fundamental microwave fre­
quency and its subharmonic. Microwave injection is then applied at either of
the frequencies to lock both of them, hence achieving frequency conversion. Fre­
quency division of 18.56 GHz to 9.28 GHz is demonstrated, with a phase variance
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of as low as 0.007 rad2 from a 10-dBm input. A large locking range of 0.61 GHz
can be obtained from a 4-dBm input. Conversely, frequency multiplication of
9.65 GHz to 19.30 GHz is also demonstrated. A phase variance of 0.027 rad2
and a locking range of 0.22 GHz at a low input power of —5 dBm are achieved.
W ith the current setup, the fundamental frequency can also be adjusted between
17.49 GHz to 19.61 GHz. In the future, the locking quality can be improved
using a phase-locked loop [92], the simple setup can be integrated, and the laser
dynamical parameters can be tailored for applications at specific frequencies.
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C H A PT E R 6
Microwave Frequency Comb G eneration by
Frequency Locking
Besides the optical injection scheme, the laser nonlinear dynamics can also be in­
voked using an optoelectronic feedback loop. Among the many complicated states
generated by optoelectronic feedback, the chaotic state and frequency-locking
states can find interesting applications. The chaotic state has already received
much attention for applications such as secure communication and broadband lid ar/radar applications. In this chapter, we focus on the frequency-locking state.
The state consists of frequency components locked by the laser nonlinearity. It
is utilized to generate a precise microwave frequency comb [130].
6.1
Introduction
Instead of optical injection, this chapter focuses on a semiconductor laser subject
to negative optoelectronic feedback [23]. The dynamics of the system is governed
by two im portant frequencies. One of them is the loop frequency /i00p, which
is equal to the reciprocal of the feedback delay time. The other is the pulsing
frequency / p, which originates from the pulsation sustained by the optoelectronic
feedback.
The pulsing frequency usually emerges at the proximity of the re­
laxation resonance frequency or its subharmonic, depending on the electronic
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bandwidth of the feedback loop [39, 23].
The two frequencies f\oop and / p are mixed through the laser nonlinearity. A
variety of nonlinear dynamical states can be obtained depending on the values of
/loop and / p [23]. For an arbitrary value of the ratio / p/ / i 00p, the frequency mixing
usually generates a complicated spectrum th at corresponds to quasi-periodic or
chaotic pulsing. But if / p//iooP equals an integer p, then the mixing can lock the
two frequencies together. The result is a clean spectrum th at consists of the linear
combinations of / p and a locking frequency f\ = I/ioop, where I is an integer. The
laser is said to be in an I : p harmonic frequency-locking state [41]. Furthermore,
when p /l is also an integer, the frequency mixing can generate only the harmon­
ics of /i; an evenly spaced microwave frequency comb is thus generated. The
harmonic frequency locking states are part of the nonlinear dynamics. They are
neighboring states of quasi-periodic and regular pulsing states in the parameter
space [23]. The values of I and p are determined according to the period-adding
route as reported previously [41].
The state can be used for microwave comb generation. However, just as many
other optical microwave generation systems, this system is susceptible to noise
sources like spontaneous emission and fluctuations in the operation parameters.
As a result, each comb frequency has a certain linewidth. Similar to the lock­
ing experiments for the period-two states, we demonstrate experimentally in this
chapter th at these comb linewidths can be simultaneously narrowed through in­
jecting a single, weak, and pure external sinusoidal microwave modulation. When
the external microwave is injected at one of the comb frequencies, the linewidths
of the whole frequency comb are narrowed. The linewidth-narrowing effect could
not be completely predicted prior to the experiments: Adding an external fre­
quency to a nonlinear system can sometimes cause competition with the original
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frequencies and lead to complicated dynamics. For example, these dynamics are
observed in external-cavity lasers [131] and self-pulsing lasers [40] under external
modulations.
The generation of the frequency locking state is described in detail in Sec­
tion 6.2, while the stabilization using the microwave injection technique is pre­
sented in Section 6.3. They are followed by a comparison with other similar
systems in Section 6.4 and a summary in Section 6.5.
6.2
Frequency Locking State
The schematic of the optoelectronic feedback setup is shown in Fig. 6.1.
A
slightly different laser is used in this setup, but it is still a single-mode distributed
feedback laser at 1.3 ^m. It is biased at 1.38 times its 29-mA threshold and
is tem perature stabilized. The output power is about 1 mW. The relaxation
oscillation frequency is roughly 2.3 GHz, which is lower than the one used in the
preceeding chapters. The slower laser is used so th at we can measure the time
waveform of the generated signal with a 3-GHz real-time oscilloscope.
Light from the laser, after a variable delay and attenuation, is detected by
a photodiode of 12 GHz bandwidth (Albis PDCS65T). The electrical output is
fedback to the laser through a 47-dB amplifier (Avantek SSF86-1592). The openloop gain, including the contributions from the laser and the amplifier, has an
electronic bandwidth from 0.5 to 2.5 GHz with 2-dB ripples. The feedback is
negative in the sense th at a current proportional to the detected optical power
is subtracted from the laser bias. The feedback strength is denoted by
as
a normalized quantity [39]. The output of the system is monitored by a power
spectrum analyzer and an oscilloscope. Again, a microwave frequency synthesizer
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VA
PD
LD
o Output
Figure 6.1: Schematic of the optoelectronic feedback experimental setup. LD:
semiconductor laser diode; VA: variable attenuator; PD: photodiode; A: mi­
crowave amplifier; and MFS: microwave frequency synthesizer. Thin and thick
lines correspond to optical and microwave paths, respectively
is used in the latter part of the experiment to stabilize the frequencies generated.
The loop frequency is kept constant at f\oop = 65.6115 MHz. Figure 6.2 shows
the time series and the power spectrum for two different values of £f. For
=
—0.22, the time series in Fig. 6.2(a-i) shows a regular pulse train. It corresponds to
the power spectrum in Fig. 6.2(a-ii) with a pulsing frequency of / p = 982.5 MHz,
which is around half of the relaxation resonance frequency [23]. The laser is in the
regular pulsing state. For
= —0.23, the time series in Fig. 6.2(b-i) shows a clear
modulation period in every 3 pulses. The power spectrum in Fig. 6.2(b-ii) reveals
the development of a locking frequency f\ — 328.0575 MHz = 5/ioop- The pulsing
frequency is slightly pulled and is locked at / p = 984.1725 MHz = 3/i = 15/ioopTherefore, the laser is in a 5:15 harmonic frequency-locked state. It generates a
frequency comb with equal spacings of f\ that extends from DC to the microwave
frequency on the order of the relaxation resonance frequency. The rest of this
chapter is focused on this 5:15 state at £f = —0.23.
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100
(a-i)
Ja
-5 0
0
5
10
Time (ns)
1
15
2
3
Frequency (GHz)
Figure 6.2: Photodiode output in (i) the time domain, and (ii) the frequency
domain. The feedback loop frequency f\oop is kept constant at 65.6115 MHz,
while the feedback strength £f is varied, (a) When £f = —0.22, the laser undergoes
regular pulsing, (b) When £f = —0.23, it enters a 5:15 harmonic frequency locking
state.
6.3
M icrowave Injection Locking
Detailed spectra of the components nf\ are shown as the black solid curves in
Fig. 6.3 before an external microwave is injected. Broad linewidths are observed
due to the intrinsic noise of the system. A stable external microwave at a mod­
ulation frequency of f m = m f\ is then applied. As long as m is an integer, the
modulation directly injection locks the comb component at m f\ and reduces its
linewidth.
Because of the nonlinear interaction among the comb frequencies,
linewidth narrowing takes place simultaneously for the whole comb. The other
curves of Fig. 6.3 shows the representative cases for / m = f\ (gray dotted curves),
fm = /p = 3/i (gray dashed curves), and f m = f P + fi = 4/i (gray solid curves).
Although only one frequency is directly applied at a time, the whole group of
curves is narrowed simultaneously. The narrowed linewidths are below the 1-kHz
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n= 4
n= 1
-4 0
-40 -
-
J
-8 0
-80
_______ i___
-200
-100
100
200
-200
-100
0
100
a
S
a
200
n=5
^10
-4 0
iu
a.
in
<5
-8 0
o£
-200
Oh
-100
0
100
200
-100
0
100
200
n= 3
-4 0
-8 0
-8 0
-200
-100
0
100
200
Frequency Offset (kHz)
-200
Frequency Offset (kHz)
Figure 6.3: Power spectra of the n-th harmonic of f\ with and without exter­
nal microwave modulation. Broad linewidths are recorded as the black solid
curves when there is no modulation. Linewidth narrowing is observed for all
the frequency components when a modulation is applied at f\, / p(= 3/i), or 4f\.
The resulting spectra are shown respectively as the gray dotted curves, the gray
dashed curves, and the gray solid curves. The measurements are limited by the
3-dB resolution bandwidth of 1 kHz.
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3-dB resolution limit of our instruments.
As the modulation strength increases, the signal generally improves in pu­
rity. However, strong modulation can push the comb components away from
its original frequency through the nonlinear dynamics. Optimal stabilization re­
quires iterative adjustments of / m and /ioop to maintain the frequency-locked
state while the modulation strength increases. The optimal comb therefore has a
slightly shifted /j, although the comb is still comprised of the exact harmonics of
the shifted f\. Phase control between the modulation and the feedback is achieved
when the feedback delay time is fine tuned. In our experiments, the power level
of the microwave modulation is kept between —37 and —10 dBm. Adjustments
are made in Fig. 6.3 for clarity, so that the overlapping curves are re-centered to
the respective harmonic of the shifted f\. In any case, f\ is shifted by no more
than 1.07 MHz and the frequency comb remains strictly evenly spaced. A similar
optimization method has been adopted for an optical injection laser system under
microwave modulation [113].
In order to quantify the stability of the comb, the suppression of the phase
noise is estimated using the method similar to th at described in Section 5.2.
Assuming th at the noisy sidebands in Fig. 6.3 come mainly from small phase
fluctuations, the statistical variance of the phase noise is approximated by inte­
grating the normalized single sidebands within a frequency offset of 2 to 500 kHz.
The phase noise suppression for the harmonics of f\ is shown in Fig. 6.4 when
modulation is applied at m f\ for m = 1, 2 , . . . , 6. For each value of m, the stabi­
lization is coarsely optimized at / p, which receives noise suppression between 17
and 26 dB. All the other components are also improved by 8 to 35 dB.
Modulation is also tested at f m = /ioop for the completeness of the study,
but it fails to stabilize the frequency comb with the best effort. The result is
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Modulation applied at:
CO
1
2
3
4
5
6
7
8
Harmonic Order of f v n
9
Figure 6.4: Phase noise suppressions of the frequency comb components at n f\
under different external modulations as indicated.
not surprising because /ioop is not a dominant frequency component according
to the spectrum in Fig. 6.2(b-ii). Extension of the stabilization method is also
tried on an 1 : p state with a non-integral p /l [41]. Modulation at neither fi
nor / p stabilizes the frequencies generated. Careful examination reveals th at the
ratio / p/ / i of the I : p state is not exactly rational. When the system is tuned
in trying to approach a truly rational ratio, it jumps into other nonlinear states
due to resonated frequency mixing, preventing us from obtaining the exact I : p
states with a non-integral p /l. In other words, frequency-locked states with a
truly non-integer rational / p/ / i cannot be found in this system. In this work,
only the I : p states of integral p /l ratios can be found and stabilized.
6.4
Com parison
The feedback loop of our system resembles th at in the OEO setup [132]. In a
conventional OEO, a laser source is used to pump a high-speed optoelectronic
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modulator th at is connected in an electronic feedback loop. Various methods
of microwave generation using the OEO have been investigated. Because the
laser is external to the loop, the OEO can be explained as a pure oscillator
without considering the laser dynamics. However, in our case, the semiconduc­
tor laser is part of the feedback loop. Although it can be viewed as a special
kind of OEO [133], the laser dynamics and nonlinearities have to be considered.
The dynamics of the whole system has to be described by the nonlinear laser
rate equations, which have been shown to agree well with experimental obser­
vations [39, 23]. As a result, when the delay time is varied sufficiently in our
experiment, the state changes from the frequency-locking state to other states
that have irrational / p/ / i 00p ratios, such as the quasi-frequency locking, quasiperiodic pulsing, and chaotic pulsing states [41]. These phenomena cannot be
explained by a simple oscillator theory without considering the laser dynamics
and nonlinearity. Therefore, our system is fundamentally different from an ordi­
nary OEO.
Furthermore, the system is compared to gain switching in Fig. 6.5 [134]. The
black curve shows the comb generated by the frequency-locking state, which is
stabilized by a weak current modulation of —12 dBm at f\. The gray curve shows
a similar comb th at is generated by gain switching the laser without the feedback
loop. The solitary laser is biased at the threshold and is modulated by a rela­
tively strong current of - 2 dBm at f\. The spectrum shows a deteriorated noise
performance due to the stochastic noise of gain switching and the enhancement
by the relaxation resonance. By contrast, the frequency-locking state has a better
noise performance due to the effect of the feedback loop.
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0
1
2
Frequency (GHz)
3
Figure 6.5: Comparison of microwave frequency combs generated by frequency
locking (dark curve: —12-dBm current modulation at /i) and gain switching
(gray curve: —2-dBm current modulation at f\). Note the substantially higher
modulation power required and worse noise performance for gain switching.
6.5
Sum m ary
To summarize, a technique of generating a precise microwave frequency comb is
demonstrated using a semiconductor laser under both electrical feedback and ex­
ternal modulation. The corresponding time domain output is a pulse train with
a periodic envelope. The pulses originates from the microwave modes of the op­
toelectronic feedback loop. There are finite microwave linewidths associated with
these microwave modes, which correspond to the long-term jittering of the pulse
train. By applying the modulation at an existing microwave mode frequency,
the microwave mode is injection-locked to attain a narrow linewidth. Locking of
all the other existing modes follows because they are connected to one another
through the laser nonlinearity. Therefore, a frequency comb with components
precisely locked to the external microwave is obtained. The phenomenon can be
seen as active microwave mode locking facilitated by the nonlinearity of the semi-
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conductor laser. Our method can be applied to microwave frequency conversion.
By treating the external modulation as the input and the comb frequencies as
the outputs, frequency conversions at many rational ratios are achieved. In the
future, practical application of the system requires tailoring the frequency comb
by designing the laser dynamical parameters and optimizing the stabilization
conditions.
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C H A PT E R 7
Conclusion
Semiconductor lasers are one of the most important lasers because of their fast
modulation response and inherent nonlinearity. When a semiconductor laser is
operated under proper perturbations, the laser nonlinearity enables the laser to
exhibit rich and complex nonlinear dynamics. The dynamical states typically
evolve at microwave frequencies. The laser can therefore generate optical waves
th at carry different microwave waveforms, which are not easily generated other­
wise. The objective of this research is to demonstrate control over the nonlinear
dynamics of semiconductor lasers for photonic microwave applications. A laser
under an external optical injection from another laser is first considered. The
instabilities of the dynamics are applied to the generation of high-frequency mi­
crowaves th at exceeds electronic bandwidth limitations. The period-one state is
mainly considered, but the higher-order period-two state is also useful. A laser
under proper optoelectronic feedback is also investigated, where the frequencylocking state is examined.
The main achievements in this research are: (1) generation of narrow-linewidth
microwave frequencies beyond the conventional bandwidth using the period-one
state [73], (2) analysis of the immunity of the period-one state to the power
penalty in RoF systems [75, 74], (3) demonstration of all-optical AM-to-FM con­
version by optically modulating the period-one state [108, 109], (4) demonstration
of photonic microwave frequency division and multiplication using the period-two
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state [113], and (5) generation of a precise microwave frequency comb [130]. This
research consolidates our knowledge in laser dynamics and enriches the function­
ality of semiconductor lasers in the area of photonic microwave communication
systems.
In the future, more research should be devoted to semiconductor laser dy­
namics and their applications. Theoretical analysis invoking nonlinear dynamical
theories should be applied for the improvement of microwave photonics applica­
tions. For instance, a theory th at describes the analytical behavior of the optical
injection period-one oscillation state would help to optimize the system for mi­
crowave generations. The currently available analytical theories usually rely on
perturbation analysis and often become inaccurate in quantitatively describing
the system [46]. Some analytical solutions exist for the simple states such as the
stable locking state [80] and the four-wave mixing states [81]. The extension of
the analysis to the more complicated states is certainly necessary.
In addition, there are more applications to be developed using semiconductor
lasers under nonlinear dynamics as the light source. The emerging area of chaotic
radar is one example [49]. Another example is the application of the locked
period-one state described in this dissertation for Doppler lidar measurements
since the stability of the photonic microwave enables long-range optical detection
of extremely slow targets [135]. Therefore, more interesting microwave photonic
applications utilizing semiconductor lasers are anticipated in the future.
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R
eferences
[1] R. N. Hall, G. E. Fenner, J. D. Kingsley, T. J. Soltys, and R. 0 . Carlson,
“Coherent light emission from GaAs junctions,” Phys. Rev. Lett., vol. 9,
pp. 366-368, Nov. 1962.
[2] M. I. Nathan, W. P. Dumke, G. Burns, F. H. Dill, and G. Lasher, “Stim­
ulated emission of radiation from GaAs p-n junctions,” Appl. Phys. Lett.,
vol. 1, pp. 62-64, Nov. 1962.
[3] J. M. Liu, Photonic Devices.
Cambridge, 2005.
[4] K. Sato, S. Kuwahara, and Y. Miyamoto, “Chirp characteristics of 40G b/s directly modulated distributed-feedback laser diodes,” J. Lightwave
Technol., vol. 23, pp. 3790-3797, Nov. 2005.
[5] B. Krauskopf and D. Lenstra, Eds., Nonlinear Laser Dynamics: Concepts,
Mathematics, Physics, and Applications. AIP Conf. Proc, vol. 548, 2000.
[6] F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and J. R. Tredicce, “Deter­
ministic chaos in laser with injected signal,” Opt. C o m m u n vol. 51, pp.
308-314, Oct. 1984.
[7] J. R. Tredicce, F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, “Instabilities
in lasers with an injected signal,” J. Opt. Soc. Am. B, vol. 2, pp. 173-183,
Jan. 1985.
[8] R. Lang, “Injection locking properties of a semiconductor laser,” IEEE J.
Quantum Electron., vol. 18, pp. 976-983, 1982.
[9] I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, “Locking bandwidth
and relaxation oscillations of an injection-locked semiconductor laser,”
IEEE J. Quantum Electron., vol. 24, pp. 148-154, Feb. 1988.
[10] T. B. Simpson, J. M. Liu, K. F. Huang, K. Tai, C. M. Clayton,
A. Gavrielides, and V. Kovanis, “Cavity enhancement of resonant frequen­
cies in semiconductor lasers subject to optical injection,” Phys. Rev. A,
vol. 52, pp. R4348-R4351, Dec. 1995.
[11] S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurca­
tions in a semiconductor laser subject to optical injection,” Opt. Commun.,
vol. 172, pp. 279-295, Dec. 1999.
88
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[12] S. Wieczorek, T. B. Simpson, B. Krauskopf, and D. Lenstra, “Global quan­
titative predictions of complex laser dynamics,” Phys. Rev. E, vol. 65, p.
045207R, Apr. 2002.
[13] S. Eriksson, “Dependence of the experimental stability diagram of an op­
tically injected semiconductor laser on the laser current,” Opt. Commun.,
vol. 210, pp. 343-353, Sept. 2002.
[14] A. Gavrielides, V. Kovanis, M. Nizette, T. Erneux, and T. B. Simpson, “Pe­
riod three limit-cycles in injected semiconductor lasers,” Quantum Semi­
class. Opt., vol. 4, pp. 20-26, Feb. 2002.
[15] S. Wieczorek, T. B. Simpson, B. Krauskopf, and D. Lenstra, “Bifurcation
transitions in an optically injected diode laser: theory and experiment,”
Opt. Commun., vol. 215, pp. 125-134, Jan. 2003.
[16] K. E. Chlouverakis and M. J. Adams, “Temperature sensitivity of injectionlocked vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.,
vol. 40, pp. 189-196, Mar. 2004.
[17] C. H. Lee, S. Y. Shin, and S. Y. Lee, “Optical short-pulse generation using
diode lasers with negative optoelectronic feedback,” Opt. Lett., vol. 13, pp.
464-466, June 1988.
[18] G. Giacomelli, M. Calzavara, and F. T. Arecchi, “Instabilities in a semicon­
ductor laser with delayed optoelectronic feedback,” Opt. Commun., vol. 74,
pp. 97-101, Dec. 1989.
[19] D. Pieroux, T. Erneux, and K. Otsuka, “Minimal model of a class-B
laser with delayed feedback: cascading branching of periodic solutions and
period-doubling bifurcation,” Phys. Rev. A, vol. 50, pp. 1822-1829, Aug.
1994.
[20] G. F. Li, R. K. Boncek, X. L. Wang, and D. H. Sackett, “Transient and
optoelectronic feedback-sustained pulsation of laser diodes at 1300 nm,”
IEEE Photon. Technol. Lett., vol. 7, pp. 854-856, Aug. 1995.
[21] E. V. Grigorieva, H. Haken, and S. A. Kaschenko, “Theory of quasiperiodic­
ity in model of lasers with delayed optoelectronic feedback,” Opt. Commun.,
vol. 165, pp. 279-292, July 1999.
[22] D. Pieroux, T. Erneux, T. Luzyanina, and K. Engelborghs, “Interacting
pairs of periodic solutions lead to tori in lasers subject to delayed feedback,”
Phys. Rev. E, vol. 63, p. 036211, Mar. 2001.
89
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[23] F. Y. Lin and J. M. Liu, “Nonlinear dynamics of a semiconductor laser with
delayed negative optoelectronic feedback,” IEEE J. Quantum Electron.,
vol. 39, pp. 562-568, Apr. 2003.
[24] R. Lang and K. Kobayashi, “External optical feedback effects on semicon­
ductor injection laser properties,” IEEE J. Quantum Electron., vol. 16, pp.
347-355, 1980.
[25] J. Mprk, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with
optical feedback: theory and experiment,” IEEE J. Quantum Electron.,
vol. 28, pp. 93-108, Jan. 1992.
[26] A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, “Localized synchro­
nization in two coupled nonidentical semiconductor lasers,” Phys. Rev.
Lett., vol. 78, pp. 4745-4748, June 1997.
[27] F. Rogister and J. Garcia-Ojalvo, “Symmetry breaking and high-frequency
periodic oscillations in mutually coupled laser diodes,” Opt. Lett., vol. 28,
pp. 1176-1178, July 2003.
[28] R. Vicente, J. Mulet, C. R. Mirasso, and M. Sciamanna, “Bistable polariza­
tion switching in mutually coupled vertical-cavity surface-emitting lasers,”
Opt. Lett., vol. 31, pp. 996-998, Apr. 2006.
[29] R. Vicente, S. Tang, J. Mulet, C. R. Mirasso, and J. M. Liu, “Dynamics of
semiconductor lasers with bidirectional optoelectronic coupling: Stability,
route to chaos, and entrainment,” Phys. Rev. E, vol. 70, p. 046216, Oct.
2004.
[30] S. Tang, R. Vicente, M. C. Chiang, C. R. Mirasso, and J. M. Liu, “Nonlinear
dynamics of semiconductor lasers with mutual optoelectronic coupling,”
IEEE J. Select. Topics Quantum Electron., vol. 10, pp. 936-943, Sept./Oct.
2004.
[31] M. C. Chiang, H. F. Chen, and J. M. Liu, “Experimental synchronization
of mutually coupled semiconductor lasers with optoelectronic feedback,”
IEEE J. Quantum Electron., vol. 41, pp. 1333-1340, Nov. 2005.
[32] Y. C. Chen, H. G. Winful, and J. M. Liu, “Subharmonic bifurcations and
irregular pulsing behavior of modulated semiconductor lasers,” Appl. Phys.
Lett., vol. 47, pp. 208-210, Aug. 1985.
[33] T. B. Simpson and J. M. Liu, “Enhanced modulation bandwidth in
injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett., vol. 9,
pp. 1322-1324, Oct. 1997.
90
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[34] P. C. DeJagher, W. A. van der Graaf, and D. Lenstra, “Relaxationoscillation phenomena in an injection-locked semiconductor laser,” Quan­
tum Semiclass. Opt., vol. 8, pp. 805-822, Aug. 1996.
[35] A. Gavrielides, T. Erneux, V. Kovanis, P. M. Alsing, and T. B. Simpson,
“Subharmonic transition in an optically injected semiconductor laser: the­
ory and experiments,” Quantum Semiclass. Opt., vol. 9, pp. 575-585, Aug.
1997.
[36] B. Krauskopf, N. Tollenaar, and D. Lenstra, “Tori and their bifurcations
in an optically injected semiconductor laser,” Opt. Commun., vol. 156, pp.
158-169, Nov. 1998.
[37] S. K. Hwang and D. H. Liang, “Effects of linewidth enhancement factor
on period-one oscillations of optically injected semiconductor lasers,” Appl.
Phys. Lett., vol. 89, p. 061120, Aug. 2006.
[38] C. H. Lee and S. Y. Shin, “Self-pulsing, spectral bistability, and chaos in a
semiconductor laser diode with optoelectronic feedback,” Appl. Phys. Lett.,
vol. 62, pp. 922-924, Mar. 1993.
[39] S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos
in a semiconductor laser with delayed opto-electronic feedback,” IEEE J.
Quantum Electron., vol. 37, pp. 329-336, Mar. 2001.
[40] H. G. Winful, Y. C. Chen, and J. M. Liu, “Frequency locking, quasi­
periodicity, and chaos in modulated self-pulsing semiconductor lasers,”
Appl. Phys. Lett., vol. 48, pp. 616-618, Mar. 1986.
[41] F. Y. Lin and J. M. Liu, “Harmonic frequency locking in a semiconductor
laser with delayed negative optoelectronic feedback,” Appl. Phys. Lett.,
vol. 81, pp. 3128-3130, Oct. 2002.
[42] T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing,
“Period-doubling route to chaos in a semiconductor laser subject to optical
injection,” Appl. Phys. Lett., vol. 64, pp. 3539-3541, June 1994.
[43] J. B. Gao,
S. K. Hwang, and J. M. Liu, “When can noise induce chaos?”
Phys. Rev. Lett., vol. 82, pp. 1132-1135, Feb. 1999.
[44] S. Wieczorek, B. Krauskopf, and D. Lenstra, “Unnested islandsof period
doublings in an injected semiconductor laser,” Phys. Rev. E., vol. 64, p.
056204, Nov. 2001.
91
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[45] V. Kovanis, A. Gavrielides, T. B. Simpson, and J. M. Liu, “Instabilities
and chaos in optically injected semiconductor lasers,” Appl. Phys. Lett.,
vol. 67, pp. 2780-2782, Nov. 1995.
[46] T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, “Mechanism
for period-doubling bifurcation in a semiconductor laser subject to optical
injection,” Phys. Rev. A., vol. 53, pp. 4372-4380, June 1996.
[47] S. Eriksson and A. M. Lindberg, “Periodic oscillation within the chaotic
region in a semiconductor laser subjected to external optical injection,”
Opt. Lett., vol. 26, pp. 142-144, Feb. 2001.
[48] J. M. Liu, H. F. Chen, and S. Tang, “Synchronization of chaos in semicon­
ductor lasers,” Nonlinear Analysis, vol. 47, pp. 5741-5751, Aug. 2001.
[49] F. Y. Lin and J. M. Liu, “Diverse waveform generation using semiconductor
lasers for radar and microwave applications,” IEEE J. Quantum Electron.,
vol. 40, pp. 682-689, June 2004.
[50] A. J. Seeds, “Microwave photonics,” IEEE Trans. Microwave Theory Tech.,
vol. 50, pp. 877-887, Mar. 2002.
[51] N. Dagli, “W ide-bandwidth lasers and modulators for RF photonics,” IEEE
Trans. Microwave Theory Tech., vol. 47, pp. 1151-1171, July 1999.
[52] J. Han, B. J. Seo, Y. Han, B. Jalali, and H. R. Fetterman, “Reduc­
tion of fiber chromatic dispersion effects in fiber-wireless and photonic
time-stretching system using polymer modulators,” J. Lightwave Technol.,
vol. 21, pp. 1504-1509, June 2003.
[53] H. Al-Raweshidy and S. Komaki, Eds., Radio over Fiber Technologies for
Mobile Communications Networks. Artech House Publishers, 2002.
[54] J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical
asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett., vol. 5,
pp. 787-790, July 1993.
[55] Y. Han and B. Jalali, “Time-bandwidth product of the photonic timestretched analog-to-digital converter,” IEEE Trans. Microwave Theory
Tech., vol. 51, pp. 1886-1892, July 2003.
[56] S. K. Hwang, J. M. Liu, and J. K. White, “35-GHz intrinsic bandwidth
for direct modulation in 1.3-pm semiconductor lasers subject to strong in­
jection locking,” IEEE Photon. Technol. Lett., vol. 16, pp. 972-974, Apr.
2004.
92
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[57] L. Chrostowski, X. X. Zhao, and C. J. Chang-Hasnain, “Microwave per­
formance of optically injection-locked VCSELs,” IEE E Trans. Microwave
Theory Tech., vol. 54, pp. 788-796, Feb. 2006.
[58] Y. Okajima, S. K. Hwang, and J. M. Liu, “Experimental observation of
chirp reduction in bandwidth-enhanced semiconductor lasers subject to
strong optical injection,” Opt. Commun., vol. 219, pp. 357-364, Apr. 2003.
[59] A. C. Bordonalli, C. Walton, and A. J. Seeds, “High-performance phase
locking of wide linewidth semiconductor lasers by combined use of opti­
cal injection locking and optical phase-lock loop,” J. Lightwave Technol.,
vol. 17, pp. 328-342, Feb. 1999.
[60] C. Walton, A. C. Bordonalli, and A. J. Seeds, “High-performance hetero­
dyne optical injection phase-lock loop using wide linewidth semiconductor
lasers,” IEEE Photon. Technol. Lett., vol. 10, pp. 427-429, Mar. 1998.
[61] J. M. Liu, H. F. Chen, and S. Tang, “Optical-communication systems based
on chaos in semiconductor lasers,” IEEE Trans. Circuits Syst. I, vol. 48,
pp. 1475-1483, Dec. 2001.
[62] J. M. Liu, H. F. Chen, and S. Tang, “Synchronized chaotic optical com­
munications at high bit rates,” IEEE J. Quantum Electron., vol. 38, pp.
1184-1196, Sept. 2002.
[63] Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J. M. Liu, “Injection
locking and synchronization of periodic and chaotic signals in semiconduc­
tor lasers,” IEEE J. Quantum Electron., vol. 39, pp. 269-278, Feb. 2003.
[64] J. M. Liu and S. Tang, “Chaotic communications using synchronized semi­
conductor lasers with optoelectronic feedback,” Comptes Rendus Physique,
vol. 5, pp. 657-668, July/Aug. 2004.
[65] H. F. Chen and J. M. Liu, “Complete phase and amplitude synchroniza­
tion of broadband chaotic optical fields generated by semiconductor lasers
subject to optical injection,” Phys. Rev. E, vol. 71, p. 046216, Apr. 2005.
[66] A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer,
J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaosbased communications at high bit rates using commercial fibre-optic links,”
Nature, vol. 438, pp. 343-346, Nov. 2005.
[67] L. E. Larson, J. M. Liu, and L. S. Tsimring, Eds., Digital Communications
Using Chaos and Nonlinear Dynamics. Springer, 2006.
93
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[68] J. Dellunde and M. C. Torrent, “Optoelectronic feedback stabilization of
current modulated laser diodes,” Appl. Phys. Lett., vol. 68, pp. 1601-1603,
Mar. 1996.
[69] S. Rajesh and V. M. Nandakumaran, “Suppression of chaos in a di­
rectly modulated semiconductor laser with delayed optoelectronic feed­
back,” Phys. Lett. A, vol. 319, pp. 340-347, Dec. 2003.
[70] A. Uchida, T. Heil, Y. Liu, P. Davis, and T. Aida, “High-frequency broad­
band signal generation using a semiconductor laser with a chaotic optical
injection,” IEE E J. Quantum Electron., vol. 39, pp. 1462-1467, Nov. 2003.
[71] F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Select. Topics Quantum
Electron., vol. 10, pp. 991-997, Sept./Oct. 2004.
[72] F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,”
IEEE J. Quantum Electron., vol. 40, pp. 815-820, June 2004.
[73] S. C. Chan and J. M. Liu, “Tunable narrow-linewidth photonic microwave
generation using semiconductor laser dynamics,” IEEE J. Select. Topics
Quantum Electron., vol. 10, pp. 1025-1032, Sept./O ct. 2004.
[74] S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber transmission
from an optically injected semiconductor laser in period-one state,” SPIE,
vol. 6468, p. 646811, 2007.
[75] S. C. Chan, S. K. Hwang, and J. M. Liu, “Period-one oscillation for photonic
microwave transmission using an optically injected semiconductor laser,”
Opt. Express, submitted.
[76] D. Novak, G. H. Smith, A. J. Lowery, H. F. Liu, and R. B. Waterhouse,
“Millimetre-wave fibre-wireless transmission systems with reduced effects
of fibre chromatic dispersion,” Opt. and Quantum Electron., vol. 30, pp.
1021-1031, Dec. 1998.
[77] L. A. Johansson and A. J. Seeds, “Generation and transmission of
millimeter-wave data-modulated optical signals using an optical injection
phase-lock loop,” J. Lightwave Technol, vol. 21, pp. 511-520, Feb. 2003.
[78] A. Kaszubowska, P. Anandarajah, and L. P. Barry, “Improved performance
of a hybrid radio/fiber system using a directly modulated laser transm itter
with external injection,” IEEE Photon. Technol. Lett., vol. 14, pp. 233-235,
Feb. 2002.
94
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[79] T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics
induced by external optical injection in semiconductor lasers,” Quantum
Semiclass. Opt., vol. 9, pp. 765-784, Oct. 1997.
[80] T. B. Simpson, J. M. Liu, and A. Gavrielides, “Small-signal analysis of
modulation characteristics in a semiconductor laser subject to strong op­
tical injection,” IEEE J. Quantum Electron., vol. 32, pp. 1456-1468, Aug.
1996.
[81] T. B. Simpson and J. M. Liu, “Phase and amplitude characteristics of
nearly degenerate four-wave mixing in Fabry-Perot semiconductor lasers,”
J. Appl. Phys., vol. 73, pp. 2587-2589, Mar. 1993.
[82] T. B. Simpson, “Mapping the nonlinear dynamics of a distributed feedback
semiconductor laser subject to external optical injection,” Opt. Commun.,
vol. 215, pp. 135-151, Jan. 2003.
[83] A. Gavrielides, V. Kovanis, and T. Erneux, “Analytical stability boundaries
for a semiconductor laser subject to optical injection,” Opt. Commun., vol.
136, pp. 253-256, Mar. 1997.
[84] J. M. Liu, H. F. Chen, X. J. Meng, and T. B. Simpson, “Modulation
bandwidth, noise, and stability of a semiconductor laser subject to strong
injection locking,” IEEE Photon. Technol. Lett., vol. 9, pp. 1325-1327, Oct.
1997.
[85] A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and
bandwidth enhancement in semiconductor lasers with strong light injec­
tion,” IEE E J. Quantum Electron., vol. 39, pp. 1196-1204, Oct. 2003.
[86] S. K. Hwang, J. M. Liu, and J. K. White, “Characteristics of period-one
oscillations in semiconductor lasers subject to optical injection,” IEEE J.
Select. Topics Quantum Electron., vol. 10, pp. 974-981, Sept./O ct. 2004.
[87] W. A. van der Graaf, A. M. Levine, and D. Lenstra, “Diode lasers locked
to noisy injection,” IEEE J. Quantum Electron., vol. 33, pp. 434-442, Mar.
1997.
[88] S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically
injected semiconductor laser,” Opt. Commun., vol. 183, pp. 195-205, Sept.
2000 .
95
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[89] L. Noel, D. Wake, D. G. Moodie, D. D. Marcenac, L. D. Westbrook, and
D. Nesset, “Novel techniques for high-capacity 60-GHz fiber-radio trans­
mission systems,” IEEE Trans. Microwave Theory Tech., vol. 45, pp. 1416—
1423, Aug. 1997.
[90] T. B. Simpson and F. Doft, “Double-locked laser diode for microwave pho­
tonics applications,” IEEE Photon. Technol. Lett., vol. 11, pp. 1476-1478,
Nov. 1999.
[91] P. Saboureau, J. P. Foing, and P. Schanne, “Injection-locked semiconductor
lasers with delayed optoelectronic feedback,” IEEE J. Quantum Electron.,
vol. 33, pp. 1582-1591, Sept. 1997.
[92] T. B. Simpson, “Phase-locked microwave-frequency modulations in
optically-injected laser diodes,” Opt. Commun., vol. 170, pp. 93-98, Oct.
1999.
[93] A. Kaszubowska, L. P. Barry, and P. Anandarajah, “Multiple RF carrier
distribution in a hybrid radio/fiber system employing a self-pulsating laser
diode transm itter,” IEEE Photon. Technol. Lett., vol. 14, pp. 1599-1601,
Nov. 2002.
[94] D. Novak, Z. Ahmed, R. B. Waterhouse, and R. S. Tucker, “Signal gener­
ation using pulsed semiconductor lasers for application in millimeter-wave
wireless links,” IEEE Trans. Microwave Theory Tech., vol. 43, pp. 22572262, Sept. 1995.
[95] C. Lim, D. Novak, A. Nirmalathas, and G. H. Smith, “Dispersion-induced
power penalties in millimeter-wave signal transmission using multisection
DBR semiconductor laser,” IEEE Trans. Microwave Theory Tech., vol. 49,
pp. 288-296, Feb. 2001.
[96] B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K. Y. Jen,
W. H. Steier, and H. R. Fetterman, “Electrooptic polymer ring resonator
modulation up to 165 GHz,” IEEE J. Select. Topics Quantum Electron.,
vol. 13, pp. 104-110, Jan./Feb. 2007.
[97] Y. D. Chung, Y. S. Kang, K. S. Choi, S. B. Kim, and J. Kim, “Character­
istics of radio-over-fiber link with 60-GHz narrow band electroabsorption
m odulator,” IEEE LEOS Annual Meeting, pp. 573-574, 2005.
[98] A. Kaszubowska, P. Anandarajah, and L. P. Barry, “Multifunctional oper­
ation of a fiber Bragg grating in a WDM/SCM radio over fiber distribution
system,” IEE E Photon. Technol. Lett., vol. 16, pp. 605-607, Feb. 2004.
96
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[99] C. Lim, A. Nirmalathas, D. Novak, R. Waterhouse, and G. Yoffe,
“Millimeter-wave broad-band fiber-wireless system incorporating baseband
data transmission over fiber and remote LO delivery,” J. Lightwave Tech­
nol., vol. 18, pp. 1355-1363, Oct. 2000.
[100] G. H. Smith, D. Novak, and Z. Ahmed, “Overcoming chromatic-dispersion
effects in fiber-wireless systems incorporating external modulators,” IEEE
Trans. Microwave Theory Tech., vol. 45, pp. 1410-1415, Aug. 1997.
[101] U. Gliese, “Multi-functional fibre-optic microwave links,” Opt. and Quan­
tum Electron., vol. 30, pp. 1005-1019, Dec. 1998.
[102] M. Hyodo, K. S. Abedin, and N. Onodera, “Generation of millimeter-wave
signals up to 70.5 GHz by heterodyning of two extended-cavity semicon­
ductor lasers with an intracavity electro-optic crystal,” Opt. Commun., vol.
171, pp. 159-169, Nov. 1999.
[103] D. Wake, C. R. Lima, and P. A. Davies, “Transmission of 60-GHz signals
over 100 km of optical fiber using a dual-mode semiconductor laser source,”
IEEE Photon. Technol. Lett., vol. 8, pp. 578-580, Apr. 1996.
[104] K. Sato, “Semiconductor light sources for 40-Gb/s transmission systems,”
J. Lightwave Technol., vol. 20, pp. 2035-2043, Dec. 2002.
[105] K. S. Lee and C. Shu, “Stable and widely tunable dual-wavelength
continuous-wave operation of a semiconductor laser in a novel Fabry-Perot
grating-lens external cavity,” IEEE J. Quantum Electron., vol. 33, pp.
1832-1838, Oct. 1997.
[106] K. E. Razavi and P. A. Davies, “Semiconductor laser sources for the gen­
eration of millimetre-wave signals,” IEE Proc. Optoelectron., vol. 145, pp.
159-163, June 1998.
[107] H. S. Ryu, Y. K. Seo, and W. Y. Choi, “Dispersion-tolerant transmis­
sion of 155-Mb/s d ata at 17 GHz using a 2.5-Gb/s-grade DFB laser with
wavelength-selective gain from an FP laser diode,” IEEE Photon. Technol.
Lett., vol. 16, pp. 1942-1944, Aug. 2004.
[108] S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM
upconversion using an optically injected semiconductor laser,” Opt. Lett.,
vol. 31, pp. 2254-2256, Aug. 2006.
[109] S. C. Chan and J. M. Liu, “Frequency modulation on single sideband using
controlled dynamics of an optically injected semiconductor laser,” IEEE J.
Quantum Electron., vol. 42, pp. 699-705, July 2006.
97
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[110] S. Haykin, Communication systems, 3rd ed.
Wiley, 1994.
[111] U. Gliese, T. N. Nielsen, S. N0rskov, and K. E. Stubkjaer, “Multifunctional
fiber-optic microwave links based on remote heterodyne detection,” IEEE
Trans. Microwave Theory Tech., vol. 46, pp. 458-468, May 1998.
[112] X. J. Meng, D. T. K. Tong, T. Chau, and M. C. Wu, “Demonstration of
an analog fiber-optic link employing a directly modulated semiconductor
laser with external light injection,” IEEE Photon. Technol. Lett., vol. 10,
pp. 1620-1622, Nov. 1998.
[113] S. C. Chan and J. M. Liu, “Microwave frequency division and multiplica­
tion using an optically injected semiconductor laser,” IEE E J. Quantum
Electron., vol. 41, pp. 1142-1147, Sept. 2005.
[114] A. E. Kelly, R. J. Manning, A. J. Poustie, and K. J. Blow, “All-optical
clock division at 10 and 20 GHz in a semiconductor optical amplifier based
nonlinear loop mirror,” Electron. Lett., vol. 34, pp. 1337-1339, June 1998.
[115] H. J. Lee and H. G. Kim, “Polarization-independent all-optical clock divi­
sion using a semiconductor optical amplifier/grating filter switch,” IEEE
Photon. Technol. Lett., vol. 11, pp. 469-471, Apr. 1999.
[116] R. J. Manning, I. D. Phillips, A. D. Ellis, A. E. Kelly, A. J. Poustie, and
K. J. Blow, “All-optical clock division at 40 GHz using semiconductor op­
tical amplifier based nonlinear interferometer,” Electron. Lett., vol. 35, pp.
827-829, May 1999.
[117] X. S. Yao and G. Lutes, “A high-speed photonic clock and carrier recovery
device,” IEEE Photon. Technol. Lett., vol. 8, pp. 688-690, May 1996.
[118] H. Tsuchida and M. Suzuki, “40-Gb/s optical clock recovery using an
injection-locked optoelectronic oscillator,” IEEE Photon. Technol. Lett.,
vol. 17, pp. 211-213, Jan. 2005.
[119] Z. X. Wang, T. Wang, C. Y. Lou, L. Huo, and Y. Z. Gao, “A novel ap­
proach for clock recovery without pattern effect from degraded signal,” Opt.
Commun., vol. 219, pp. 301-306, Apr. 2003.
[120] J. Lasri, P. Devgan, R. Y. Tang, and P. Kumar, “Ultralow timing jitter 40G b/s clock recovery using a self-starting optoelectronic oscillator,” IEEE
Photon. Technol. Lett., vol. 16, pp. 263-265, Jan. 2004.
98
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[121] H. Yokoyama, Y. Hashimoto, H. Kurita, and I. Ogura, “Two-stage
all-optical subharmonic clock recovery using modelocked semiconductor
lasers,” Electron. Lett., vol. 36, pp. 1577-1578, Aug. 2000.
[122] E. Tangdiongga, J. P. Turkiewicz, G. D. Khoe, and H. de W aardt, “Clock
recovery by a fiber ring laser employing a linear optical amplifier,” IEEE
Photon. Technol. Lett., vol. 16, pp. 611-613, Feb. 2004.
[123] G. Farrell, P. Phelan, J. Hegarty, and J. A. Shields, “All-optical timing
extraction with frequency division using a twin-section laser-diode,” IEEE
Photon. Technol. Lett., vol. 5, pp. 718-721, June 1993.
[124] H. F. Liu and W. F. Ngai, “Nonlinear dynamics of a directly modu­
lated 1.55-/mi InGaAsP distributed feedback semiconductor laser,” IEEE
J. Quantum Electron., vol. 29, pp. 1668-1675, June 1993.
[125] Y. Matsui, S. Kutsuzawa, S. Arahira, Y. Ogawa, and A. Suzuki, “Bifurca­
tion in 20-GHz gain-switched 1.55-pm MQW lasers and its control by CW
injection seeding,” IEEE J. Quantum Electron., vol. 34, pp. 1213-1223,
July 1998.
[126] K. K. Chow, C. Shu, and H. F. Liu, “Low-power optical control of pe­
riod doubling in injection-seeded Fabry-Perot laser diode,” Electron. Lett.,
vol. 37, pp. 429-431, Mar. 2001.
[127] Y. M. Yang, H. F. Liu, and Y. Matsui, “Scheme for all-optical clock division
based on period doubling in semiconductor lasers,” Electron. Lett., vol. 36,
pp. 1852-1854, Oct. 2000.
[128] K. K. Chow, C. Shu, and H. F. Liu, “All-optical control of clock frequency
division using injection-locked Fabry-Perot laser diode,” Electron. Lett.,
vol. 39, pp. 1136-1138, July 2003.
[129] K. K. Chow, C. Shu, Y. M. Yang, and H. F. Liu, “Optical control of period
doubling in a gain-switched Fabry-Perot laser diode and its application in
all-optical clock division,” IEE Proc. Optoelectron., vol. 150, pp. 239-245,
June 2003.
[130] S. C. Chan, G. Q. Xia, and J. M. Liu, “Optical generation of a precise
microwave frequency comb by harmonic frequency locking,” Opt. Lett., ac­
cepted.
[131] D. Baums, W. Elsasser, and E. O. Gobel, “Farey tree and devil’s staircase of
a modulated external-cavity semiconductor laser,” Phys. Rev. Lett., vol. 63,
pp. 155-158, July 1989.
99
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
[132] T. Sakamoto, T. Kawanishi, and M. Izutsu, “Optoelectronic oscillator using
a LiN b03 phase modulator for self-oscillating frequency comb generation,”
Opt. Lett., vol. 31, pp. 811-813, Mar. 2006.
[133] X. S. Yao and L. Maleki, “Dual microwave and optical oscillator,” Opt.
Lett., vol. 22, pp. 1867-1869, Dec. 1997.
[134] M. Jinno, “Correlated and uncorrelated timing jitter in gain-switched laser
diodes,” IEEE Photon. Technol. Lett., vol. 5, pp. 1140-1143, Oct. 1993.
[135] R. Diaz, S. C. Chan, and J. M. Liu, “Lidar detection using a dual-frequency
source,” Opt. Lett., vol. 31, pp. 3600-3602, Dec. 2006.
100
R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.
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