University of Southern California Dissertations and Theses

Nonlinear optical signal processing for high-speed, spectrally efficient fiber optic systems and networks

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Nonlinear optical signal processing for high-speed, spectrally efficient fiber optic systems and networks

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Content NONLINEAR OPTICAL SIGNAL PROCESSING FOR HIGH-SPEED,
SPECTRALLY EFFICIENT FIBER OPTIC SYSTEMS AND NETWORKS

by

Bo Zhang

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)

May 2009

Copyright 2009 Bo Zhang
ii
Acknowledgements

First of all, I would like to express my thankfulness to my thesis advisor, Prof. Alan
E. Willner, for bringing me into this fascinating optical fiber communication world.
During my five years at USC, he not only taught me technical perspectives from
thinking about new research ideas to conducting complicated experiments, but also
taught me invaluable lessons on how one could be a true professional as well. I am
also grateful to Prof. William H. Steier and Prof. Eugene N. Bickers for always being
available as members of my dissertation committee and my Ph.D. qualifying exam
committee. Sincere thanks also go to Prof. B. Keith Jenkins and Prof. Zhen Zhang
who were members of my qualifying exam committee and provided me with
opportunities to be either teaching assistant or grader of their courses in my early
part of graduate studies.

My research achievements would not have been accomplished without the wonderful
collaborations with several outstanding research groups. First, I would like to thank
Prof. Daniel Gauthier and Dr. Zhaoming Zhu at Duke University, as well as Prof.
Robert Boyd at the University of Rochester, for their breakthrough research work on
broadband SBS slow light, which serves as one of the important cornerstones for our
series of high-speed slow light projects. Memorable collaborations with Prof. Connie
Chang-Hasnain, Wendy Xiaoxue Zhao and Devang Parekh from the University of
California-Berkeley on the system applications of optical injection-locked VCSELs
iii
have resulted in several fruitful publications. I am greatly impressed by Wendy’s
nice personality and her detail-oriented attitude, and would love to work with her
again in the near future if possible. Another group at the University of California-
Berkeley, Prof. Ming Wu and Dr. David Leuenberger, provides me with their novel
bandwidth tunable micro-disk resonator filter. Working with David was really fun
and relaxing and I have gained tremendous research confidence during that project. I
would also like to thank Dr. X. Steve Yao at General Photonics Corp. My three years
part-time internship experience in his company has been a wonderful asset in
addition to my academic achievements. Technical interactions with Steve on one of
the three projects I have done have truly been a wonderful learning experience.

My former and current colleagues at the optical communications laboratory
(OCLAB) definitely deserve respectful acknowledgement. OCLAB, and particularly
optical table B, has witnessed most of my exciting experimental demonstrations
during the past five years. It is indeed and will always be my sweet home in Los
Angeles. Prof. Lianshan Yan is the first person I would like to thank at OCLAB. He
not only recommended me to Steve for the internship opportunity, but more
importantly, he guided me on several of my early research projects and trained me
useful experimental skills on how to conduct projects efficiently. Dr. Saurabh Kumar
is another person I am indebted to. Saurabh led me into the DOD-N project and I am
fortunate to be interacting with him during that two years. I learnt tremendously from
his exceptional logical thinking and the way he approaches research problems. Prof.
iv
Changyuan Yu, Dr. Yan Wang and Dr. Ting Luo were my three senior Chinese
members in the lab. I will not forget the numerous help and advices they provided
me during my early Ph.D. career and during my job-hunting days. Earlier members
like Prof. Zhongqi Pan, Dr. Yong-won Song, Dr. Reza Motaghian, Dr. Paniz
Ebrahimi, Dr. John Mcgeenhan, and Dr. Poorya Saghari have helped and influenced
me here and there and will always be good professionals to resort to during my
future career. Among the current members, I would like to especially express my
gratitude to Lin Zhang. Technical discussions with Lin have always been stimulating
and Lin’s perspective on research topics or even personal issues is generally deep
and comprehensive. Every single member of OCLAB has contributed to my life at
USC being a memorable one and I will always cherish the fun moments we shared
together.

Outside OCLAB, I am also thankful to Dr. Tingye Li, Dr. Jin-Xing Cai at Tyco
Telecommunications, Dr. Xiang Liu at Alcatel-Lucent Bell Labs and Prof. Kai-Ming
Feng at National Tsinghua University, for always being available to answer my
questions and providing nice encouragement during my Ph.D. studies.

My sincere thanks also go to the electrical engineering staffs at USC. In particular, I
wish to thank Milly Montenegro, Gerrielyn Ramos, Mayumi Thrasher, Diane
Demetras and Tim Boston in EE-systems for all their gracious help.

v
None of my achievements would have been possible without the love and support of
my caring parents and wonderful parents-in-law. It is all my four parents who have
encouraged and supported me for my further education abroad and who have
determinedly motivated me through each and every stage of my academic career.
This dissertation is undoubtedly the fruit of their sacrifices and hopes.

Last but not least, I wish to express my deepest gratitude to my lovely wife, Di Lou.
I will never forget the countless mails she sent for love and encouragement from the
United Kingdom during our tough separation in my first year at USC. I can hardly
imagine my selfishness that I even requested her to wake me up for my first final at
USC when she was not feeling well. Starting from my second year at USC, we are
fortunate to be together ever since, and that’s also when I start to gradually lose my
cooking skills. Her wholeheartedly prepared meals everyday have allowed me to stay
away from burgers. Besides the material support, Di has also provided me with
spiritual support from my early PhD screening exam, to PhD qualifying exam and all
the way to the final PhD defense. This dissertation is for you, my darling.

vi
Table of Contents

Acknowledgements ii

List of Figures viii

Abstract xx

Chapter 1: Introduction 1
1.1 Present fiber-optic telecommunication networks 1
1.2 The role of optical signal processing 2
1.3 Advanced modulation formats 7
1.4 Outline of the dissertation 8

Chapter 2: Nonlinear signal processing using slow-light based tunable
optical delay lines 11
2.1 Fundamentals of slow light 14
2.2 Applications of slow-light based tunable delay lines 15
2.3 Techniques to achieve slow light phenomenon 19
2.4 Slow-light induced data-pattern dependence and its mitigation 22

Chapter 3: Nonlinear signal processing using semiconductor optical
amplifiers (SOAs) 33
3.1 Cross-gain modulation (XGM) 33
3.2 Cross-phase modulation (XPM) 36
3.3 Cross-polarization modulation (XPolM) 38

Chapter 4: Phase-preserving slow light using advanced phase-
modulated formats 40
4.1 Motivation 40
4.2 Slow light on differential-phase-shift-keying (DPSK) signals 41
4.3 DPSK data-pattern dependence and its reduction 45
4.4 Spectrally-efficient slow light using DQPSK format 51

Chapter 5: Design of functional modules using slow-light-based
tunable delay lines 59
5.1 Motivation 59
5.2 A multi-channel synchronizer using a single slow-light element 60
5.3 A continuously tunable 2:1 OTDM multiplexer 67
5.4 Multi-channel slow light using incoherent pumping 73

vii
Chapter 6: Compensation of deleterious effects in high-speed SOA-
based wavelength converters 87
6.1 Differential mode wavelength converters 87
6.2 Sub-pulses and its suppression 90
6.3 Data-pattern dependence and its elimination 95

Chapter 7: Enhancing system performance using novel optical devices 106
7.1 Reach extension and dispersion pre-compensation using
adjustable-chirp optically-injection-locked (OIL)-VCSELs 107
7.2 Multifunctional generation of ultra-wideband (UWB) signals,
format conversion, and data-clock recovery using OIL-VCSELs 115
7.3 Dynamic bandwidth allocation using a bandwidth-tunable
MEMS-actuated micro-disk resonator filter 125

Chapter 8: Design and demonstration of novel polarization-based
optical components and instruments 134
8.1 Novel polarimeter-based fast-swept optical spectrum analyzer 135
8.2 All-optical automatic de-multiplexing of polarization
multiplexed 1.12-Tb/s (14 channel x 40-Gb/s x 2) systems 152

Chapter 9: Design and evaluation of a re-circulating fiber loop test-bed
for 40-Gb/s WDM long-haul transmission 166
9.1 Fundamentals of a circulating fiber loop 167
9.2 Design guidelines 171
9.3 Experimental results at 10-Gb/s and 40-Gb/s 194

Chapter 10: Conclusions 200

Bibliography 201

viii
List of Figures

Figure 1-1: Future synergistic signal processing, utilizing advantages in both
electronic and optical domain. 3

Figure 1-2: Key signal processing functions at a router node. 4

Figure 2-1: The concept of slow light. 14

Figure 2-2: Applications of slow-light based tunable delay lines in the field of
optical signal processing. 16

Figure 2-3: Gain and delay profiles of (a) SBS and (b) OPA based slow light,
indicating that various slow light schemes could be categorized by
their characteristic amplitude and phase responses. 20

Figure 2-4: Origin of data-pattern dependent distortion. Pattern dependent gain
and delay are shown as the two main degrading effects. 24

Figure 2-5: Quantification of slow-light-induced pattern dependent gain and
delay. (a) Level ratio versus slow light bandwidth for two typical
combinations of data patterns. (b) Delay versus slow light
bandwidth for two typical patterns. 25

Figure 2-6: Isolating the effect of amplitude response and phase response on
the signal quality (Q factor). Amplitude response is shown as the
dominating effect for data distortion. 27

Figure 2-7: (a) FOM I versus normalized slow-light bandwidth. (b) FOM II
versus normalized slow-light bandwidth. Both FOMs show that the
optimized slow-light bandwidth equals 1.4 times the signal
bandwidth. 29

Figure 2-8: Concept of data-pattern dependence reduction by detuning the
channel away from the slow light resonance peak. 30

Figure 2-9: Simulation results of data-pattern dependence reduction by
detuning the channel away from the gain peak. 2-dB Q-factor
improvement is achieved by either red or blue detuning 40% of the
signal bandwidth. 31

ix
Figure 3-1: Cross gain modulation. High power pump pulses deplete the
carriers in the SOA leading to a suppression of the gain. A CW
probe beam passing through the SOA experiences this varying gain
and as a result an inverted copy of the data gets imprinted on the
probe wavelength. 34

Figure 3-2: XGM-based inverted wavelength conversion of RZ data. The gain
exhibits slow recovery, which can lead to pattern dependence in
the converted bits. The high level of the converted signal’s eye
diagram is extremely noisy due to pattern dependence. 35

Figure 3-3: Cross phase modulation. The phase-shifter is adjusted to provide a
π phase shift to the CW probe passing through the lower arm of the
MZI. As a result, in the balanced situation the CW probe
components interfere destructively in the absence of any pump
signal. When a pump pulse enters the upper SOA it alters the
phase of the probe leading to a constructive interference at the MZI
output. Thus wavelength-converted pulses appear at the output for
each incoming pump pulse. By adjusting the phase-shifter to
introduce no additional phase shift, inverted conversion can also be
achieved. 37

Figure 4-1: A) Concept of slow light on phase-modulated optical signals. B)
Slow-light-induced data-pattern dependence on demodulated two
output ports. 41

Figure 4-2: Simulation result of phase patterns of a 10-Gb/s DPSK signal
before and after 8GHz BW slow light element. Phase is preserved
and delayed by 46 ps. 42

Figure 4-3: Experimental Setup for DPSK slow-light based on broadband SBS. 43

Figure 4-4: Observation of DPSK slow-light: continuous delay of up to 42 ps
for a 10.7Gb/s DPSK signal. 44

Figure 4-5: Slow-Light-induced data-pattern dependence: 10.7-Gb/s NRZ-
DPSK through an 8-GHz slow light element. Bit patterns before
(NRZ-DPSK) and after (DB and AMI) demodulation are shown
before and after slow light. 46

Figure 4-6: BER measurement of DB port from 10.7-Gb/s DPSK signals after
SBS slow light element. Data-pattern dependence and Rayleigh
crosstalk (shown in the spectrum) are the two main reasons for
DPSK signal degradation. 47
x

Figure 4-7: Power penalty comparison between 2.5-Gb/s and 10-Gb/s NRZ-
DPSK shows that data-pattern dependence is bit-rate specific. 48

Figure 4-8: Reduction of DPSK data-pattern dependence by detuning the SBS
gain peak: 3-dB Q factor improvement on the AMI port
demodulated from 10.7-Gb/s DPSK signals is achieved. 49

Figure 4-9: Left: Delay for 2.5-Gb/s NRZ and RZ-DPSK with the same 5-GHz
SBS BW. The fractional delays for both NRZ and RZ-DPSK are
comparable. Right: RZ-DPSK outperforms NRZ-DPSK by as
much as 2 dB, which shows its robustness to data-pattern
dependence. 50

Figure 4-10: Simulation results of (a) 4-level phase patterns of 10-Gbaud
DQPSK signals before and after 10-GHz slow-light element. (b)
Demodulated eye diagrams of both 10Gbaud DQPSK and D8PSK
signals after a 10-GHz slow light element, showing the ability to
transmit very high spectrally-efficient multi-level formats through
BW-limited slow light elements. 52

Figure 4-11: Experimental setup: 10-Gb/s RZ-DQPSK signals transmitted
through SBS-based slow light medium. 54

Figure 4-12: Bit patterns of balance-detected I and Q channels from 10-Gb/s
DQPSK signals, for three different pump power cases. 55

Figure 4-13: Symbol delay versus SBS pump power for both I and Q. Eye
diagrams of I channel at three pump power values with slow-light
delay exhibits good quality of delayed signal. 56

Figure 4-14: BER measurement of both I and Q channel from 10-Gb/s DQPSK
signals show error-free operation even at maximum 60-ps slow-
light delay. 57

Figure 5-1: Conceptual diagram of independent delay control and
synchronization on multiple data-channels within a single slow-
light element. The key enabler is the generation of multiple slow-
light resonances from multiple pumps inside a single piece of
slow-light fiber medium (inset). Independent fine-grained delay
controls are thus achieved from their corresponding resonances. 61

xi
Figure 5-2: Experimental Setup of multi-channel slow-light synchronizer.
Three 2.5-Gb/s NRZ-OOK signals are independently delayed and
synchronized. 63

Figure 5-3: Left: Bit-patterns before and after synchronization confirm
independent delay control on individual channels. Right bottom:
Spectrum of all three channels after synchronization. Right top:
Zoomed-in spectrum of channel #1. 64

Figure 5-4: BER and eye diagrams before and after multi-channel slow-light
synchronization. Data pattern dependence and residual Rayleigh
crosstalk are believed to be the two main contributors to power
penalty. 65

Figure 5-5: Crosstalk between multiple channels. One channel slightly affects
the other channel’s delay. 66

Figure 5-6: System power penalties due to crosstalk between multiple
channels. Clear tradeoff exists between slow-light delay and signal
power penalty. 67

Figure 5-7: Concept of the advantages of slow-light-based OTDM compared
with conventional fiber-based fixed length OTDM. Slow-light-
based tunable delay line also enables variable-bit-rate OTDM. 68

Figure 5-8: Experimental setup of SBS-based continuously controllable 2:1
OTDM multiplexer. 69

Figure 5-9: Bit patterns and spectrum show efficient OTDM after continuously
tunable slow light of 75 ps delay. 70

Figure 5-10: Power penalty versus fractional delay and the corresponding eye
diagrams. 9-dB power penalty reduction is achieved. 71

Figure 5-11: Variable bit-rate OTDM: Efficient multiplexing of two data
streams at three different input bit-rates. 72

Figure 5-12: System power penalty and fractional delay at three different input
bit-rates. 72

Figure 5-13: Concept of broadband SBS pump, as compared to the conventional
SBS pump. The broadened SBS gain spectrum is the convolution
of the intrinsic gain spectrum and the broadband pump power
spectrum. 74
xii

Figure 5-14: (a). Concept of broadband SBS pump using “coherent sources”.
Three different approaches are depicted. (b). Concept of broadband
SBS pump using “spectrally-sliced incoherent source”. PRBS:
pseudo-random bit sequence; TLS: tunable laser source; PM: phase
modulator. Pol.: polarizer. 75

Figure 5-15: Concept of the multi-channel SBS slow light operation using a
periodically spectrally sliced incoherent ASE source. BPF: band-
pass filter. 77

Figure 5-16: Single channel experimental setup: Polarized ASE source followed
by an FBG is served as our proposed spectrally sliced pump. Both
OOK and DPSK signals are delayed and evaluated. 79

Figure 5-17: Slow light delay on both 2.5-Gb/s NRZ-OOK and NRZ-DPSK
signals using a 4-GHz spectral-sliced pump. 80

Figure 5-18: Slow light delay on both 2.5-Gb/s NRZ-OOK and NRZ-DPSK
signals using a 2-GHz spectral-sliced pump. 80

Figure 5-19: Comparison of slow-light delay as a function of increased pump
power for two different spectrally sliced conditions. This shows
that the optimization of SBS pump spectra-width is essential for
the slow-light delay performance. 81

Figure 5-20: BER measurement of both the 4-GHz and the 2-GHz spectrally
sliced cases. Less than 4 dB power penalty at the maximum delay
conditions shows the effectiveness of our proposed technique. 82

Figure 5-21: Multi-channel experimental setup: Polarized ASE source followed
by a periodic Fabry-Perot filter (FPF) is served as our proposed
multi-channel spectrally-sliced pump. 2.5-Gb/s RZ-DPSK, NRZ-
OOK and NRZ-DPSK signals are independently delayed and
evaluated. 83

Figure 5-22: Top: Initial status for all three channels without slow light delay.
Bottom: Eye diagrams for all three channels after the multi-
channel slow light module. 84

Figure 5-23: BER measurement before and after multi-channel slow light
module, for both 2.5-Gbit/s RZ-DPSK and NRZ-DPSK signals. 85

xiii
Figure 6-1: Structure of the DISC wavelength converter. 88

Figure 6-2: Operating principle of the DISC. The pump input signal imposes
phase variation on the CW probe. This phase modulated signal is
made to interfere with its own delayed copy using the AMZI. As a
result narrow switching windows are formed due to the phase
difference, which are not limited by the slow carrier recovery time.
Sub-pulses are also generated due to overshoot of the delayed
component. 89

Figure 6-3: 40-Gb/s simulation results: Time-resolved chirp in both MZI arms.
Sub-pulses and main-pulses are oppositely chirped. 91

Figure 6-4: Experimental setup: Off-centered filtering technique for Extinction
Ratio Enhancement. MLL: Mode-Locked Laser. 92

Figure 6-5: Experimental verification of the temporal chirp waveform using
the chirp form analyzer. 92

Figure 6-6: Sub-pulse suppression ratio as a function of filter detuning, for the
case of phase bias = ‘π’. Two inserted eye diagrams show effective
sub-pulse suppression. 93

Figure 6-7: (a). Eye diagrams showing the interplay of phase bias and filter
detuning. AC: no detuning, only phase bias adjustment. BD:
both detuning and bias optimization. (b). Red-detuned filtering
suppresses the sub-pulses, resulting in >3dB ER improvement
(CD) for the optimum phase bias case. 94

Figure 6-8: Data-pattern dependence due to slow carrier recovery in SOA
based wavelength converters. 95

Figure 6-9: Eye-closure penalty due to increasing bit-rate for differential mode
wavelength converters. 96

Figure 6-10: Operation of the DISC assuming only linear pattern dependence
exists in the SOA. All pulses induce the same amount of phase-
swing and the differential mode completely compensates for linear
pattern dependence. 98

Figure 6-11: Operation of the DISC including nonlinear pattern dependence in
the SOA. The amount of phase-swing induced by input pulses
reduces in a long string of 1’s leading to a reduction in output
pulse amplitudes. 98
xiv

Figure 6-12: Correspondence between gain suppression and pattern dependence.
Output pulses that exhibit lower power correspond to larger gain
saturation in the SOA. 99

Figure 6-13: Experimental setup to observe polarization state of DISC’s output
for an input (pump) pulse train. As the pump power increases, the
amount of gain saturation and polarization rotation increases. 100

Figure 6-14: Gain suppression and polarization rotation as a function of input
optical signal power. Pulses that correspond to larger gain
suppression undergo greater polarization rotation. 101

Figure 6-15: Experimental setup. The SOA and the 25 ps delay-interferometer
form the DISC. The polarization controller and polarizer are
added to control the pattern dependence of the output signal. 101

Figure 6-16: Principle of polarimetric pattern dependence reduction. The
polarization controller and polarizer placed after the DISC are
adjusted such that the pulses with larger amplitude are
preferentially attenuated relative to the smaller pulses. 103

Figure 6-17: Reduction of pattern dependence in DISC wavelength converter. 103

Figure 6-18: Bit-patterns and eye diagrams showing control over the pattern
dependence. Through appropriate adjustment of the output
polarization controller, the pattern dependence can be reduced
from 3.3 dB to 0 dB or increased to >7 dB. 104

Figure 6-19: Bit-error-rate measurements showing 2.6 dB power penalty
improvement at BER=1e-9. Eye opening is improved by more
than 33%. 105

Figure 7-1: Experimental setup. OIL VCSELs with tunable chirp for
dispersion compensation. Chirp form analyzer is used to
investigate the polarity flipping of the frequency chirp. Multiple
spools of SSMF are used to study the effect of the flipped chirp on
chromatic dispersion. 109

Figure 7-2: Experimental measurement of time-resolved chirp and intensity
waveforms at 10-Gb/s for (a) free-running VCSEL, (b-d) OIL
VCSEL with injection ratios of (b) 6.21 dB (c) 8.58 dB (d) 11.12
dB. 110

xv
Figure 7-3: Peak-to-peak chirp and extinction ratio at 10-Gb/s as functions of
injection ratio. 111

Figure 7-4: Optical spectra of free-running and OIL VCSEL with 8.58-dB
injection ratio, both modulated at 10 Gbit/s. 111

Figure 7-5: BER measurements and error-free eye diagrams of an OIL VCSEL
with back-to-back, 25-km and 100-km SSMF transmission. 114

Figure 7-6: Power penalty vs. SSMF transmission distance for free-running
VCSEL, commercial DFB DML and OIL VCSEL. 115

Figure 7-7: Concept of multifunctional generator using OIL-VCSEL followed
by a delay-line interferometer (DLI). Three unique and
reconfigurable functions are achieved by utilizing the adjustable-
chirp from the OIL-VCSEL and subsequent tunable filtering. 118

Figure 7-8: Experimental setup of multifunctional generator using a chirp
adjustable injection-locked VCSEL followed by a tunable
interferometer. 119

Figure 7-9: Time-resolved frequency chirp measurement of OIL single mode
VCSEL under the transition state, which has residual IM. 120

Figure 7-10: Polarity-switchable differentiator from positive or negative slope
of DLI. (SM-VCSEL). 121

Figure 7-11: Measured UWB signals using OIL multi-mode VCSEL. 122

Figure 7-12: RF spectrum of the UWB-monocycle of Fig. 5 (a), showing 129%
fractional bandwidth at 5.1 GHz. 123

Figure 7-13: (a) Rising-edge detection. (b) Falling-edge detection. (c) Eye
diagrams of NRZ and format converted RZ from the rising-edge
detection. 124

Figure 7-14: (a) Edge detection of both rising and falling edges. (b) RF
spectrum showing the recovered 10-GHz clock and the 0.3-MHz
tone spacing. 124

xvi
Figure 7-15: Conceptual diagram of system-level applications of a tunable
bandwidth optical filter for dynamic bandwidth allocation: (i)
Efficient allocation for variable bit-rate systems; (ii) Optimization
of OSNR using matched optical filtering for a specific data-rate;
(iii) Reconfigurable channel banding for common routing, signal
processing of data channels. 125

Figure 7-16: Principle of the MEMS-actuated microdisk resonator filter. The
bandwidth of the filter can be tuned by controlling the gap spacing,
which results in changing the power coupling ratio. 127

Figure 7-17: Experimental setup of both single and WDM channel systems for
the demonstration of dynamic bandwidth allocation functions. 129

Figure 7-18: Matched optical filtering: One 5-Gb/s NRZ data signal is passed
through the MEMS-actuated microdisk resonator filter. The filter
bandwidth is tuned so that the system power penalty is minimized. 130

Figure 7-19: Reconfigurable channel banding: The filter is adjusted to either
route a single data channel (when the bandwidth is 6.5 GHz), or a
group of two data channels (when the bandwidth is opened up to
9.5 GHz). 131

Figure 7-20: Error-free wavelength de-multiplexing: Spectrum on the left shows
14.5 dB suppression ratio under the worst-case scenario. BER
measurement shows error-free operation. 132

Figure 8-1: Concept of the proposed real-time polarimeter-based optical
spectrum analyzer used for a swept-wavelength source. 138

Figure 8-2: P-OSA experimental setup for analyzing two types of swept
sources. Note that only one source is connected at a time. The
SOP of the input light is adjusted to 45 degrees with respect to the
birefringent axis of the DGD. 141

Figure 8-3: 1-KHz tuning F-P filter (a): SOP (S1) trace. (b): swept wavelength.
Note that the starting wavelength is obtained from a commercial
spectrum analyzer, although the P-OSA can also determine the
absolute starting wavelength directly, as described in the next
section. 142

xvii
Figure 8-4: 10-KHz tuning F-P filter (a): SOP (S1) trace. (b): swept
wavelength. Note that the starting wavelength is obtained with a
commercial spectrum analyzer, although the P-OSA can also
determine the absolute starting wavelength directly, as described in
the next section. 143

Figure 8-5: POD-101D oscilloscope mode. SOP evolutions are recorded when
the input is swept at a speed of 0.1 sec. 143

Figure 8-6: Instantaneous wavelength and power as the input light source is
swept at a speed of 0.1 sec. The starting wavelength is from the
setting of the commercial tunable laser. Note that the transient
dynamics of the swept laser source can be clearly revealed, as
shown in the inset. 144

Figure 8-7: Concept and principle of the proposed real-time polarimeter-based
optical spectrum analyzer used for spectral shape analysis. Curve
fitting of (A) determines the center frequency while Fourier
transform of (B) yields the spectral shape and width. The spectral
resolution is inversely proportional to the range of the variable
DGD. 146

Figure 8-8: Experimental setup for spectrum analysis of fixed wavelength
source. 148

Figure 8-9: (a) Experimental results of DOP values when the DGD is changed
from 0 to 1000 ps for both 40-Gb/s NRZ-OOK and RZ-OOK
signals. (b) The measured OSA spectra. (c) The derived P-OSA
spectra for comparison. 149

Figure 8-10: A 3-D plot using the proposed P-OSA. Swept wavelength is the
added dimension compared to the conventional OSAs. Note that
the absolute wavelengths are directly obtained with P-OSA via
curving fitting. 150

Figure 8-11: Illustration of a polarization division multiplexing (PDM) system. 152

Figure 8-12: Conceptual diagram of proposed Polarization DEMUX using
automated feedback control (solid-line: optical path; dotted-line:
electronic control). PBC: polarization combiner, PBS: polarization
splitter, BS: beamsplitter, DPC: dynamic polarization controller,
G1 & G2: electrical amplifiers, PD1 & PD2: photodetectors. 157

xviii
Figure 8-13: Concept proof using two static wavelength channels with different
power levels: here the power difference is ~0.5-dB (before Pol.
DEMUX), and an ER of ~ 28 dB is achieved with the proposed
polarization demultiplexing scheme (after Pol. DEMUX). >35-dB
ER is possible as the power difference increases. 159

Figure 8-14: Evaluation of proposed polarization demultiplexing scheme in a
single-channel 10-Gb/s RZ back-to-back transmission setup. (a)
Power penalties of both polarization channels (PDM_H and
PDM_V) as a function of power difference between them. (b) Bit-
error-rate (BER) curves as the power difference between two
orthogonal channels is set to 0.5 dB (i.e. the power of PDM_V is
0.5-dB higher than that of PDM_H); the corresponding power
penalties for the two orthogonal channels compared to the case
without PDM are ~ 0.25 dB and 0.75 dB, respectively. Square:
back-to-back without PDM. Circle: PDM-V. Triangle: PDM-H. 160

Figure 8-15: Experimental demonstration of 14-channel 1.12-Tb/s WDM-PDM
transmission: (a) experimental setup; (b) optical spectrum of all 14
channels. 163

Figure 8-16: Transmission results (a) Power penalties of both polarization
channels (PDM_V and PDM_H) for all 14 wavelength channels
compared to the back-to-back PDM system sensitivity measured at
10-9 BER. (b) Typical BER curves of one wavelength channel
with eye diagrams inserted: bk_bk (back-to-back case without
PDM transmitter); PDM bk_bk (back-to-back case with PDM
transmitter). 164

Figure 9-1: A comparison of implementing 2000 km transmission (a) Real
straight-line optical link. (b) Re-circulating loop test-bed. 166

Figure 9-2: Block diagram of a re-circulating loop transmission test-bed. 167

Figure 9-3: Optical Switches operating at the (a) load and (b) loop states. 168

Figure 9-4: Loop timing scheme of the control signals [x]. The error-gating
signal needs to be carefully designed in order to avoid the error
bursts on the seams of the revolutions, which is mainly caused by
the finite speed of the optical switches. 170

Figure 9-5: A typical experimental setup of a re-circulating loop test-bed
designed for 40-Gb/s WDM systems. 171
xix

Figure 9-6: Experimental configuration of a typical 40-Gb/s WDM transmitter,
with various modulation formats enabled. 174

Figure 9-7: Experimental configuration of a typical 40-Gb/s DPSK receiver,
with electronic clock recovery and de-multiplexer for bit error rate
measurement. 176

Figure 9-8: Acousto-optic modulator (AOM) system configuration and
principle. 180

Figure 9-9: Dynamic extinction ratio measurement of the AOM switch. 182

Figure 9-10: Non-uniform EDFA gain accumulation and spectrum narrowing. 185

Figure 9-11: Gain flattening methods: individual equalization and block
equalization with customized broadband filter. 187

Figure 9-12: The impact of LSPS on the statistical distribution of first-order
PMD. 192

Figure 9-13: Experimental setup of a 10-Gb/s re-circulating loop. 194

Figure 9-14: Simulation and experimental results of OSNR evolution up to
3,000 km. 195

Figure 9-15: Eye diagrams of RZ-OOK and NRZ-OOK up to 3,000 km loop
transmission. 196

Figure 9-16: BER measurement of 10-Gb/s RZ-OOK and NRZ-OOK
transmission. 197

Figure 9-17: Eye diagrams of 40-Gb/s RZ-OOK up to 800 km loop
transmission. 198

Figure 9-18: BER measurement of 40-Gb/s RZ-DPSK transmission. 199

xx
Abstract

The past decade has witnessed astounding boom in telecommunication network
traffic. With the emergence of multimedia over Internet, the high-capacity optical
transport systems have started to shift focus from the core network towards the end
users. This trend leads to diverse optical networks with transparency and
reconfigurability requirement. As single channel data rate continues to increase and
channel spacing continues to shrink for high capacity, high spectral efficiency, the
workload on conventional electronic signal processing elements in the router nodes
continues to build up. Performing signal processing functions in the optical domain
can potentially alleviate the speed bottleneck if the unique optical properties are
efficiently leveraged to assist electronic processing methodologies. Ultra-high
bandwidth capability along with the promise for multi-channel and format-
transparent operation make optical signal processing an attractive technology which
is expected to have great impact on future optical networks.

For optical signal processing applications in fiber-optic network and systems, a
laudable goal would be to explore the unique nonlinear optical processes in novel
photonic devices. This dissertation investigates novel optical signal processing
techniques through simulations and experimental demonstrations, analyzes
limitations of these nonlinear processing elements and proposes techniques to
enhance the system performance or designs for functional photonic modules.
xxi
Two key signal-processing building blocks for future optical networks, namely slow-
light-based tunable optical delay lines and SOA-based high-speed wavelength
converters, are presented in the first part of the dissertation. Phase preserving and
spectrally efficient slow light are experimentally demonstrated using advanced
modulation formats. Functional and novel photonic modules, such as multi-channel
synchronizer and variable-bit-rate optical time division multiplexer are designed and
demonstrated using slow-light tunable delay lines. Deleterious signal degrading
effects on SOA-based differential mode wavelength converters are experimentally
identified and techniques to alleviate or eliminate them are proposed.

The second part of the dissertation discusses enabling technologies for enhancing the
system performance or enriching the system functionalities. Two novel
optoelectronic devices, namely the optical injection-locked VCSEL and MEMS
actuated micro-disk resonator, are utilized for the demonstration of transmission
reach extension and dynamic bandwidth allocation, respectively. Additionally,
polarization-based novel optical instruments, such as a polarimeter-enabled optical
spectrum analyzer and an all-optical automatic polarization de-multiplexer, are
designed and demonstrated. Finally, a 40-Gb/s capable re-circulating fiber loop test-
bed is constructed and design guidelines as well as experimental results are discussed
in detail.
1
Chapter 1
Introduction
1.1 Present fiber-optic telecommunication networks
Fiber-optic technology has advanced tremendously over the last three decades and it
has formed the backbone of most long-haul communication links and networks
today. With the emergence of bandwidth-hungry applications over the Internet, the
advanced technology development is trying its best to keep pace with the ever-
increasing capacity demand. The evolving fiber optic advances and the established
wavelength division multiplexing (WDM) technology are waiting to fulfill the next-
generation telecommunication and network services [1].

The appearance of an optical network, which comprises optical transmission and
switching architectures, has taken about two decades from the original concept to the
initial deployment of limited optical switching. The huge growth in demand for
capacity from consumer users, due to the penetration of broadband services, together
with the increasing needs of scientific high-end users, has made the economic
deployment of advanced optical technology in a growing number of application
fields. The maturity and the availability of photonic and communication technologies
have made it possible for communities to construct their own networks independent
of operators, a situation that has greatly changed in the past decade [2].

2
New network architectures do not abruptly appear and real optical networks must
grow carefully. It is obvious during the past few years that the communication world
has changed to a data-centric rather than a voice-centric model. It is shown that
between 2000 and 2006 the volume of data generated has grown by a factor of more
than 50, and unpredicted huge data traffics were generated during the past two years
and will grow even higher for the years to come [2]. Therefore, initial network
changes are being implemented to move from the current SDH/SONET transmission
and switching technologies to one model that is more amenable to high volume data
traffic. In conjunction with these near term changes, there is a strong move toward
carrier-grade Ethernet, in particular 100-G Ethernet on a single channel wavelength,
and it is likely that this trend will come to dominate in the near future [3].

From a fiber-optic transmission perspective, current networks operate mainly at 10-
Gb/s, but 40-Gb/s technology is now available for deployment. As the overall
network load increases, studies show that the optimum line rate also increases, so
line rates of 100 Gb/s are being actively researched and implemented, assisted by
some key enabling technologies, such as advanced photonic modulation formats,
coherent detection, and digital signal processing [4, 5].

1.2 The role of optical signal processing
Ever since the deployment of the first terrestrial fiber link at Mb/s rate, “larger
bandwidth, and longer distance” remains to be the dominant banner for fiber optics
3
in telecommunication networks. Almost all the control and processing functions in
today’s networks are realized purely in the electronic domain. At a router node, the
received optical signal is converted to electronic bits, undergoes extensive processing
steps implemented through electronic chips and is then converted back to optical
domain before being retransmitted to the next node. This inefficient optical-
electronic-optical (OEO) conversion is considered as a significant source of latency.
The reason for this dominant role of electronics in current networks can be attributed
to the following. (i). The industry of electronics is significantly more mature than
that of optics. (ii). Electronic solutions are masters of computer-driven network
functionalities. (iii). Even very simple building blocks (e.g., logic gates, data
conversion) for optical processing can represent a significant research challenge.

Fig. 1-1. Future synergistic signal processing, utilizing advantages in both electronic
and optical domain.
Nevertheless, as can be predicted in the near future, electronic signal processing
techniques might not be able to keep pace with the backbone speeds of fiber optic
links due to the increased bandwidth demands. Beyond a certain single channel bit-
rate, it may become economically more viable to explore and employ inherently
high-bandwidth optical techniques rather than expensive electronic solutions.
4
Future optical networks will probably utilize optics and electronics in a
complementary fashion, harnessing their individual advantages to produce an
efficient control and processing platform [2]. As shown in Fig. 1-1, highly-
integrated electronics may still handle computation-intensive tasks while optics may
enable ultra-high speed “on-the-fly” processing, potentially manipulating all
dimensions offered by photons, such as time, wavelength, intensity, phase,
frequency, or even polarization. The outcome could well be a packet-switched core
network that enables interconnection of a diverse set of heterogeneous networks,
operating on multiple wavelength channels simultaneously, with different signal bit-
rates, different data modulation formats and different protocols.

At each router node within a packet-switched core network, data packets are required
to undergo various processing steps, as shown in Fig. 1-2. The path of the data
packets that are to be forwarded to the next node is highlighted in shaded blocks.

Fig. 1-2. Key signal processing functions at a router node.
5
In order to reduce latency and enhance throughput, these key blocks should not
involve O-E-O conversion, and thus will benefit greatly from all-optical
implementations. Input WDM wavelength channels need to be synchronized first so
that being processed under a universal clock is a possibility. Based on feedback
signals obtained from a set of data-degradation monitors, compensation modules
need to be controlled in order to regenerate the distorted signals. Some of the traffic
may be dropped and routed to the access networks and new packets added to the
network core. The remaining packets that need to be forwarded to another node
require update of several fields in their headers, and finally any contention occurring
at the output ports needs to be resolved through optical buffering, or all-optical
wavelength conversion of the packets [6].

There have been several demonstrations of all-optical subsystems that perform key
processing tasks on data packets [7-9]. Fulfilling the following criteria is essential
for the development of all-optical modules for functional processing.
• Ultra-high speed operation (scalable towards and beyond 100 Gb/s)
• Simultaneous operation on multiple wavelength data channels within a
single nonlinear optical element
• Preserving information (e.g. carrier phase) in optical domain, usually lost in
optical-to-electrical-to-optical (OEO) conversion

6
Two functions that represent a broad class of optical signal processing techniques are
tunable optical delay lines and wavelength conversion. The former requires
controlling light with light, while the latter involves modification of the carrier
frequency while maintaining the signal contents. The non-idealities in the nonlinear
processing techniques that are employed to realize these functions, almost always
lead to unwanted effects. For example, optical buffers delay the data-signal but
introduce deleterious patterning effects, while high-speed wavelength converters
usually degrade the signal due to limited frequency response. The successful
introduction of optical processing modules into the field requires research on novel
processing methodologies as well as the signal degradation caused by them.
Understanding the limitations of such techniques and devising methods to enhance
their performance is an essential part of optical signal processing research.

For the research of optical signal processing, a three-step approach can be
summarized as follows:
• Distinguish distinctive nonlinear properties of optical materials and devices
for optical signal processing and identify potential applications to assist or
replace electronic solutions.
• Design and implement novel optical signal processing modules for the
development of advanced signal generation, processing, and detection
subsystems.
7
• Investigate non-ideal and deleterious effects of the nonlinear processing
elements and the resulting system penalties and propose optical techniques
for prevention or compensation.

1.3 Advanced modulation formats
Over the past few years, there has been an increased interest in phase-based
modulation formats (e.g. DPSK: differential-phase-shift-keying) due to their
increased receiver sensitivity and robustness to chromatic dispersion and
nonlinearities [4]. Furthermore, multi-level formats (e.g. DQPSK, D-8PSK and
QAM) are also being explored for further enhancing spectral efficiency and
robustness to fiber impairments [10].

The development of optical signal processing module for future heterogeneous
optical networks should address the need for transparency to differential data
modulation formats. This format independent feature of future processing module
will accommodate a convergence of different traffic types. The reason is that future
optical networks will possibly be used for various types of applications, for which
each one might have different optimal requirements (i.e., data formats, signal bit-
rates, and variable quality-of-service (QoS)).

Research in the field of advanced modulation format-enabled optical signal
processing lies in the following main areas,
8
• Wavelength conversion of advanced modulation formats [11]
• Format conversion between conventional and advanced modulation formats
[12]

The key challenges researchers have to overcome is to preserve the information (e.g.
phase or polarization) after the signal-processing module. This imposes an added
complexity along with the unwanted effects the processing element introduces.
Identifying the degradation coming from both the signal processor and the advanced
modulation format, as well as designing techniques to alleviate these degrading
effects opens up another fascinating research field.

1.4 Outline of the dissertation
This dissertation is mainly organized as follows.

The upcoming chapter 2 and 3 introduce the fundamental nonlinear optical signal
processes using fiber based slow light and using semiconductor optical amplifiers
(SOAs), respectively. Applications of slow light technology and the key signal
degrading effect, namely the data pattern dependence, are also discussed briefly in
chapter 2.

Results from simulations as well as experiments of slow light on advanced
modulation formats (DPSK and DQPSK) are presented in chapters 4, with an
9
emphasize of slow-light induced DPSK data pattern dependence and the concept of
spectrally-efficient slow light technique.

Chapter 5 describes novel designs of signal processing modules (multi-channel
synchronizer and bit-rate variable OTDM multiplexer) using slow light technology.
This represents the importance of slow-light based tunable optical delay lines for the
application of advanced optical signal processing.

Chapter 6 investigates SOA-based differential-mode wavelength converters, with an
emphasis on the analysis of the induced non-idealities. Techniques to compensate
these deleterious effects are demonstrated experimentally.

Chapter 7 talks about using novel optoelectronic devices for the enhancement of
system performances. Optically-injection-locked VCSELs (OIL-VCSEL) is
presented as the first novel device. Transmission reach extension and dispersion pre-
compensation of single mode fiber by utilizing its unique adjustable chirp feature is
demonstrated. Multifunctional and reconfigurable operations are also demonstrated
using OIL-VCSEL. A novel bandwidth-tunable MEMS-actuated microdisk resonator
is used for demonstrating dynamic bandwidth allocation functions.

Chapter 8 discusses two projects that utilize polarization properties for the design of
novel optical instruments and components. A novel polarization-based optical
10
spectrum analyzer is proposed and demonstrated experimentally. An all-optical
technique for automatically de-multiplex polarization division multiplexed systems
is also shown in this chapter.

Chapter 9 discusses the detailed experimental design guidelines of a useful 40-Gb/s
capable re-circulating fiber loop test-bed, for the emulation of high-speed long-haul
fiber-optic transmission systems. Experimental results of both 10-Gb/s and 40-Gb/s
WDM transmission are presented using this powerful test-bed.

11
Chapter 2
Nonlinear signal processing using
slow-light based tunable optical delay lines
As a potential enabling technology, slow light has captured much research interests
over the past few years for achieving a continuously-tunable optical delay line [13].
In principle, slow light is generated by tailoring an enhanced group-index resonance
within a given medium. This effective refractive index change is experienced by the
data stream passing through and thus induces a controllable group delay onto the
signal. The main feature of a slow-light-based optical delay line is the capability for
fine-grain temporal manipulation of optical pulses. This fine tunable delay element is
envisioned to be useful for various high-bandwidth signal processing functions and
applications.

In general, optical signal processing is considered as an efficient and powerful
enabler for a host of communication functions as well as a system performance
enhancer [14-15]. The hope is that performing signal processing purely in the
optical domain might reduce any optical-electronic conversion inefficiencies and
take advantage of the ultra-high bandwidth inherent in optics [16-17]. One of the
most basic building blocks to achieve efficient and reconfigurable signal processing
is a continuously-tunable optical delay line, and yet this element has historically been
difficult to realize [18]. Applications of such a delay line could include: (a) accurate
12
synchronization for bit-level interleaving, (de)multiplexing, and switching [19], (b)
tapped delay lines for signal equalization, optical filtering, and dispersion
compensation [20, 21], and (c) data packet synchronization, switching, time-slot
interchanging, and buffering in dynamic network environments [22].

Tunable delay lines have typically been accomplished by varying a free-space or
optical waveguide propagation path, choosing from a combination of pre-designed
optical path lengths [19]. This technique produces only a finite set of discrete time
delays, and tends to be bulky and lossy with increased number of stages. Moreover,
the delay resolution is usually limited to sub-nanoseconds, which is determined by
the shortest optical path [23]. From a systems perspective, a partial “wish list” for a
tunable optical delay line should include: (1) continuous tunability, (2) wide
bandwidth, (3) amplitude-, frequency- and phase-preserving, (4) large tuning range,
and (5) fast reconfiguration speed. Such delays provide flexible time domain data
grooming in the optical domain.

Slow light is now viewed as a strong candidate for achieving such tunable optical
delay lines. However, in order to achieve the maximum possible delay on the data
signals with minimal system power penalty, one needs to combat and compensate for
any slow-light-induced signal degrading effects [24-27]. The data fidelity is
considered one of the main issues to be tackled before any practical signal processing
modules can be designed.
13

As an initial step in identifying potential target areas for slow light delay-based
applications, a good understanding of the properties unique to the optical domain is
required. Some of the desirable features are listed as follows. (1) High speed
capability: a judicious choice of the slow light medium with different bandwidth
limitations to support high speed data streams; (2) Preservation of optical properties:
the ability to maintain the phase information so as to support various data modulation
formats; (3) Multiple channel operation: the ability to delay multiple wavelength
channels independently in a single slow light device; (4) Input bit-rate variability:
accommodation of different input bit rates by dynamically adjusting the delay
elements; (5) Simultaneous multiple functions: simultaneously perform more than
one processing tasks in a single medium. These properties in conjunction with the
attractive tunable delay feature are the key to building a reconfigurable signal
processing platform to extract and process multi-dimensional information at ultra-
high speed.

This chapter is structured as follows. In section 2.1, we discuss the fundamentals of
slow light physics. Section 2.2 talks about the applications of using slow-light based
tunable delay lines, especially for optical signal processing. An overview of various
slow light techniques is presented in section 2.3. Slow-light-induced data
degradation is carefully discussed in section 2.4 and data-pattern dependence is
identified as one of the main reasons for signal distortion.
14
2.1 Fundamentals of slow light
The basic idea behind slow light [13] can be illustrated in the following Fig. 2-1.

Fig. 2-1. The concept of slow light.
It shows a pulse train passing through a material designed to produce a very small
value of the group velocity, which is defined roughly as the velocity at which the
peak of an optical pulse (information) propagates through a material. The basic
principle of slow light centers on the definition of group velocity, valid for most
signals we use for optical communications because the bandwidth of the signal
(1~100 GHz) is a very small portion compared to the carrier frequency (~193 THz).
The group velocity v
g
is defined as,
[2.1]
where c is the speed of light in vacuum and n
g
is the group index, which is related to
the usual refractive index n by,
[2.2]
The time it takes for a pulse to pass through the optical material is known as the
group delay, which is expressed as,
15
[2.3]
Consequently, the controllable delay T
del
is given by
[2.4]
Thus, to make the controllable delay as large as possible, one wants to make L as
large as possible and to maximize the value of the group index. In practice, the
effective length L of the optical material is usually limited not by its physical length
but by the requirement that absorption losses and dispersion-induced pulse
broadening be kept to acceptably low levels. The requirement for maximizing the
controllable delay therefore often relies on the engineering of introducing a sharp
variation of the refractive index that occurs in the vicinity of the material resonance.
We will introduce various techniques to achieve this sharp index variation and thus
the slow light phenomenon in section 2.3.

2.2 Applications of slow light based tunable delay lines
It is believed that the efficiency and throughput of future reconfigurable optical
networks can be significantly enhanced by the availability of a tunable, wideband
delay line [22]. Accurate, widely tunable optical delays are thus a critical
requirement for future optically switched networks to enable synchronization, header
recognition, buffering, optical time multiplexing, and equalization. Promising slow-
16
light based tunable delays are believed to have direct applications in the following
signal processing areas, as shown in Fig. 2-2.

Fig. 2-2. Applications of slow-light based tunable delay lines in the field of optical
signal processing.
(1) Optical synchronization and multiplexing [28-32]: Synchronizing multiple
misaligned input streams is one of the basic functions and thus a prerequisite for
almost any subsequent processing. Optical time division multiplexing (OTDM) is
one example that requires precise allocation of each lower rate signals into specific
time slots. This may also see significant use in synchronous optical packet-switched
networks where header recognition, buffering and time switching take place.
Advanced modules relying on bit or packet level synchronizers can also be
constructed, such as serial-to-parallel (TDM to WDM), parallel-to-serial (WDM to
TDM) converters and time slot interchangers.
(2) Optical equalization [20, 33-34]: Equalizers can be used to mitigate the
impairments of inter-symbol interference and fiber dispersive effects. Typically,
interferometric structures incorporating tapped optical delay lines are employed for
the design of optical equalizer. Slow-light-based tunable delay lines are potential
candidates in that the delays can be accurately and flexibly adjusted, enabling
17
bandwidth-tunable operation and thus supporting variable input bit rate signals.
Delay-line interferometer based DPSK demodulator can also be considered as one
type of filter-like equalizers.
(3) Optical correlation [35-36]: Optical correlation is viewed as an indispensable
function for pattern/header matching and thresholding. The fundamental “delay and
stack” function imposes the requirement of fast tuning speed as well as high tuning
resolution. Slow-light based delay features these merits and can thus be considered
as a potential candidate.
(4) Optical logic gates [37-38]: Performing logic operations purely in the optical
domain is desired for future optical networks which have the aggressive goal of
>100-Gbit/s processing with the potential of format and bit-rate transparency. Slow
light-based tunable delays are expected to find value in XOR-type parity checks,
differential phase encoders, and more complicated looping adder based checksum
processing.
(5) Enhanced nonlinear interaction [39-40]: By reducing the group velocity of light,
enhanced nonlinearities can be achieved in certain photonic devices by dramatically
increasing the induced phase shifts caused by small changes in the index of
refraction. Foreseeable key applications by utilizing this enhanced nonlinear phase
shift may include: wavelength conversion, wavelength multicasting, 2R/3R
regeneration and optical switching. Key parameters such as nonlinear coefficient,
bandwidth, effective interaction length, polarization sensitivity and tuning speed are
directly related to the slow light medium. Expected advantages include high
18
extinction ratio, negligible frequency chirp, data format transparency and scalability
to multiple channels.

However, for slow light to be useful in practical systems, critical parameters related
to tunable delay lines should be carefully examined. Each application imposes
certain metrics that must be met by the slow-light-based devices in order to justify a
specific use in real optical systems. Some typical delay metrics are listed as follows.
a) Delay bandwidth: the optical bandwidth over which a certain delay is achieved;
b) Maximum Delay: the maximum achievable delay value;
c) Delay Range: the tuning range that the delay can be achieved;
d) Delay Resolution: the minimum incremental delay-tuning step;
e) Delay Accuracy: the precision percentage of the actual delay to that of the desired
delay value;
f) Delay Reconfiguration Time: the amount of time it takes to switch a delay from
one state to another steady state;
g) Fractional (Normalized) Delay: the absolute delay value divided by the pulse
width (bit time). This is important to the delay/storage capacity;
h) Loss over Delay: The amount of loss incurred per unit delay for a given slow light
mechanism. Lower loss per unit delay is desired.

19
2.3 Techniques to achieve slow light phenomenon
As discussed in section 2.1, slow light technology is aimed at reducing and
controlling the group velocity of optical pulses. The key feature of the slow light
technique centers on the ability to introduce a relatively large change in the refractive
index seen by the light as it passes through a medium. This causes different wave
components within an optical pulse to travel with different speeds and therefore
affects the group velocity of the pulse envelope. By making the dispersion of the
material sufficiently strong, the group velocity can be reduced to significantly less
than the speed of light in vacuum. This opens up great opportunities to manipulate
the speed of information being transmitted. Typically, the resonance is achieved in
the amplitude response of the slow light media by either a sharp absorption or gain
peak or a transparent window in a lossy background that has an effect similar to a
gain spectrum [41]. In most of the cases, this understanding may provide a clue to
search for a slow light phenomenon in a potential medium.

To date, various physical mechanisms in a host of media have been reported in
literature to have observed slow light. These include electromagnetically induced
transparency (EIT) [42-43], coherent population oscillations (CPOs) [44-45],
stimulated scattering effects (stimulated Brillouin scattering (SBS) [46-50] and
stimulated Raman scattering (SRS) [51-53]), optical parametric amplification (OPA)
[54-56], coupled resonator optical waveguide (CROW) [57-59], photonic crystal
structures [60-62], and various other schemes [63-65].
20
Given the specific physics involved, the properties of various slow light media could
be quite different. For example, slow light bandwidth may vary from ~Hz to ~THz
depending on the slow light material and the nonlinear processes [44, 52]. One can
also categorize different schemes based on the amplitude and phase responses of the
slow light resonance. For instance, as shown in Fig. 2-3, in the SBS effect, both the
gain and delay spectra feature narrowband single peak profiles. The maximum delay
occurs at the gain peak wavelength where dispersion is zero in theory. In contrast, in
nonlinear parametric processes, if the pump is placed on the red side of the zero-
dispersion wavelength, the gain profile features double-sided peaks while the delay
tends to be linear over the frequency. This indicates that the delay might not
necessarily occur at the gain peak and the dispersion should be considered
throughout the gain bandwidth. More detailed comparative analyses for a variety of
slow light techniques can be found in [54-57].

Fig. 2-3. Gain and delay profiles of (a) SBS and (b) OPA based slow light, indicating
that various slow light schemes could be categorized by their characteristic
amplitude and phase responses.
21
We note that, as a typical slow light resonance, Lorentzian shaped gain profiles are
widely observed [41-42, 46-51, 53, 70]. The generality fundamentally originates
from the Kramers–Kronig relation which governs the imaginary and real parts of the
refractive index. As a good representative of Lorentzian resonances, the stimulated
Brillouin scattering based slow light has attracted fair amount of research attention in
recent years. Moreover, SBS-based slow light also features the following
advantages: (1) wide wavelength tunability, (2) low control power requirement, (3)
room-temperature operation, and (4) seamless integration with fiber-optic systems.
However, the major issue for the conventional SBS slow light is the limited tens of
MHz bandwidth. Therefore, the bit rates are commonly restricted to the order of tens
of Mbit/s due to this narrow intrinsic Brillouin gain spectral-width.

Recent breakthroughs of broadening the SBS gain bandwidth from tens of MHz [46-
47] to tens of GHz [48-50] have enabled the transmission of multi-Gbit/s data
streams. In general, broadband SBS is achieved by frequency modulating a coherent
pump laser so as to broaden the pump spectral-width and consequently the SBS
gain/delay bandwidth. Techniques involving pump broadening include: (1) direct
modulation of the pump laser using either pseudo-random bit sequence (PRBS)
modulation [48] or Gaussian noise modulation [49], (2) external phase modulation
[71], and (3) a simple and incoherent spectrally-sliced ASE pumping [72]. These
advances made it possible to transmit multi-Gbit/s data signals through the SBS slow
22
light medium [26, 71, 73-74] which makes the SBS mechanism promising for
practical systems.

Other promising wideband slow light techniques which have also been shown to be
capable of transmitting Gbit/s and beyond optical signals include: (i) stimulated
Raman scattering in fiber and on silicon chips [52-53], (ii) optical parametric
amplification process in fiber [27, 56], and (iii) nonlinear processes in semiconductor
optical amplifiers [75-76]. These techniques together with the SBS effect hold great
promise for future multi-Gbit/s and beyond optical switching and signal processing.

2.4 Slow-light induced data-pattern dependence and its mitigation
From a signal processing and telecommunication perspective, one would like to
transmit as high bit rate signals as possible by making full use of the slow light
bandwidth and, in the mean time, achieve as large delays as possible. This would
require a perfect yet unrealistic slow light medium that should feature a constant
amplitude response and a linear phase response. However, almost all types of slow
light media exhibit nonlinear dependencies of the group index over frequency. This
induces not only dispersive effects accompanying the achieved delay, but some
‘filtering’ effects from the amplitude response as well. The signal delay and signal
quality tradeoff originates from the delay-bandwidth product and has long been
considered as the fundamental limitation in slow light systems. This fundamental
23
tradeoff has been extensively studied in systems described by Lorentzian shaped [25,
66, 73, 77] and non-Lorentzian shaped resonances [27, 66-67, 69].

We emphasize that most of the studies have only considered a single or a few pulses
propagating through the slow light media. However, telecommunication systems
transmit true data streams with a variety of information-bearing patterns. Different
kinds of slow light media might lead to various patterning effects [24-27] and require
careful analysis based on the specific amplitude and phase responses. Furthermore,
designing and optimizing the slow-light element to reduce pattern dependent
distortion while simultaneously maximizing the induced delay becomes an important
aspect of slow-light research.

2.4.1 Data-pattern dependent distortion
We start off by modeling the slow-light element with a typical Lorentzian-shaped
imaginary part of the refractive index, while the real part is determined by the
Kramers-Kronig relation. The slow-light bandwidth can be flexibly tuned from 5
GHz to 50 GHz so as to accommodate 10-Gb/s non-return-to-zero (NRZ) on-off-
keying (OOK) signals [25]. We note that the dispersion is zero when both the delay
and the gain reach their maximum value, and the signal carrier is centered at the gain
peak wavelength to experience the highest delay.
24

Fig. 2-4. Origin of data-pattern dependent distortion. Pattern dependent gain and
delay are shown as the two main degrading effects.
To highlight the impact of slow-light-induced pattern dependent distortions, we
characterize the output data patterns by looking into both the amplitude and the
phase response, which are reflected on the data signals as pattern dependent gain and
pattern dependent delay.

With the assistance of Fig. 2-4, we can see that the peak power of the optical pulse
after slow light clearly depends on the data patterns. For example, consecutive “1”
bits (‘0110’ pattern) have a much higher “1” level power than that of a single “1” bit
(010 pattern). This gives rise to “1”-level splitting in the eye diagram and thus
severely distorts the signal. This type of distortion is caused by pattern dependent
gain and can be explained as follows. When the signal carrier is located exactly at
the gain peak and the bit rate is comparable with the bandwidth of the slow light
element, we note that the lower and higher frequency components in the signal
spectrum, compared to the carrier, are in the low-gain region. The frequency
components of consecutive “1”s are closer to the carrier and thus see more gain than
25
a single “1”, whose frequency components spread out over the low-gain region. As a
result, the consecutive “1”s obtain higher peak power and causes the “1”-level
splitting at the output.

Lorentzian shaped resonances not only feature a narrowband amplitude response,
which causes the aforementioned pattern dependent gain, but also a narrowband
delay response as well (Fig. 2-3). As a result, the frequency components of the
consecutive “1”s are closer to the delay peak and thus experience larger delay
compared to the single “1”. This pattern dependent delay effect is illustrated also in
Fig. 2-4.

Fig. 2-5. Quantification of slow-light-induced pattern dependent gain and delay. (a)
Level ratio versus slow light bandwidth for two typical combinations of data
patterns. (b) Delay versus slow light bandwidth for two typical patterns.
We quantify both of these patterning effects in Fig. 2-5. Level ratio (defined as B/A,
see Fig. 2-4) is used as the key parameter to access the pattern dependent gain. We
consider here the level ratios among three typical patterns by using two
26
combinations, “010” over “01110”, and “0110” over “01110”. As shown in Fig. 2-5
(a), the level ratios of both these two combinations go down quickly as the slow-light
bandwidth decreases. For a typical situation where the slow light bandwidth is the
same as the signal bit rate, more than a 30% level ratio difference can exist in the
case of “010” over “01110”, indicating the “010” pattern is the limiting factor to the
data fidelity.

Fig. 2-5 (b) shows the pulse delay versus the slow-light bandwidth for different data
patterns. The calculated peak delay (the maximum delay in the frequency-dependent
delay profile, Fig. 2-3) serves as an upper bound for different types of data patterns.
Two typical patterns “010” and “0110” are shown and the delay difference grows
with the reduced slow-light bandwidth. In some extreme cases, the pattern-
dependent delay might cause pulse collision between specific patterns (e.g., for a
data stream of “011010”, the “0110” pattern might catch up with the “010” pattern)
and thus could induce a high bit-error-rate.

After the identification and quantification of the two degrading effects from the
amplitude and phase responses, it is of importance to determine which of the two
responses plays a dominating role for the data degradation. In our slow-light model,
we isolate either amplitude or phase response by artificially eliminating one response
at a time. Fig. 2-6 shows signal Q-factor as a function of slow-light bandwidth for
the cases of amplitude-only response, phase-only response, and the combined
27
response. The amplitude-only response curve is almost identical to the combined
effects curve, while the phase-only response curve shows an overall better
performance. This indicates that the narrowband amplitude response and thus the
pattern dependent gain is the dominating effect for data degradation. We emphasize
that the second-order dispersion at the gain peak is zero for Lorentzian shaped
resonances, which means that the pulse broadening induced by dispersive effects is
relatively small.

Fig. 2-6. Isolating the effect of amplitude response and phase response on the signal
quality (Q factor). Amplitude response is shown as the dominating effect for data
distortion.
As a comparison, non-Lorentzian shaped slow light might exhibit different types of
pattern dependent distortion. For OPA based slow light schemes, the amplitude
response does not significantly contribute to the patterning effect. Rather, the phase
response induced dispersive effect plays a dominant role. Furthermore, various phase
28
patterns associated with different formats are also signal degrading factors. As a
result, the data pattern dependent distortion reveals itself as not only pulse
broadening and merging, but ‘1’ level fluctuation and ‘0’-level rising as well [27].

2.4.2 Figures of merit
There has been much interest in developing a set of universal figures of merit
(FOMs) to compare the tradeoff among various slow light schemes. Therefore, one
may have to carefully consider slow-light-induced data degradation in order to keep
a balance between pulse delay and signal quality. The question that becomes critical
to answer is what operating conditions of a slow light element are optimal.

Here, we define two FOMs in order to find an optimized slow-light bandwidth. To
make it more general, the slow-light bandwidth is normalized by signal bit rate, and
the pulse delay is normalized by the bit time, which is named the normalized delay.
The pulse delay is measured for a single “1” pulse. Compared to the fractional delay
(defined as pulse delay divided by pulse width) that is used often in literature, the
normalized delay defined here is a more practical consideration, from the point of
view of communication systems.

The first FOM (FOM I) is defined as the product of the normalized delay and the
signal Q-factor. In Fig. 2-7 (a), we show FOM I as a function of the normalized
slow-light bandwidth. An optimized value is found for NRZ signal when FOM I is
29
maximized, i.e., the normalized slow-light bandwidth is equal to 1.4. For narrow
spectra slow-light devices, FOM I drops down rapidly due to the decreased signal Q-
factor. FOM I is also small in the wider bandwidth region due to the reduced delay.
The level ratio (B/A, as shown in Fig. 2-5) can also be used to measure the distortion
of the data signal after a slow-light element. We define FOM II as the product of the
normalized delay and the (level-ratio)
2
, which has similar trends, as shown in Fig. 2-
7 (b), and predicts a very similar optimized slow-light bandwidth as that given by
FOM I. This confirms that the vertical eye closure caused by “1” level splitting in the
output data streams is the dominant factor for signal degradation. Using FOM II, the
system impact of the narrow-band slow-light elements can be estimated by
calculating a much simpler parameter (level ratio), so that device researchers do not
need to simulate the whole system and measure the complicated signal Q-factor to
optimize the slow light design.

Fig. 2-7. (a) FOM I versus normalized slow-light bandwidth. (b) FOM II versus
normalized slow-light bandwidth. Both FOMs show that the optimized slow-light
bandwidth equals 1.4 times the signal bandwidth.

30
We note that the definition of FOMs should be adjusted based on the specific slow
light scheme involved [68]. This indicates that FOMs are dependent on the specific
amplitude and phase responses of the slow light mechanism. For example, delay over
eye opening penalty (DOE) might be more appropriate to be used in evaluating and
optimizing OPA based slow light schemes [27].

2.4.3 Distortion Mitigation
We introduce in this subsection various methods of mitigating the signal distortion
by either optimizing the system operating conditions or designing novel slow light
systems.

Fig. 2-8. Concept of data-pattern dependence reduction by detuning the channel
away from the slow light resonance peak.
We first show here one way for reducing the data-pattern dependence for NRZ-OOK
signals in Lorentzian slow light elements [25, 77]. We understand that when the
signal spectrum is centered at the resonance peak, the data suffers the most
distortion, as the pattern dependent gain seen by “010” and “0110” has the largest
difference. However, if the data channel is managed to be detuned from the
31
resonance peak by a certain value, frequency components of both single “1” and
consecutive “1”s might experience a much similar gain, as illustratively depicted in
Fig. 2-8. This configuration potentially results in the equalization of the peak power
at the output of the slow light element and thus the reduction of pattern dependent
distortion. We note that detuning the slow light resonance with respect to the channel
will have the similar effect in terms of distortion reduction.

Figure 2-9 quantifies the improvement of the 10-Gb/s NRZ-OOK signal quality by
detuning the channel away from a 14-GHz bandwidth fixed slow-light element. An
approximate 2-dB signal Q-factor enhancement, compared to the no detuning case, is
achieved for both positive and negative detuning. The optimal detuning value is
found to be around 40% of the signal bandwidth and the improvement also features
symmetry, as expected.

Fig. 2-9. Simulation results of data-pattern dependence reduction by detuning the
channel away from the gain peak. 2-dB Q-factor improvement is achieved by either
red or blue detuning 40% of the signal bandwidth.
32
Approaches for combating and mitigating signal distortions have also been proposed
by judiciously tailoring the shape of the gain or absorption resonances. Interesting
techniques involving the design of two or multiple gain resonances [78-81] have
been shown to effectively extend the delay while still maintaining good signal
quality. For example, Stenner et al. [78] have demonstrated that distortion
management using a gain doublet can provide approximately a factor of 2 increase in
slow light pulse delay and a factor of 5 improvement in the delay at the optimum
bandwidth, as compared with the optimum single-line case.

Realizing that the delay-bandwidth tradeoff is inherent to linear, resonant systems,
some of the research efforts have been made to move beyond linear systems to
nonlinear systems. A recent demonstration [65] exploited the nonlinear behavior of
Bragg gratings in fibers, where the pulse can travel slowly but still remain
undistorted over long propagation lengths, by the formation of a gap soliton. Using
this method, Mok et al. have obtained a slow-light delay that is two and a half pulse
widths by adjusting the intensity of the input pulse.

We will show in chapter 4 and 5 various advanced signal processing techniques of
using SBS based slow-light delay lines. Data pattern dependent distortions are
carefully analyzed in the various signal processing elements or modules.

33
Chapter 3
Nonlinear signal processing using
semiconductor optical amplifiers (SOAs)
One crucial photonic device for enabling advanced optical signal processing
techniques is the semiconductor optical amplifier (SOA), which has emerged as one
of the popular candidates for use as nonlinear elements during the last two decades
[82]. They feature high nonlinearity with a small footprint, as well as fairly low
optical power requirement. Another important aspect is that SOAs can also be
integrated with various waveguide structures and therefore lend themselves to stable
interferometric processing techniques. Various nonlinearities in SOAs including
cross-gain modulation (XGM), cross-phase modulation (XPM), cross-polarization
modulation (XPolM) and four-wave mixing (FWM) have been exploited for
implementing all-optical processing modules [82-88]. Here, the three popular and
widely adopted nonlinear processes (XGM, XPM and XPolM) in SOAs are carefully
discussed.

3.1 Cross Gain Modulation (XGM)
The SOA gain relies on the total number of carriers available to produce stimulated
photons. Therefore, any variation in the carrier density of the semiconductor
medium directly alters the SOA gain seen by an optical wave propagating through
[89]. If a high power modulated signal (called “pump”) and a low power CW beam
34
(called “probe”) are coupled into an SOA, the modulation of the pump can be
translated to the probe, as shown in Fig. 3-1.

Fig. 3-1. Cross gain modulation. High power pump pulses deplete the carriers in the
SOA leading to a suppression of the gain. A CW probe beam passing through the
SOA experiences this varying gain and as a result an inverted copy of the data gets
imprinted on the probe wavelength.
Carriers in the SOA are depleted by a high pump power pulse, leading to a
suppression of the gain seen by the probe light. The output power in the probe beam
is thus reduced. When the pulse passes the SOA and the pump signal goes low, the
carriers in the SOA recover and the gain consequently returns to a high value,
thereby increasing the output probe power. Thus an inverted data copy of the pump
signal gets imprinted onto the probe wavelength. This process of translation of
modulation of one optical signal onto another, via gain modulation of the SOA, is
called cross gain modulation (XGM) [90]. XGM has been utilized for various
applications including wavelength conversion [91], optical logic gates [92], and
clock recovery [93]. XGM has been studied extensively and various SOA numerical
models [94-96] have been developed to enable simulation of this phenomenon.

35
The XGM process is limited to low tens of GHz bandwidth due to the slow carrier
recovery time [97]. This speed limitation represents itself as pattern dependence in
the output signal. Fig. 3-2 shows an experimental trace of RZ signals being
wavelength converted via XGM.

Fig. 3-2. XGM-based inverted wavelength conversion of RZ data. The gain exhibits
slow recovery, which can lead to pattern dependence in the converted bits. The high
level of the converted signal’s eye diagram is extremely noisy due to pattern
dependence.
As is visible from the inverted output, a pump pulse that enters the SOA after a long
string of 0s sees its unsaturated gain and induces greater XGM than a pulse that
follows another pulse, if the gain doesn’t recover to its unsaturated value between the
two pulses. As a result the high level of the output shows large variations. Such a
signal suffers from eye-closure due to unequal pulse amplitudes that leads to power
penalty.

The recovery time can be reduced by operating the SOA in deep saturation (driving
it with a higher bias current and injecting a higher CW probe power). Sometimes a
third CW input, called a reservoir channel or assist light is also injected to reduce the
36
recovery time [98]. Gain saturation is also accompanied by a shift of the SOA gain
spectrum towards higher wavelengths. As a result wavelength up-conversion is not
as efficient as down-conversion. The gain modulation also induces frequency
chirping on the output wavelength converted signal since the carrier density also
determines the refractive index of the semiconductor medium. For the conventional
inverting operation, a red shift is observed at the falling edge of the output, while a
blue chirp is present on the rising edge. This temporal relation between power and
frequency-shift is referred to as positive chirp and leads to quicker pulse broadening
due to chromatic dispersion (CD) when the converted signal is transmitted over
single mode fiber (positive dispersion). On the other hand, the chirping that leads to
broadening of the spectrum can itself be utilized for wavelength conversion by
selectively filtering the red-shifted part of the spectrum [99]. Since the red shift is
induced by fast carrier depletion and not the slow carrier recovery, it enables high
speed wavelength conversion. Under special conditions XGM based wavelength
conversion has been demonstrated up to 320 Gb/s [100].

3.2 Cross Phase Modulation (XPM)
As explained in the above paragraph, the modulation of the carrier density in an SOA
also accompanies a variation of the refractive index (RI) of the material. This RI
modulation imposes a phase variation onto the optical probe waves propagating
through the SOA. This process, which is technically referred to as cross-phase
modulation (XPM), can be converted into amplitude modulation using
37
interferometric configurations [101]. The simplest configuration utilizes XPM
induced in one arm of a Mach Zehnder Interferometer (MZI) with SOAs as shown in
Fig. 3-3. The light from a CW laser (probe) is split equally into the two SOAs of the
MZI while the high power input signal (pump) is coupled into only one of the SOAs
(referred to as the common SOA). By adjusting the phase shifter in the lower arm to
introduce a phase shift of π radians, the CW probe light can be made to interfere
destructively in the absence of a pump pulse.

Fig. 3-3. Cross phase modulation. The phase-shifter is adjusted to provide a π phase
shift to the CW probe passing through the lower arm of the MZI. As a result, in the
balanced situation the CW probe interfere destructively in the absence of any pump
signal. When a pump pulse enters the upper SOA, it alters the phase of the probe
leading to a constructive interference at the MZI output. Thus converted pulses
appear at the output for each incoming pump pulse. By adjusting the phase-shifter to
introduce no additional phase shift, inverted conversion can also be achieved.
However, whenever a pump pulse enters the common SOA, it causes depletion of the
carrier density in the common SOA, which leads to a modulation of the RI. The RI
variation leads to a modulation of the phase of the CW probe propagating through
the common SOA. Thus the destructive interference condition is no longer satisfied
at the MZI output and a pulse appears on the probe wavelength, which can be
separated via optical filtering. The rise time of the output pulse is determined by the
38
rise time of the input pulse but slow carrier recovery still leads to slow fall times.
The MZI SOAs can be driven in a differential push-pull configuration to eliminate
the effects of the slow carrier recovery [102]. These switches, called differential
mode switches, are discussed further in chapter 6.

Inverted wavelength conversion is also possible in the SOA-MZI configuration if the
phase-shifter is set to introduce no additional phase shift. In such a situation, the CW
probe components interfere constructively in the absence of a pump pulse and a
phase variation causes a drop in the probe power at the MZI output. XPM-based
wavelength converters have been demonstrated at very high bit-rates (up to 160
Gb/s). Since the process relies on interferometric properties, it is possible to obtain
high output extinction ratios by minimizing the power in the output 0s through
destructive interference. Equally efficient up and down conversion can be realized
since the RI variation affects all wavelengths equally, as long as the probe power
doesn’t contribute to the SOA’s saturation. The XPM wavelength converter,
however, has limited input signal dynamic range due to its sensitivity to its operating
conditions.

3.3 Cross-polarization modulation
SOAs typically exhibit asymmetry in their structure that leads to different
confinement factors, effective guide refractive indices and carrier distributions along
the TE and TM orientations. Thus, there exists a small amount of birefringence in
39
the SOA. Additional birefringence can be introduced in the SOA by injecting a high
power pump pulse. Thus the components of the probe along the TE and TM
orientations experience different phase shifts. This difference in the phases of the
TE and TM mode leads to a polarization rotation of the probe light passing through
the SOA [103]. This process is called cross-polarization modulation (XpolM). A
polarizer placed after the filter at the output can be used to convert this polarization
rotation into amplitude modulation. Inverted as well as non-inverted wavelength
conversion can be achieved. Since the inverted mode works in conjunction with
XGM it leads to higher extinction ratio, unlike the non-inverted mode that operates
against XGM.

XpolM has become popular recently because it enables processing based on
refractive index changes without the need for an interferometric configuration.
Differential XpolM has also been demonstrated [104] as a method to enhance the
operational bandwidth of the technique. Moreover, since refractive index changes
occur even for wavelengths which lie in the transparency window of the SOA,
wavelength conversion between the 1550 and 1310 nm bands can be achieved [105].

40
Chapter 4
Phase-preserving slow light
using advanced phase-modulated formats
4.1 Motivation
We emphasize that almost all previously published slow light system results were for
intensity-modulated signals. However, phase-encoded formats, such as differential-
phase-shift-keying (DPSK) signals, have not been explored in a slow light element
before. DPSK is becoming ever more important in the optical communications
community due to its potential for increased receiver sensitivity, tolerance to various
fiber impairments, and better spectral efficiency [4]. It is highly desirable to
understand how the phase information of the DPSK signal could be preserved and
how much fractional delay it could experience. Furthermore, it is important to
explore how slow light nonlinearities could affect differently the demodulated two
ports of a delay interferometer-based DPSK receiver. A laudable goal would thus be
to examine critical system limitations on Gbit/s DPSK data as it traverses a tunable
slow light element.

In this chapter, we show, experimentally and via simulation, slowing down of a
phase-modulated optical signal. A 10.7-Gb/s DPSK signal can be delayed by as
much as 42 ps (45% fractional delay) while still achieving error free via broadband
SBS-based slow-light element. We further analyze slow-light-induced DPSK data-
41
pattern dependence on demodulated output ports. By detuning the SBS gain profile,
signal quality improvement is achieved via reducing the DPSK data-pattern
dependence. System level comparisons of NRZ-DPSK with RZ-DPSK under the
same slow light bandwidth show different robustness to slow-light-induced data-
pattern dependence. Slow light on spectrally efficient differential-quadrature-phase-
shift-keying (DQPSK) signals is also experimentally demonstrated, showing the
ability of transmitting very-high bit-rate signals through a bandwidth-limited slow
light element.

4.2 Slow light on differential-phase-shift-keying (DPSK) signals

Fig. 4-1. A) Concept of slow light on phase-modulated optical signals. B) Slow-
light-induced data-pattern dependence on demodulated two output ports.
The concept of slowing down phase-modulated optical signals is shown in Fig. 4-1.
When a DPSK signal passes through the slow light element, one expects that its
42
phase patterns get delayed according to the slow light gain and bandwidth.
Meanwhile, phase preservation should also be expected for information integrity.
However, commonly generated DPSK signals feature unavoidable residual intensity
modulation, which also experiences slow-light nonlinearities. Demodulation of such
delayed DPSK signal encounters the problem of data-pattern dependence on both the
constructive “DB” (Duo-binary) and the destructive “AMI” (Alternate-Mark-
Inversion) ports after the one-bit delay interferometer (DI), as shown in Fig. 4-1. It is
thus crucial to analyze critical system limitations on Gbit/s DPSK signals transmitted
through a narrowband tunable slow-light element.

Fig. 4-2. Simulation result of phase patterns of a 10-Gb/s DPSK signal before and
after 8GHz BW slow light element. Phase is preserved and delayed by 46 ps.
Figure 4-2 shows the simulation result of slow light on the phase patterns of a 10-
Gb/s DPSK signal. The slow-light element is analytically modeled to have a
Lorentzian-shaped imaginary part of the refractive index, with controllable
43
bandwidth and gain. Kramers–Kronig relationship determines the real part of the
refractive index, whose derivative gives the slow- light delay profile. A 10-Gb/s
NRZ-DPSK signal is simulated using a Mach-Zehnder modulator with proper bias
and driving voltage. The phase patterns of the DPSK signal are shown both before
and after an 8-GHz slow-light element. We show that phase patterns can be delayed
by up to 46-ps and the differential ‘π’ phase relationship preserves quite well. This
confirms the concept of slow light delays on phase information.

Fig. 4-3. Experimental Setup for DPSK slow-light based on broadband SBS.
We further carry out DPSK slow-light experiment and the setup is shown in Fig. 4-3.
The slow-light mechanism is based on broadband SBS [49] in a piece of highly
nonlinear fiber (HNLF). Broadband SBS pump is used to accommodate Gbit/s
optical signals. We use a Gaussian noise source driven by 400-MHz clock to
modulate the injection current of a commercial directly modulated laser (DML). The
44
pump spectral-width is adjusted by an RF attenuator. The broadband pump is then
amplified by a high-power EDFA and enters a 2-km HNLF, with the measured
Brillouin shift to be 10.3-GHz. An NRZ-DPSK probe data stream is generated by
externally modulating the tunable laser source (TLS) using a Mach-Zehnder
modulator (MZM), which is biased at its transmission null and driven by
approximately 2V
π
. A sinusoidally-driven second pulse carver modulator is used to
generate 50% RZ-DPSK signals. The amplified and attenuated DPSK signal with
controllable power counter-propagates with the pump in the HNLF. One polarization
controller is used on the signal path to maximize the SBS interaction. The amplified
and delayed DPSK signal is finally demodulated using a one-bit DI and both DB and
AMI ports are detected. An optical attenuator is adjusted accordingly to the SBS gain
so as to keep the input power into the EDFA fixed. BER measurements are taken on
both the DB and AMI demodulated signals.

Fig. 4-4. Observation of DPSK slow-light: continuous delay of up to 42 ps for a
10.7Gb/s DPSK signal.
45
Figure 4-4 shows the measured delay of a 10.7-Gb/s NRZ-DPSK signal with 0 dBm
power under an 8 GHz SBS gain bandwidth. The measured delay scales fairly
linearly with the increased pump power, demonstrating the ability to continuously
control the delay of the DPSK phase pattern. The detected balanced DPSK eyes are
shown for three different pump powers, with a maximum of 42 ps delay at a pump
power of 800 mW. The achieved 42 ps delay of a 10.7-Gb/s NRZ-DPSK signal
corresponds to a fractional delay of 45%.

4.3 DPSK data-pattern dependence and its reduction
As shown in Fig. 4-4, delayed DPSK eyes exhibit severe signal distortion with the
increased slow light delay. In order to assess the signal quality, we analyze both the
constructive and destructive ports of the DI after demodulation individually. Figure
4-5 shows the 10.7-Gb/s NRZ-DPSK intensity patterns before and after passing
through the slow light element, with positions recorded right before demodulation
(NRZ-DPSK) and right after demodulation (DB and AMI), respectively.

The typical and well recognized method for generating an NRZ-DPSK signal, using
an MZM, has several advantages: (i) exact ‘π’ phase modulation, (ii) insignificant
frequency chirping, and (iii) increased tolerance to driving voltage imperfections [4].
However, residual intensity modulation occurs unavoidably during phase transitions.
We can categorize these “intensity dips” as isolated “1”s (between two consecutive
dips) and consecutive “1”s (between two long separated dips). Isolated “1”s occupy
46
higher frequency components compared to consecutive “1”s, and will therefore
experience much less gain after passing through a narrowband slow-light resonance.
This effect can be clearly seen for the distorted NRZ-DPSK intensity patterns after
slow light.

Fig. 4-5. Slow-Light-induced data-pattern dependence: 10.7-Gb/s NRZ-DPSK
through an 8-GHz slow light element. Bit patterns before (NRZ-DPSK) and after
(DB and AMI) demodulation are shown before and after slow light.
The pattern-dependent gain NRZ-DPSK signal experiences will translate into two
different types of data-pattern dependence on demodulated two signals. In the DB
port, the peak power is much higher for long “1”s, compared with single “1”s. This
can be explained from the fact that single “1”s are only demodulated from two
consecutive “1”s in NRZ-DPSK which has a much slower rising time due to slow-
light third-order dispersion [106]. This leads to an insufficient constructive
interference for the generation of single “1”s. The AMI port exhibits strong pattern
dependence within a group of “1” pulses. Compared with the “1”s in the middle, the
leading and the trailing “1”s always have much higher peak powers in that they both
47
experience unequal-power constructive interference from the edge pulses in a group
of “isolated dips” in delayed NRZ-DPSK pattern. Both DB and AMI eye diagrams
exhibit vertical data-pattern dependence. Furthermore, the AMI port also features
non-negligible pulse walk-off, which can be attributed to the slower rising and
falling times of the two edge pulses compared with fast-transitioned middle pulses,
in a group of “1” pulses.

Fig. 4-6. BER measurement of DB port from 10.7-Gb/s DPSK signals after SBS
slow light element. Data-pattern dependence and Rayleigh crosstalk (shown in the
spectrum) are the two main reasons for DPSK signal degradation.
BER measurements on the DB port of a demodulated 10.7-Gb/s NRZ-DPSK signal
under different delay conditions are shown in Fig. 4-6. We emphasize that we could
still achieve error free at a delay of up to 42 ps with a power penalty of 9.5 dB. The
clear tradeoff between signal fidelity and delay can be explained by the following
two main reasons. Data-pattern dependence due to limited slow-light bandwidth is
one major factor for signal degradation, as confirmed by the vertically closed eyes.
Not only the gain but also the phase (delay) spectrum of the broadband SBS [73] will
48
affect the delayed PRBS data quality. Spectra in Fig. 4-6 show that crosstalk from
Rayleigh pump backscattering is another contributor to the power penalty, especially
when the bit-rate is comparable to the Brillouin shift. The performance of the
demodulated AMI port from 10.7-Gb/s DPSK signals is worse than that of the DB
port because of severe pulse-walkoff and increased Rayleigh spectral overlapping
due to much wider AMI bandwidth. Figure 4-7 shows the performance comparison
of 10.7-Gb/s and 2.5-Gb/s NRZ-DPSK data with a fixed SBS gain bandwidth of 7-
GHz. System performance of 2.5-Gb/s NRZ-DPSK exhibits 6.5 dB better
performance at 800 mW pump power, the main reason being lower bit-rate signals
see much less data-pattern dependence and much smaller Rayleigh crosstalk, as can
be confirmed by the two DB eyes.

Fig. 4-7. Power penalty comparison between 2.5-Gb/s and 10-Gb/s NRZ-DPSK
shows that data-pattern dependence is bit-rate specific.
49
Realizing that the slow-light-induced data-pattern dependence mainly comes from
the pattern-dependent gain, we red-detune the peak of the SBS gain profile by
0.016nm from the channel center, resulting in gain equalization and thus pattern-
dependence reduction between isolated “1”s and consecutive “1”s within NRZ-
DPSK “intensity dips”, shown in Fig. 4-8. Bit-patterns and eye diagrams with and
without detuning for both demodulated DB and AMI ports are also recorded for
comparison. The optimum 3-dB Q factor (determined from BER measurement)
improvement (from 12 to 15dB) for the AMI eyes confirms the effectiveness of this
detuning method. The detuning not only resolves vertical data-pattern dependence,
but also reshapes the rising and falling times of the edge pulses in a group of “1”
pulses, such that pulse walk-off is also alleviated, as can be seen from the AMI eye
diagram after detuning.

Fig. 4-8. Reduction of DPSK data-pattern dependence by detuning the SBS gain
peak: 3-dB Q factor improvement on the AMI port demodulated from 10.7-Gb/s
DPSK signals is achieved.
50
Motivated by the fact that RZ-DPSK is also another popular modulation format
thanks to the increased tolerance to fiber nonlinearities, we conduct performance
comparison of NRZ-DPSK with RZ-DPSK at a bit rate of 2.5-Gb/s. The reason we
are not comparing them at 10-Gb/s is that RZ-DPSK bandwidth exceeds the 10-GHz
Brillouin shift. Figure 4-9 shows delay and power penalty comparison as a function
of increased pump power. Under a fixed 5-GHz SBS gain bandwidth, the fractional
delay (absolute delay divided by pulse-width) of RZ-DPSK is comparable with that
of NRZ-DPSK. In terms of signal quality, RZ-DPSK outperforms NRZ-DPSK by as
much as 2dB at 700 mW pump power. The inset AMI eye diagrams show that RZ-
DPSK is much more tolerant than NRZ-DPSK in terms of slow-light-induced data-
pattern dependence. The main reason can be understood from the fact that pulse
carver modulator used in RZ-DPSK extracts only the amplitude-modulation-free
center portions of the bits, thus largely eliminating any residual dips, which is the
main cause of data-pattern dependence in NRZ-DPSK.

Fig. 4-9. Left: Delay for 2.5-Gb/s NRZ and RZ-DPSK with the same 5-GHz SBS
BW. The fractional delays for both NRZ and RZ-DPSK are comparable. Right: RZ-
DPSK outperforms NRZ-DPSK by as much as 2 dB, which shows its robustness to
data-pattern dependence.

51
4.4 Spectrally-efficient slow light using DQPSK format
It is crucial to emphasize that advanced modulation formats have become an
extremely exciting research area. A primary example is differential-phase-shift-
keying (DPSK) due to its tolerance to nonlinearities and higher receiver sensitivity
[4]. However, there is a strong trend towards higher-order (i.e., multi-level)
modulation formats since they are more spectrally efficient, and thus more robust to
dispersion effects. A highly popular format is differential-quadrature-phase-shift-
keying (DQPSK), especially RZ-DQPSK [107]. The challenges of passing a
DQPSK signal through slow light center around the ability to effectively delay both
quadratures and recover them successfully.

In this section, we first show via modeling and simulation that four-level phase
information in DQPSK signals are delayed and well preserved under slow light
control [108]. Simulation extension to D8PSK [109] illustrates that slow light, in
principle, can be generalized for delaying M-ary (M=2, 4, 8, 16…) DPSK signals.
This verifies the potential value of sending highly spectrally-efficient phase-encoded
formats through a bandwidth-limited slow-light element. Experimental results on
10-Gbit/s (5-Gbaud) RZ-DQPSK signals show continuous symbol delay on both
quadratures (I and Q data channel) of up to 60-ps while still achieving error-free
demodulation via a broadband stimulated-Brillouin-scattering (SBS)-based slow
light element.

52

Fig. 4-10. Simulation results of (a) 4-level phase patterns of 10-Gbaud DQPSK
before and after 10-GHz slow-light element. (b) Demodulated eye diagrams of both
10Gbaud DQPSK and D8PSK signals, showing the transmission of highly
spectrally-efficient multi-level formats through BW-limited slow light elements.
In general, slow light is achieved by tailoring an enhanced group-index resonance
within a given medium, which results in control of the group velocity of the light and
53
thus the slowing down of the optical pulses. When binary-phase-modulated optical
signals pass through the slow light element, differential “p” phase correlation
between bit slots can be delayed and well-preserved, which is essential for ensuring
correct demodulation after slow-light delay [26].

Simulation results in Fig. 4-10 show that the slow-light delay on binary-phase
patterns can be generalized to multi-level phase-modulated signals. The slow-light
element is analytically modeled to have a Lorentzian-shaped imaginary part of the
refractive index, with controllable bandwidth and gain. Kramers–Kronig relationship
determines the real part of the refractive index, whose derivative provides the slow-
light delay spectrum. Fig. 4-10(a) shows the results of four-level phase patterns of a
20-Gbit/s (10-Gbaud) RZ-DQPSK signal, both before and after a fixed 10-GHz
bandwidth slow-light element. The phase patterns can be delayed by as much as 35-
ps while the four-level differential phase relationships are well-maintained. This
could be explained by the fact that compared with phase transitions, the four
deterministic relative phase levels occupy low frequency components within the
slow-light resonance bandwidth and are thus immune to slow-light narrowband
filtering-induced distortions. Based on this understanding, slow light can be
generalized to delaying arbitrary-level phase-encoded formats. Fig. 4-10(b) extends
10 Gbaud RZ-DQPSK to RZ-D8PSK signals, in which the bit-rate is tripled to 30-
Gb/s compared with 10-Gb/s binary DPSK signals. Under the same 10-GHz limited
slow-light bandwidth, since the spectral-width for DQPSK and D8PSK are almost
54
identical to that of DPSK, the maximum achieved delays for both DQPSK and
D8PSK formats are almost the same (ΔT
1
=ΔT
2
), regardless the increased bit-rates.
We conclude that, in theory, a bandwidth-limited B-GHz slow-light element could
provide almost identical maximum-achievable delays for log
2
(M)*B-Gbit/s M-ary
(M=2, 4, 8, …) very high bit-rate DPSK signals. We also note here that due to
reduced phase-noise tolerance and thus reduced receiver sensitivity, distortion-
constraint delay might have to be compromised for higher-order DPSK signals in
practical slow light systems.

Fig. 4-11. Experimental setup: 10-Gb/s RZ-DQPSK signals transmitted through
SBS-based slow light medium.
The above findings motivate us to transmit multi-level, spectrally-efficient DQPSK
signals through a bandwidth-limited slow-light element. The experimental setup is
shown in Fig. 4-11. The slow-light mechanism is based on broadband SBS [49] in 2-
km of highly-nonlinear fiber (HNLF), whose Brillouin frequency is measured to be
10.3 GHz. The broadband SBS pump is achieved by noise modulating the current of
55
a directly-modulated-laser (DML) at 400MHz clock frequency. The pump spectral-
width is controlled by adjusting the input driving voltage Vp-p to the laser diode and
the spectral-width is fixed at 8-GHz for this experiment. 10Gbit/s RZ-DQPSK is
generated by independently driving two parallel Mach-Zehnder modulators in an
interferometric structure with a relative π/2 phase shift between arms. A subsequent
pulse carver modulator is biased at quadrature point for 50% duty-cycle RZ
generation. The RZ-DQPSK signal at 0 dBm, with polarization control for SBS
effect maximization, counter-propagates with respect to the high power EDFA-
controlled broadband pump inside the HNLF. The amplified and delayed signal is
sent to a pre-amplified balanced DQPSK receiver with a one-symbol delay-line-
interferometer (DLI) aligned for either quadrature (I or Q) demodulation. The error
detector is post-programmed for BER measurement on both I and Q data channels.

Fig. 4-12. Bit patterns of balance-detected I and Q channels from 10-Gb/s DQPSK
signals, for three different pump power cases.
56
Fig. 4-12 and Fig. 4-13 show the experimental results of slow-light symbol delay on
10-Gbit/s (5-Gbaud) RZ-DQPSK signals. Demodulated bit patterns after balance-
detection for both I and Q channels in Fig. 4-12 show very similar delays of around
35 ps and 60 ps at pump powers of 400 mW (10-dB SBS gain) and 800 mW (19-dB
SBS gain), respectively. Enhanced pulse broadening and patterning effect [26] on
both quadratures with increased pump power is observed due to the SBS narrowband
filtering effect as the gain increases.

Fig. 4-13. Symbol delay versus SBS pump power for both I and Q. Eye diagrams of
I channel at three pump power values with slow-light delay exhibits good quality of
delayed signal.
Fig. 4-13 quantifies very similar symbol delays on both I and Q data channels. We
can see that the symbol delays on both quadratures scale fairly linearly with
increased pump power. The maximum achievable symbol delay of 60-ps corresponds
to 60% of the fractional pulse-width delay for either I or Q channels by itself,
57
considering 10-Gbit/s 50% duty-cycle RZ-DQPSK pulses. Three typical balance-
detected eye diagrams before and after slow-light delays are also shown in Fig. 4-13.

Fig. 4-14. BER measurement of both I and Q channel from 10-Gb/s DQPSK signals
show error-free operation even at maximum 60-ps slow-light delay.
In order to access the signal quality after slow light delay, Fig. 4-14 shows BER
measurements on both I and Q data channels for 10-Gbit/s RZ-DQPSK signals. Both
I and Q channels show very similar power penalty under the same pump power case
(i.e. same delay value). ~0.2-dB power penalty difference is observed between
channels. At 400mW pump power, the system power penalty is around 3.5-dB at a
BER of 10
-9
. Another 3-dB penalty is added at 800mW pump power, which
corresponds to the maximum delay condition. Clear tradeoff exists between delay
and signal quality. Signal power penalties are mainly attributed to the pulse
broadening and the slow-light-induced data-pattern dependence [24-26], which
exhibit itself as vertical eye closure.
58
Based on both simulation and experimental results, we conclude that slow light is not
only applicable to binary amplitude- and phase-modulated signals, but also to
quadrature or even multi-level modulated optical signals as well. Introducing
advanced modulation formats to the slow-light community will enable interesting
applications which require spectral efficiency. Optimization among the symbol
delay, signal quality, receiver sensitivity and spectral efficiency remains to be an
ongoing research topic.

59
Chapter 5
Design of functional modules
using slow-light-based tunable delay lines
5.1 Motivation
Although many techniques have been shown for achieving slow-light delay on a
single pulse or PRBS data streams, there have been very few reports of using such a
tunable delay for implementing true signal processing modules. As discussed in
chapter 2, several of these system functional modules will benefit a lot from the one-
bit continuously tunable slow light delay line. Potential applications might include
 Optical buffers
 True time delay for antenna remote of phased array radar
 Synchronization mechanisms for time division multiplexed systems
 All optical correlation
 Encoders and decoders for optical code division multiple access systems

In this chapter, three designs of slow-light-based system functional modules are
presented. The first design demonstrates independent delay control and bit-level
synchronization of multiple G-bit/s data channels using a single slow light element.
This design slows important steps towards multi-channel enabled slow-light-based
signal processing. The second design demonstrates variable bit-rate enabled 2:1
OTDM multiplexer using SBS-based slow light element. Dynamic control of the
60
tunable delay that slow light offers reduces the system power penalty up to 9 dB. The
tunable feature of such delay line also enables variable input-bit-rate operation. The
third design uses incoherent spectrally sliced pumping for the demonstration of
broadband stimulated Brillouin scattering (SBS) slow light. This technique is also
generalized to periodic spectrally sliced pumping for simple multiple channel slow
light synchronization.

5.2 A multi-channel synchronizer using a single slow-light element
Future slow-light applications might need independent delay controls over more than
one data channel. This is particularly true for the most obvious implementations of
synchronization and optical time-division-multiplexing (OTDM), or even
equalization or regeneration on multiple data channels [110-111], possibly on
different modulation formats [26]. In these applications, it is imperative to have
independent fine-grained control over the delays of each channel. For N channels,
this can certainly be achieved by brute-force approach of incorporating N-1 slow-
light elements in parallel and then coupling together all channels at the output.

However, a laudable goal would be to achieve individually controllable delays of
multiple channels within a single slow-light element. A key challenge in achieving
such capability is to generate multiple, independently tunable slow-light resonances
within the same medium. To the best of our knowledge, there has been no report of
61
multiple channels being independently delayed and synchronized using a single slow
light element.

Fig. 5-1. Conceptual diagram of independent delay control and synchronization on
multiple data-channels within a single slow-light element. The key enabler is the
generation of multiple slow-light resonances from multiple pumps inside a single
piece of slow-light fiber medium (inset). Independent fine-grained delay controls
are thus achieved from their corresponding resonances.
In this section, we demonstrate independent delay control and synchronization of
multiple 2.5-Gbit/s data channels through a single stimulated Brillouin scattering
(SBS) based slow-light medium [30]. Multiple, independently tunable SBS gain
resonances are generated in a single piece of highly nonlinear fiber from multiple
broadened SBS pumps [49]. Bit-level synchronization on three 2.5-Gb/s NRZ-OOK
channels shows independent and continuous delay control of up to 112-ps. Bit-error-
rate (BER) measurements on the two synchronized channels shows < 3.5dB power
62
penalty. Effect of one channel on the other channel’s delay is also characterized and
the reason is attributed to the nonlinear crosstalk.

Generation of multiple, individually tunable slow-light resonances within a single
medium is essential for independent delay control of multiple data channels. Inspired
by the fact that SBS slow-light gain resonance is stimulated by its unique pump
which is ~10-GHz blue-shifted, we thus utilize multiple such pumps spaced
sufficiently apart in a single piece of highly nonlinear fiber (HNLF) to achieve
multiple resonances (Fig. 5-1 inset). Figure 5-1 illustrates conceptually one
application of those independently controllable slow-light delays for multi-channel
data synchronization within a single slow-light element.

Fig. 5-2 shows the experimental setup of the slow-light synchronizer on three 2.5-
Gb/s data channels. Two (1546.8nm and 1554.7nm) of the three channels have their
own controllable pumps (Pump 1 and Pump 2) and the middle channel (1550.9nm) is
served as a reference without any pump. Broadband SBS pumps are realized by
modulating the injection current of directly modulated lasers (DML) using amplified
Gaussian noise source at 400 MHz clock frequency [49]. Both Pumps’ spectral-
widths are adjusted to be ~3.5 GHz by controlling the injection Vp-p using electrical
amplifier and RF attenuator. Broadband pumps are then amplified by their own high-
power EDFAs and enter a 2-km HNLF (~10.3 GHz Brillouin shift). The zero-
dispersion wavelength of the HNLF is at 1552 nm, the dispersion slope is 0.045
63
ps/(nm
2
km), the effective mode area is 14.5 µm
2
and the gamma coefficient is 9.1 W
-
1
km
-1
. Three independently modulated and de-correlated 2.5-Gb/s NRZ-OOK data
channels counter-propagate with the two broadband pumps inside the HNLF.
Polarization controllers are used on the two delaying signal paths to ensure
independent maximization of their own SBS interaction. One 7 GHz filter chooses
the intended data channel for synchronization. An optical attenuator is used
afterwards to adjust to the SBS gain so as to keep the input power into the EDFA
constant and thus the OSNR fixed. The delayed signals are detected by a 2.5-GHz
receiver and BER measurements are taken for evaluation of the signal qualities.

Fig. 5-2. Experimental Setup of multi-channel slow-light synchronizer. Three 2.5-
Gb/s NRZ-OOK signals are independently delayed and synchronized.
Figure 5-3 shows the bit patterns before and after multi-channel slow-light
synchronizer. When both pumps are off, channel #3 (1554.7nm) and channel #1
(1546.8nm) are offset from reference channel #2 (1550.9nm) by 80ps and 112ps,
respectively. By controlling their individual pump powers, both channel #3 and #1
64
can be delayed independently. With 150 mW for pump #3 and 250 mW for pump #1,
all three channels are perfectly synchronized. Note that synchronization ranges
(original offset) could be increased by further optimizing the slow-light bandwidth
and pump power. The spectrum of all three channels after synchronization is shown
on the bottom right of Fig. 5-3, with the spectrum of channel #1 zoomed in after 7
GHz narrowband filtering.

Fig. 5-3. Left: Bit-patterns before and after synchronization confirm independent
delay control on individual channels. Right bottom: Spectrum of all three channels
after synchronization. Right top: Zoomed-in spectrum of channel #1.
BER measurements are then taken to evaluate system performance of multi-channel
synchronizer. Both delayed and synchronized channels (#1 and #3) are shown to be
error free in Fig. 5-4, with < 3.5dB power penalty at a delay of up to 112-ps (#1).
Data-pattern dependence due to limited SBS gain bandwidth is believed to be one
source of power penalties. This can be confirmed from the recorded eye diagrams
(after sync), which are vertically closing. For the two delayed signals (#1 and #3),
65
their corresponding Rayleigh pump backscattered spectral component (enhances
with increased pump power) partially overlaps with the delayed signal component, as
can be seen from the bottom right spectrum of Fig. 5-3. This spectral-overlapping-
induced crosstalk from Rayleigh pump backscattering also tends to degrade the
signal quality and induce power penalty. Fig. 5-3 (top right) also shows that 7-GHz
filtering for suppression of Rayleigh backscattered component is imperative and
quite effective for 2.5-Gb/s NRZ signals. Note that the seemingly noisier eye
diagram for channel #3 after synchronization (Fig. 4) might be caused from small
wavelength fluctuations of the 7-GHz filter.

Fig. 5-4. BER and eye diagrams before and after multi-channel slow-light
synchronization. Data pattern dependence and residual Rayleigh crosstalk are
believed to be the two main contributors to power penalty.
It is also interesting to study the crosstalk effects between data signals in a multi-
channel environment. Fig. 5-5 shows that, when channel #3 is amplified and delayed
by its pump of 200 mW, the amount of delay channel #1 gets with its pump power is
66
25% smaller (at 400 mW pump #1 power) compared to the case when pump #3 is
off. Meanwhile, channel #3 also experiences similar effects. When pump #3 is fixed
at 200 mW, the amount of delay channel #3 gets is decreased up to 33% with
increased channel #1’s pump power. The abovementioned crosstalk can be attributed
to nonlinear interactions between delayed channels due to high pump powers. Cross
phase modulation between multiple channels might be one cause of nonlinear
interaction, which will broaden further the pump spectrum and thus reduce the
efficiency of SBS gain and slow-light delay.

Fig. 5-5. Crosstalk between multiple channels. One channel slightly affects the
other channel’s delay.
Fig. 5-6 investigates system power penalty under the same multi-channel condition.
Clear tradeoff exists between slow-light delay and signal power penalty. Reduced
slow-light delay one channel experiences when the other channel is on results in
more than 2-dB power penalty improvement for that specific channel. This requires
67
not only optimization inside single channel, but also global optimization (such as
respective pump power and resonance bandwidth) in a multi-channel slow-light
environment.

Fig. 5-6. System power penalties due to crosstalk between multiple channels. Clear
tradeoff exists between slow-light delay and signal power penalty.

5.3 A continuously tunable 2:1 OTDM multiplexer
Although many methods have been shown for achieving slow-light delay, there has
been no report of using such a delay to completely control the time multiplexing of
two data streams as well as to quantify the reduction of system power penalty due to
any misalignment. Furthermore, future heterogeneous optical networks might require
variable-bit-rate OTDM multiplexing.

68
In this section, we experimentally demonstrate continuously controllable OTDM of
two 2.5-Gb/s RZ channels using SBS slow light [31]. We show that the time slot of
one path can be manipulated relative to the other by as much as 75 ps. This slow-
light tunability dramatically enhances the performance of time-multiplexed 5-Gb/s
signals that results in a power penalty reduction of 9 dB at a BER of 10
-9
. We also
demonstrate variable-bit-rate OTDM by adjusting the delay according to the input
bit-rate. We show error-free 2:1 OTDM of three different input data streams at 2.5-
Gb/s, 2.67-Gb/s and 5-Gb/s.

Fig. 5-7. Concept of the advantages of slow-light-based OTDM compared with
conventional fiber-based fixed length OTDM. Slow-light-based tunable delay line
also enables variable-bit-rate OTDM.
Conventional fiber-based OTDM incorporates a fixed length of fiber which is only
suitable for a given bit misalignment for the input data streams. As shown in Fig. 5-
7, when two input streams from two different locations pass through a fiber-based
fixed-length multiplexer (MUX), it is highly likely that they will be misaligned and
69
cause bit-overlap. By utilizing the continuously controllable delay feature of slow-
light-based OTDM MUX, one could possibly manipulate in time domain the relative
misalignment by changing the slow-light control knob (e.g., pump power) and get
the two streams well aligned. Another very important feature of slow-light-based
OTDM MUX is its flexibility to be dynamically adaptive to the input data-rates so
that it could enable a variable-bit-rate OTDM system.

Fig. 5-8. Experimental setup of continuously controllable 2:1 OTDM multiplexer.
The experimental setup is shown in Fig. 5-8. The laser is modulated with 2
15
-1 PRBS
by two MZ modulators to generate 2.5-Gb/s RZ signals. The second modulator is
driven by half-rate clock with 2*Vπ swing to generate 33% duty cycle. The 33% RZ
data is then split by a 50:50 fiber coupler. The upper channel serves as a reference
and the lower channel is passed through the SBS-based slow light delay line.
Broadband SBS is realized by noise modulating the directly modulated laser (DML)
at 400 MHz clock. The RF amplifier and attenuator are used to set the pump spectral
width at 7-GHz. The pump is then amplified and enters a 2-km Highly Nonlinear
Fiber (HNLF). The lower channel then counter-propagates in the HNLF with
70
polarization states controlled so as to maximize SBS interaction. One optical delay-
line (ODL) is used to emulate the initial offset of the upper and lower arms. The
amplified and delayed lower channel is routed out via a circulator. The attenuator is
used to adjust to the SBS gain so as to balance with the upper arm. One 6.75 GHz
Fabry-Perot filter is used to suppress the spectral crosstalk from Rayleigh
backscattering. BER measurement is taken on the detected multiplexed 5-Gb/s RZ
signals.

Fig. 5-9. Bit patterns and spectrum show efficient OTDM after continuously
tunable slow light of 75 ps delay.
When the pump is off, the ODL is initially set such that upper and lower arms are
offset by 75-ps away from the well-multiplexed condition. We can clearly see from
Fig. 5-9 that the recorded bit patterns after OTDM have a severe beating region of
around 75-ps. By turning on the pump power, the lower channel can be delayed by
up to 75-ps at a pump power of 600-mW so that the bits are right interleaved with
71
respect to the upper arm. Slow-light multiplexed bit patterns show that the data
stream has doubled the bit-rate to 5-Gb/s with good signal quality. Slight beating still
remains on the non-delayed bit slot since slow light broadens the bits whose tails
penetrate into the next slot. Spectrum of both original and the well-multiplexed
streams show that spectral width remains almost the same. The asymmetry of the
spectrum is due to the residual Rayleigh backscattering.

Fig. 5-10. Power penalty versus fractional delay and the corresponding eye
diagrams. 9-dB power penalty reduction is achieved.
Figure 5-10 quantifies the relative power penalty (with respect to the well-
multiplexed case) versus the fractional delay, which is defined as the absolute slow-
light delay divided by full width half maximum (FWHM) of 33% RZ pulses. We
show that as the fractional delay increases, the relative power penalty can be reduced
gradually, resulting in maximum power penalty reduction of 9 dB. The eye diagrams
corresponding to three pump power levels are shown. The main reason for the
improvement is that the bit-overlapping region that causes the beating reduces
72
dramatically after efficient multiplexing. Another crucial requirement for efficient
2:1 OTDM is that the original RZ pulse needs to occupy less than half the bit slot so
that beating region could be minimized after multiplexing.

Fig. 5-11. Variable bit-rate OTDM: Efficient multiplexing of two data streams at
three different input bit-rates.
We also experimentally demonstrate variable bit-rate OTDM using SBS-based slow
light. Three different input bit-rates of 2.5-Gb/s, 2.67-Gb/s, and 5-Gb/s 33% RZ
PRBS data are passed through the slow-light element. Broadband SBS bandwidth is
fixed at 5GHz in order to be compatible with all three bit rates. We show in Fig. 5-11
three eye diagrams after efficient multiplexing.

Fig. 5-12. System power penalty and fractional delay at three different bit-rates.
73
We can see from Fig. 5-12 that the maximum fractional delay after OTDM is
reduced for increasing the bit-rate. In the meantime, OTDM-induced power penalty
also increases with the bit rate. This can be attributed to the fact that at higher bit-
rate, multiplexed signal not only suffers from pulse broadening of the delayed
channel, but also experiences increased crosstalk from Rayleigh backscattering.
These limitations can be alleviated if a wider slow-light BW medium, such as OPA
[27], is used. Future variable-rate N:1 OTDM could be enhanced by either cascading
2:1 OTDM or enabling multi-channel operation in a single slow light element [30].

5.4 Multi-channel slow light using incoherent pumping
In this section, we propose and experimentally demonstrate the use of an incoherent
spectrally sliced ASE source as the pump for achieving broadband SBS slow light.
By applying a periodic Fabry-Perot filter (FPF), we are able to generate multiple
controllable spectral lines for broadband SBS pumping using a single ASE source.
We further demonstrate multi-channel SBS slow light for independently and
simultaneously delaying multiple data channels in a single slow light medium. Both
on-off-keying (OOK) and differential phase-shift-keying (DPSK) signals are used in
the experiment. This shows that the spectral slicing incoherent approach can find
value in multi-channel, multi-format, and multi-bit-rate systems.

5.4.1 Concept and Theory
When a continuous-wave (CW) pump laser is used in the SBS interaction, the gain
spectrum features a Lorentzian shape whose spectral-width is around 35 MHz. If the
74
pump is frequency-modulated to several GHz, the gain bandwidth is given by the
convolution of the broadened pump spectrum and the intrinsic MHz gain spectrum.
Hence the resultant SBS gain profile is determined by the dominant ~ GHz
broadened pump spectrum [49], as conceptually depicted in Fig. 5-13.

Fig. 5-13. Concept of broadband SBS pump, as compared to the conventional SBS
pump. The broadened SBS gain spectrum is the convolution of the intrinsic gain
spectrum and the broadband pump power spectrum.
(1) Broadband SBS using “coherent sources”: As shown in the top part of Fig. 5-14,
previously published techniques involving pump broadening include: (i) direct
modulation of the pump laser source using pseudo-random bit sequence (PRBS)
modulation [48], (ii) direct modulation of the pump laser source using Gaussian
noise modulation [49, 26], (iii) external frequency modulation using an extra phase
modulator [71]. All of these methods require either direct or external modulating a
coherent laser source in order to broaden the SBS gain spectrum for each individual
data channel. Furthermore, the modulation parameters, such as the driving frequency
75
and the driving voltage, need to be carefully controlled for the design of a proper
SBS gain bandwidth and shape profile.

Fig. 5-14. (a). Concept of broadband SBS pump using “coherent sources”. Three
different approaches are depicted. (b). Concept of broadband SBS pump using
“spectrally-sliced incoherent source”. PRBS: pseudo-random bit sequence; TLS:
tunable laser source; PM: phase modulator. Pol.: polarizer
(2) Broadband SBS using “spectrally-sliced incoherent source”: The limitations of
using a coherent SBS pump require us to understand deeper into the theory behind
the generation of the broadband SBS slow light. Interestingly, if we look closer to
the convolution equation [49] shown below,

76
We observe that the phase correlation between the spectral lines within the widened
pump spectrum is not a requirement for achieving the convolution result. This can
also be verified by the experimental technique used in [49], where a Gaussian noise
source modulation randomizes the phase correlation. This confirms that the coherent
pump source is not a necessity for achieving broadband SBS process. We thus
propose our technique for the generation of broadband SBS slow light based on the
use of an incoherent SBS pump from a spectrally sliced ASE source. Our approach is
shown in the bottom half of Fig. 5-14, which also summarizes the conventional
approaches in the top half as a comparison. By applying a polarized ASE source
followed by an optical band-pass filter, our proposed technique exhibits the
following features: (i) incoherent nature of the broadband SBS pump for slow light
delay, (ii) easy setup due to the wide availability of ASE sources and optical filters,
and (iii) the SBS gain spectral width can be tailored by properly choosing the
bandwidth of the spectral-slicing filter.

We note here that the shape of the pump spectrum plays a very important role for
optimizing the achievable slow light delay and the signal quality. As shown in [74],
synthesized modulation makes the spectral shaping flexible. In our spectrally sliced
method, the shape of the pump spectrum is mainly determined by the shape of the
filter. This might limits the optimal performance using our approach. Another thing
to note here is that the ASE source after spectral slicing will lose most of the power,
77
especially for a very narrow (~ GHz) sliced pump. This is not the case for coherent
modulated source.

As mentioned in the section 5.2, another very important and interesting feature of the
spectrally-sliced technique is its scalability to multiple WDM channel operation. As
shown in Fig. 5-15, if the spectral-slicing filter is replaced by a periodic filter (e. g. a
Fabry-Perot filter), one could simultaneously generate multiple spectrally-sliced
GHz-wide SBS pumps from a single incoherent ASE source. This greatly simplifies
the system for the generation of multi-channel slow light delay lines, and can be
readily scalable to multi-channel operation by choosing a periodic filter with a
proper free spectral range (FSR).

Fig. 5-15. Concept of the multi-channel SBS slow light operation using a
periodically spectrally sliced incoherent ASE source. BPF: band-pass filter.
78
Furthermore, the periodically spectrally sliced approach can also provide
individually-tunable SBS resonances within a single slow light medium, which is
essential for independent delay control of multiple data channels [30]. This is also
conceptually depicted in Fig. 5-15. Multiple SBS pumps from the periodic filter can
be independently controlled by selectively filtering each pump using their matched
band-pass filters (BPFs), thus generating individually-controllable slow light
resonances, which are ~10 GHz away from their corresponding pumps.

5.4.2 Single channel operation
Shown in Fig. 5-16 is the experimental setup of a single channel slow light
operation. Spectrally sliced incoherent SBS pump source is realized by using an ASE
source followed by a fiber Bragg grating (FBG) filter. We note here that the
unpolarized ASE source needs to be polarized before entering the main setup since
the SBS slow light process is polarization sensitive. Both 2 GHz and 4 GHz (3-dB
bandwidth) FBGs are applied subsequently in the experiments. The inset spectrum
shows a 2 GHz spectrally sliced shape. This incoherent ~ GHz source is then
amplified by two EDFAs with one 0.25 nm filter in between for the suppression of
the introduced ASE noise. The SBS medium is a 2-km-long highly nonlinear fiber
(HNLF) whose measured Brillouin shift is ~ 10.3-GHz. The transmitter sends either
a 2.5-Gbit/s non-return-to-zero (NRZ) OOK or an NRZ-DPSK signal by adjusting
both the bias and the driving voltage to the external Mach-Zehnder modulator. The
reason why we choose both intensity and phase-encoded signals is that future slow
79
light elements require modulation format transparency [26]. The 2.5-Gbit/s NRZ-
OOK or NRZ-DPSK signals, with polarization control for maximizing the SBS
interaction, counter-propagates inside the HNLF with respect to the spectrally-sliced
incoherent pump. The amplified and delayed signal is then routed out via a
circulator. One 7-GHz filter is used for the suppression of both the ASE noise and
the Rayleigh backscattering [30]. Another attenuator is adjusted according to the
SBS gain so as to keep the input power into the EDFA constant and thus the OSNR
fixed. BER measurement is taken for the evaluation of the signal integrity after the
slow-light medium.

Fig. 5-16. Single channel experimental setup: Polarized ASE source followed by an
FBG is served as our proposed spectrally sliced pump. Both OOK and DPSK
signals are delayed and evaluated.
Figure 5-17 and Fig. 5-18 show the experimental results of delaying both 2.5-Gbit/s
NRZ-OOK and NRZ-DPSK signals using either a 4-GHz spectral-sliced or a 2-GHz
spectrally-sliced SBS pump. NRZ-DPSK signals exhibit unavoidable intensity dips
during phase transitions due to the use of the MZM modulation approach [4]. We
achieve continuously controllable slow-light delay on both the 2.5-Gbit/s NRZ-OOK
80
and NRZ-DPSK signals by adjusting the SBS pump power using the high power
EDFA. This verifies the ability of achieving SBS gain and slow-light delay from a
spectrally sliced incoherent pump source.

Fig. 5-17. Slow light delay on both 2.5-
Gb/s NRZ-OOK and NRZ-DPSK
signals using a 4-GHz spectral-sliced
pump.
Fig. 5-18. Slow light delay on both 2.5-
Gb/s NRZ-OOK and NRZ-DPSK
signals using a 2-GHz spectral-sliced
pump.
In order to measure the slow light delay, we define here a common metric
corresponding to the middle of the “1” level. We choose this metric because the
middle of the upper level carries the highest photon energy and thus represents the
information-bearing point. For 4-GHz spectrally-sliced pumping, both modulation
formats achieve slow light delay of 30 ps and 88 ps at pump powers of 100 mW and
300 mW, respectively. Eyes remain wide-open even at maximum slow-light delay.

Realizing that the delay could be enhanced by optimizing the slow-light bandwidth,
we further use a narrower filter of 2-GHz bandwidth for achieving more efficient
spectrally-sliced pumping. The system performances using a 2-GHz FBG are shown
81
in Fig. 5-18, where the slow-light delays are 60 ps and 170 ps at power powers of
100 mW and 300 mW, respectively.

Figure 5-19 further quantifies the slow-light delay performance for the two different
spectrally sliced FBG cases. The figure shows that the 2-GHz sliced pump offers
almost twice the delay compared to the 4-GHz sliced system for both 2.5-Gbit/s
NRZ-OOK and NRZ-DPSK signals. The achievable 170-ps maximum delay, which
corresponds to 43% fractional delay, is comparable to the published results using
conventional approaches [26, 49]. The larger delay of the 2-GHz slicing emphasizes
the importance of optimizing the spectral-width of the incoherent SBS pump.

Fig. 5-19. Comparison of slow-light delay as a function of increased pump power
for two different spectrally sliced conditions. This shows that the optimization of
SBS pump spectra-width is essential for the slow-light delay performance.
In order to further evaluate the signal degradation using our approach, BER
measurements for 2.5-Gb/s NRZ-OOK signals are shown in Fig. 5-20 for both 4-
GHz and 2-GHz sliced SBS pumping, at maximum delay condition (300 mW pump
82
power). Compared with the back-to-back case, less than 2-dB and 4-dB power
penalties are observed for 4-GHz and 2-GHz slicing, respectively. A fractional delay
of 43% with < 4-dB penalty proves the effectiveness of our proposed approach. The
larger penalty in the 2-GHz case is due to the increase of the excess intensity noise as
the spectral width of the incoherent light source narrows [112]. This can also be seen
in the eye diagrams in Fig. 5-18, as compared to the eye diagrams in Fig. 5-17.

Fig. 5-20. BER measurement of both the 4-GHz and the 2-GHz spectrally sliced
cases. Less than 4 dB power penalty at the maximum delay conditions is shown.

5.4.3 Multi-channel operation
We show in Fig. 5-21 the experimental demonstration of independent slow-light
delay of three 2.5-Gb/s data channels in a single piece of HNLF using a periodic
spectrally-sliced pumping. Spectrally-sliced periodic incoherent pump source is
realized by using a polarized ASE source followed by a Fabry-Perot filter (FPF),
83
whose 3-dB bandwidth and the free-spectral-range are 6 GHz and 46 GHz,
respectively. The inset spectrum shows the spectrally-sliced FPF shape. This
periodic and incoherent source is then selectively filtered and individually amplified
by two band-pass filters and high-power EDFAs.

Fig. 5-21. Multi-channel experimental setup: Polarized ASE source followed by a
periodic Fabry-Perot filter (FPF) is served as our proposed multi-channel
spectrally-sliced pump. 2.5-Gb/s RZ-DPSK, NRZ-OOK and NRZ-DPSK signals
are independently delayed and evaluated.
Two (1548.2 nm and 1551.3 nm) of the three channels have their own controllable
pumps (Pump 1 and Pump 2) and the middle channel (1549.8 nm) is served as a
reference without any pump. We intentionally choose three different modulation
formats at 2.5-Gbit/s (RZ-DPSK, NRZ-OOK and NRZ-DPSK for the left, the middle
and the right channels, respectively) in order to demonstrate that slow light system
should be multi-format capable. The two band-pass filters select the proper channels
of the FPF according to the two of the to-be-delayed RZ-DPSK and NRZ-DPSK data
signals. Three independently modulated and decorrelated data channels counter-
84
propagate with the two amplified pumps inside the HNLF. Polarization controllers
are used on the two delaying signal paths so as to ensure independent maximization
of their own SBS interaction. One tunable 7-GHz filter chooses the data channel to
be detected subsequently. The two delaying signals also go through a one-bit delay
interferometer (1-bit DI) for demodulation. The delayed signals are detected by a
2.5-GHz receiver and the BERs are taken for the evaluation of the signal qualities.

Fig. 5-22. Top: Initial status for all three channels without slow light delay.
Bottom: Eye diagrams for all three channels after the multi-channel slow light
module.
Figure 5-22 shows the demodulated eye diagrams both without and with the multi-
channel slow light delay module, for all three channels. We note here that the
alternate-mark-inversion (AMI) port is used for the RZ-DPSK signal and the duo-
binary (DB) port is used for the NRZ-DPSK channel. When both pumps are off, the
eye diagrams show the initial status. By controlling their individual pump powers,
both channel #1 and channel #3 can be delayed independently. With 450 mW pump
85
#1 power and 400 mW pump #3 power, the channel #1 and channel #3 are delayed
by as much as 105 ps and 180 ps, respectively. This verifies the capability of the
proposed technique to simultaneously and independently delay multiple channels in
a single slow light element using periodic spectrally sliced incoherent pumping.

Fig. 5-23. BER measurement before and after multi-channel slow light module, for
both 2.5-Gbit/s RZ-DPSK and NRZ-DPSK signals.
BER measurements are then taken to evaluate system performance of the multi-
channel slow light module using spectrally-sliced periodic filtering. Both delayed
channel #1 and channel #3 are shown to be error free in Fig. 5-23, together with the
back-to-back BER curves. In the initial status, 2.5-Gbit/s RZ-DPSK signal
performance 1.2 dB better than the NRZ-DPSK signals. After slow light delays, the
RZ-DPSK demodulated AMI channel exhibits 2.2 dB better performance compared
to the NRZ-DPSK demodulated DB channel, at the maximum achievable delay
values for both cases. The enhanced better performance after multi-channel slow
86
light delay for RZ-DPSK compared to NRZ-DPSK channel can be attributed to the
fact that RZ-DPSK exhibits less data pattern dependence thanks to the pulse-train
like signal patterns [26]. This can also be verified in Fig. 5-22 of the delayed AMI
and DB eye diagrams.

In conclusion, we have proposed and demonstrated the use of an incoherent
spectrally-sliced ASE source as the pump for the generation of broadband SBS slow
light. Both 2.5-Gb/s OOK and DPSK signals are continuously delayed by as much
as 170 ps, with less than 4 dB power penalty at 10
-9
bit-error-rate (BER). This 43%
fractional delay and the integrity of the delayed signal are comparable to that of the
conventional approaches. Furthermore, independent and simultaneous delay control
on multiple data channels within a single slow-light medium is proposed and
demonstrated by using a spectrally-sliced periodic filter. Three different modulation
formats, such as NRZ-OOK, NRZ-DPSK and RZ-DPSK are transmitted and
independently delayed inside the multi-channel slow light module.

87
Chapter 6
Compensation of deleterious effects
in high-speed SOA-based wavelength converters
6.1 Differential mode wavelength converters
Wavelength converters and switches based on XGM or XPM processes exhibit slow
rise/fall times of the converted pulses due to the slow carrier recovery in the SOAs.
This can lead to pattern dependent effects apart from pulse asymmetry or
broadening. In order to mitigate some of these effects, differential mode (DM)
switches have been proposed. These switches, which rely on interference of time-
offset copies of phase-modulated signals, effectively mask the slow recovery time in
the SOAs and can potentially enable very high-speed all-optical wavelength
conversion [113]. Two representatives of DM switches are,
 Delayed-interference signal converter (DISC): The structure is very simple
which incorporates one single SOA followed by a delayed interferometer.
 Differential cross-phase modulation (DXPM): The structure is more
complicated which features two SOAs in a Mach-Zehnder interferometer.

Our work is mainly focused on the first type of DM switches due to its simple yet
elegant structure. A wideband dynamic SOA model in conjunction with commercial
system simulation software is employed to study the behavior of wavelength
converted signal. Two types of non-idealities introduced by the DM switches are
88
studied and ways to mitigate these deleterious effects are proposed and demonstrated
experimentally.

The DISC provides a simple, yet elegant solution for wavelength conversion,
requiring only one SOA and an Asymmetric Mach-Zehnder Interferometer (AMZI)
[114]. It has been used in several signal processing applications [115-117]. The
structure of the DISC is shown in Fig. 6-1 and its operation can be understood from
Fig. 6-2.

A low power CW probe signal and a high power RZ modulated pump signal are
injected into an SOA. The pump imposes phase modulation on the CW probe with a
fast rise time (determined by the input pulse rise time) and slow fall time
(determined by the carrier recovery time in the SOA). This phase modulated signal
enters an AMZI, which is an MZI with a time delay in one arm.

Fig. 6-1. Structure of the DISC wavelength converter.
89

Fig. 6-2. Operating principle of the DISC. The pump input signal imposes phase
variation on the CW probe. This phase modulated signal is made to interfere with its
own delayed copy using the AMZI. As a result narrow switching windows are
formed due to the phase difference, which are not limited by the slow carrier
recovery time. Sub-pulses are also generated due to overshoot of the delayed
component.
The phase modulated probe and its time-delayed copy interfere at the output of the
AMZI. Since the output is governed by the phase difference between the two
interfering components, narrow switching windows are opened due to each pump
pulse. If the phase-bias between the arms is set to π radians, output pulses emerge
only during these switching windows. As a result, the slow carrier recovery is
nullified and narrow output pulses can be obtained. In effect, the phase modulated
probe component that arrives at the output first, opens the switching window that is
shut down by the arrival of the delayed copy. Thus the output pulse-width is
90
determined by the time differential between the two arms, instead of the slow carrier
recovery. As is visible from the phase diagrams, in an ideal case (delayed copy is a
true replica of the original phase modulated probe) the delayed copy will always
overshoot the original phase variation, leading to negative phase differences. For a
phase-bias of π, this corresponds to constructive interference too and leads to the
appearance of sub-pulses as shown in Fig. 6-2. These sub-pulses have recently been
predicted [118] and their existence has also been verified experimentally [119].

6.2 Sub-pulses and its suppression
In order to understand the properties of these sub-pulses, we develop a DISC model
at 40-Gb/s for 5 ps FWHM Gaussian-shaped pulses. We have used a wideband
numerical SOA model [101] that includes the ASE noise. Finite difference
techniques are applied to accurately predict the gain and the phase dynamics. The
MZI is modeled analytically. The SOA is biased at 210 mA and pump and probe
powers are 5 dBm and 10 dBm, respectively. A 5 ps delay, Δt, is set to enable pulse-
width maintaining conversion and a ‘π’ phase shifter is meant to have complete
destructive interference. The temporal chirp modeling results of the converted output
is shown in Fig. 6-3. Since the leading as well as the trailing edges of the converted
probe pulses are caused by input pump signal-induced refractive index increase
during carrier depletion period, almost the entire main-pulse is chirped towards
lower frequencies (red-shifted). On the other hand, the sub-pulses are generated
91
during the slow phase recovery of the SOA and are consequently blue-shifted. We
conclude that the sub-pulses are oppositely chirped with respect to the main-pulses.

Fig. 6-3. 40-Gb/s simulation results: Time-resolved chirp in both MZI arms. Sub-
pulses and main-pulses are oppositely chirped.
By utilizing the opposite chirp of the sub-pulses with respect to the main pulses, we
experimentally demonstrate an off-centered filtering technique for suppression of
these sub-pulses which results in >3 dB extinction ratio enhancement. The
experimental setup is shown in Fig. 6-4. The 2 ps short-pulses, emitted by a
semiconductor mode-locked laser, are modulated by 10-Gb/s data, with 2
15
-1 PRBS.
The SOA has a gain recovery time of ~110 ps. The MZI has a voltage controlled
phase bias in one arm and a fixed 25 ps delay in the other. The optical filter followed
92
by the DISC has a FWHM bandwidth of 0.25 nm and is off-centered towards longer
wavelength so as to suppress the sub-pulses. The experimental trace obtained from a
chirp form analyzer (Fig. 6-5) verifies with our modeling results that the main pulses
are red-shifted while the sub-pulses are blue-shifted. Different pump and probe
power settings and bit rates cause the small chirp value difference in our
experimental and simulation results, but the opposite chirping trend are verified.

Fig. 6-4. Experimental setup: Off-center filtering for Extinction Ratio Enhancement.

Fig. 6-5. Experimental verification of the temporal chirp waveform using the chirp
form analyzer.
93
For phase bias = ‘π’, the optimum filter detuning is determined by the sub-pulse
Suppression Ratio (Fig. 6-6), which is defined as the peak power ratio between the
main and sub-pulses. As the filter detuning increases towards longer wavelength, the
suppression ratio improves until the OSNR starts degrading, leading to a reduction of
the main pulse power. Experimentally, the optimum filter detuning is found to be
+0.3nm.

Fig. 6-6. Sub-pulse suppression ratio as a function of filter detuning, for the case of
phase bias = ‘π’. Two inserted eye diagrams show effective sub-pulse suppression.

94
The DISC phase bias is ideally set at ‘π’ such that the CW probe undergoes complete
destructive interference when the input pump signal is absent, thereby minimizing
the zero power level at the switched output. However, due to the large sub-pulses
(Fig. 6-7(a)-‘A’), the phase bias usually requires a fair amount of adjustment away
from ‘π’ so as to minimize these sub-pulses. This phase bias adjustment prevents the
delayed phase component from overshooting the original copy. However, this
operation inevitably increases the zero power level (Fig. 6-7(a)-‘C’) and
consequently limits the output extinction ratio (ER) significantly. In order to
improve the output ER, we first suppress these sub-pulses (Fig. 6-7(a)-‘B’) using our
off-centered filtering technique. Since the sub-pulses cannot be fully nullified, we
still have to adjust the phase bias, but the adjustment away from ‘π’ (Fig. 6-7(a)-‘D’)
is much less compared to the centered filtering case. This leads to an ER
improvement because the zero level is not increased significantly. A quantitative

Fig. 6-7 (a). Eye diagrams showing
the interplay of phase bias and filter
detuning. AC: no detuning, only
phase bias adjustment. BD: both
detuning and bias optimization.
Fig. 6-7 (b). Red-detuned filtering
suppresses the sub-pulses, resulting in
>3dB ER improvement (CD) for the
optimum phase bias case.
95
analysis of the interplay of phase bias and filter detuning is shown in Fig. 6-7 (b). As
the filter is detuned, we observe a clear ER increase for the ‘π’ phase bias case. The
red-chirped main-pulses are also enhanced thanks to the red-detuned filter. It should
be noted that the amount of phase bias adjustment is significantly reduced from 1-
0.72 = 0.28p (‘A’ to ‘C’) to 1-0.87=0.13 p (‘B’ to ‘D’) when the output filter is
detuned by +0.3 nm. This >50% reduction in the required phase bias adjustment
results in >3 dB improvement in the output extinction ratio.

6.3 Data pattern dependence and its reduction

Fig. 6-8. Data-pattern dependence due to slow carrier recovery in SOA based
wavelength converters.
As described in the previous section, in order to nullify the slow carrier recovery in
SOAs, differential mode (DM) XPM switches that utilize a push-pull configuration
have been used. Even though DM wavelength converters at bit-rates >160 Gb/s have
been demonstrated [113], they suffer from nonlinear patterning effects [120]. Large
96
variation in the amplitude of the output pulses (Fig. 6-8) is observed that can lead to
eye-closure. As shown in Fig. 6-9 (simulated using an SOA model [101]), the eye-
closure penalty increases rapidly with increasing bit-rate for long carrier recovery
times (t
r
). The problem becomes even more pronounced when many such
wavelength converters are cascaded.

Fig. 6-9. Eye-closure penalty due to increasing bit-rate for differential mode
wavelength converters.

6.3.1 Origin of nonlinear data-pattern dependence in a DISC
Recently, a technique based on detuned optical filtering [121] was proposed to
reduce the nonlinear pattern-dependence in the DISC. The technique uses the pattern
dependence in the chirp induced on the pulses to compensate for the pattern
dependence in the amplitudes of the pulses. However, the loss of signal-to-noise
97
ratio incurred due to off-center optical filtering limits the improvement in signal
quality that can be achieved.

Other properties of the output signal can be exploited to reduce the pattern
dependence in the pulse amplitudes. Previous work has shown that pattern
dependent signal distortion induced by gain saturation in SOAs leads to overshoots
at the rising edges of signals that are being amplified. Several techniques to mitigate
this effect have been explored, including ‘polarimetric filtering’ [122]. This
technique leverages the large birefringence induced in the SOA by the rising edges
of the input pulses and uses a polarizer placed after the SOA to improve the signal
quality. In order to explore the use of polarimetric filtering for the DISC, a deeper
understanding of the mechanics of XPM and the simultaneously occurring cross-
polarization modulation (XpolM) is required.

In Fig. 6-10, the SOA dynamics have been assumed to include only linear pattern
dependence. This means that the carriers recover slowly when an input pulses is
switched off, but the amount of carrier suppression (or phase-swing) induced by
consecutive pulses is always the same. As explained earlier, in the absence of a
signal pulse, the probe components in the MZI arms interfere destructively due to a
‘π’ phase offset between them. Input signal pulses suppress the carrier density in the
SOA leading to a change in the refractive index and a corresponding modulation of
the phase of the co-propagating probe beam. The phase variations of the signals in
98
the two arms are shown in Fig. 6-10 where a time offset is created by the delay Δt in
one of the arms. From Fig. 6-10 it is clear that if only linear pattern dependence is
included in the analysis, ΔΦ
A
=ΔΦ
B
i.e. consecutive pulses, A and B induce equal
amounts of cross phase modulation on the probe even if the time between the input
pulses (determined by the input signal bit-rate) is shorter than the SOA’s carrier
recovery time.

Fig. 6-10. Operation of the DISC
assuming only linear pattern
dependence exists in the SOA. All
pulses induce the same amount of
phase-swing and the differential mode
completely compensates for linear
pattern dependence.
Fig. 6-11. Operation of the DISC
including nonlinear pattern dependence in
the SOA. The amount of phase-swing
induced by input pulses reduces in a long
string of 1’s leading to a reduction in
output pulse amplitudes.
The modulated probe component that reaches the output of the MZI first opens a
switching window that is closed by the arrival of the delayed component. Since the
opening and closing of the window is induced by the fast carrier suppression, the
99
window width is controlled by the time-delay between the interferometer arms,
rather than the slow carrier recovery. Thus the DISC completely eliminates the
linear pattern dependence due to slow carrier recovery. However, the assumption of
linear pattern dependence in the SOA is not true. In reality, the pulses that enter the
SOA after a 0-bit cause a bigger phase swing than ones that follow another pulse
(ΔΦ
A
>ΔΦ
B
) as shown in Fig. 6-11. Thus, in the converted output the peak power of
the first pulse in a string of pulses is much higher than the ones that follow it. This is
called nonlinear pattern-dependence [120] since it arises from the dependence of the
optically-induced carrier density variation on the instantaneous value itself.

Fig. 6-12. Correspondence between gain suppression and pattern dependence.
Output pulses that have lower power correspond to larger gain saturation in the SOA.
100
As shown in Fig. 6-11, a long sequence of ‘1s’ leads to progressively less phase
modulation of the CW probe. However, the absolute deviation of the phase from the
original steady state continues to increase. Successive pulses keep depleting the
carrier population in the SOA, leading to increased gain suppression. This can be
verified experimentally by observing the power variation of the CW probe after the
SOA, as shown in Fig. 6-12 since gain and phase dynamics are both primarily driven
by the same source, i.e. carrier density variation. Since the gain saturation for input
pulse ‘B’ is deeper than that for ‘A’, we can conclude that the smaller pulses (e.g.
‘B
C
’) at the output of the DISC correspond to deeper gain saturation of the SOA.

6.3.2 Polarization properties of the DISC’s output

Fig. 6-13. Experimental setup to observe polarization state of DISC’s output for an
input (pump) pulse train. As the pump power increases, the amount of gain
saturation and polarization rotation increases.
101
It is well known that if the CW probe is split between the TE and TM modes of the
SOA, the pump signal induces different phase change on the two components due to
the SOA’s structural asymmetry and difference in the confinement factors of the two
modes. This optically-induced birefringence translates into a polarization rotation of
the probe. Since the polarization rotation increases with gain saturation, one can
expect the polarization states of the output pulses in a long string of ‘1s’ to be
different. A polarization controller placed at the output of the DISC, followed by a
polarizer, can be adjusted to equalize these pulses by ensuring that the projections of
the polarization states of all the pulses on the polarizer’s axis are of equal magnitude.

Fig. 6-14. Gain suppression and
polarization rotation as a function of
input optical signal power. Pulses
that correspond to larger gain
suppression undergo greater
polarization rotation.
Fig. 6-15. Experimental setup. The SOA
and the 25 ps delay-interferometer form the
DISC. The polarization controller and
polarizer are added to control the pattern
dependence of the output signal.

To explore the relationship between gain saturation and polarization rotation, a 10
GHz, 2 ps FWHM pulse train from a semiconductor mode-locked laser is injected as
the pump into the SOA. The output of the SOA is passed through a 25 ps delay
interferometer before being filtered to recover the probe wavelength. If only the
102
cross-gain modulated probe is required the delay interferometer is bypassed. While
increasing the average power of the pump signal, the polarization states of the output
pulses obtained from the DISC are observed using a polarization analyzer. The
experimental setup, cross-gain modulated probe and the observed polarization states
of the DISC output for three different pump powers are shown in Fig. 6-13.

As a representation of the amount of polarization rotation, the polarization ellipse’s
azimuth is recorded. This polarization rotation observed is plotted in Fig. 6-14 along
with the gain saturation curve. As expected a greater polarization rotation is
observed with decreasing gain. From these measurements it can be concluded that
pulses with smaller amplitude at the output of the DISC are more polarization rotated
(due to deeper carrier suppression) than the ones that have higher amplitudes.

6.3.3 Reduction of nonlinear pattern dependence using polarimetric
filtering
The experimental setup used to investigate the polarimetric pattern dependence
reduction technique is shown in Fig. 6-15. The SOA used is a commercial device,
biased at 180 mA with a 10-90 % gain recovery time in excess of 300 ps. Pulses
with 2 ps FWHM at a wavelength of 1547 nm from a semiconductor mode-locked
laser are modulated with 2
31
-1 PRBS data at 10 Gb/s and injected into the SOA with
an average power of –0.5 dBm. The CW power (wavelength = 1535 nm) coupled
into the SOA is 1 dBm. The method to suppress the pattern dependence involves
103
placing a polarization controller and a polarizer at the DISC output. The polarization
controller is adjusted such that the pulses with larger amplitude are preferentially
attenuated relative to the smaller pulses on passing through the polarizer. A
conceptual diagram is shown in Fig. 6-16 and the experimental setup in Fig. 6-17.

Fig. 6-16. Principle of polarimetric pattern dependence reduction. The polarization
controller and polarizer placed after the DISC are adjusted such that the pulses with
larger amplitude are preferentially attenuated relative to the smaller pulses.

Fig. 6-17. Reduction of pattern dependence in DISC wavelength converter.
104
Due to slow carrier recovery, at the output of the DISC, the ratio of the largest pulse
power to the smallest pulse power is 3.3 dB, which is completely nullified using the
polarizer (Fig. 6-18). If the axis of the polarizer is so aligned that it preferentially
attenuates the smaller pulses, the pattern dependence is enhanced leading to a
completely closed eye as shown in Fig. 6-18, giving further proof of the principle
involved. In fact, the variation in the polarization states of the output pulses is
significant enough to actually reverse the pattern dependence, i.e. the pulse power
increases for successive pulses in a long string of ‘1s’. By equalizing the power in
the output pulses, the eye opening can be improved by more than 33%.

Fig. 6-18. Bit-patterns and eye diagrams showing control over the pattern
dependence. Through appropriate adjustment of the output polarization controller,
the pattern dependence can be reduced from 3.3 dB to 0 dB or increased to >7 dB.
To quantify the improvement in signal quality, bit-error-rate measurements are
performed for 2
31
-1 PRBS data. The BER curves shown in Fig. 6-19 indicate a
power penalty improvement of 2.6 dB at a bit-error-rate of 1e-9.
105

Fig. 6-19. Bit-error-rate measurements showing 2.6 dB power penalty improvement
at BER=1e-9. Eye opening is improved by more than 33%.

In this experiment the SOA used has a recovery time more than three times longer
than the bit-time. Similar results should be expected for higher bit-rates if faster
SOAs are used, e.g. using an SOA with 75 ps recovery time for a 40 Gb/s system.
The same concept applies to other differential mode switches also, e.g. differential
cross-phase modulation [123]. Configurations comprising an SOA followed by a
detuned filter [100] to exploit the SOA’s chirp for wavelength conversion may
benefit from this polarimetric technique, enabling higher speed operation.

106
Chapter 7
Enhancing system performance using novel optical devices
As mentioned in the introduction, future optical systems and networks require
functional integration in order to differentiate themselves from the current versions
of optical networks. Device researchers have been devoting a lot of their energy in
exploring novel optoelectronic devices, which exhibit unique physical features for
functional integration and advanced optical signal processing [124]. In order to find
interesting applications of these novel devices, a deep understanding of the physics
behind and a systematic evaluation of their system performance must be bridged. A
thorough analysis of the physical evolution of an optical wave field propagating
along the waveguide, as well as a deep characterization of evolved optical properties
throughout the link, such as amplitude, phase, polarization, frequency chirp, must be
performed in both time and frequency domain.

This chapter summarizes the collaboration work with two UC-Berkeley groups on
the design of system applications and evaluation of link performances using novel
optoelectronic devices. The first device is an optical injection-locked (OIL) vertical
cavity surface emitting laser (VCSEL), which exhibits interesting properties such as
greatly enhanced modulation bandwidth and substantially reduced frequency chirp.
We describe two novel applications by exploring the time-resolved frequency chirp
from OIL-VCSEL. We demonstrate in Section 7.1 that the VCSEL after injection
locking features negative frequency chirp with adjustable magnitude and polarity.
107
Chromatic dispersion tolerance is enhanced by greater than 10 times at 10-Gb/s
compared to that of a directly modulated VCSEL [125]. Section 7. 2 shows that by
utilizing the adjustable chirp, together with a tunable optical interferometer, three
novel functions can be reconfigurably operated in a single OIL-VCSEL device,
showing ultra-wideband monocycle generation, non-return-to-zero (NRZ) to pseudo-
return-to-zero (PRZ) format conversion, and NRZ-data clock recovery [126]. The
second novel optoelectronic device is a MEMS-actuated bandwidth-tunable micro-
disk resonator filter. By utilizing its unique tunable bandwidth feature, we
experimentally demonstrate in section 7.3 three dynamic bandwidth allocation
functions, namely the variable bit-rate operation, matched optical filtering and
reconfigurable channel banding [127].

7.1 Reach extension and dispersion pre-compensation using
adjustable-chirp optically-injection-locked (OIL) - VCSELs
VCSELs are highly desirable for cost-effective wavelength-division-multiplexed
(WDM) optical communication systems because of their excellent single-mode
behavior and potential for low-cost manufacturing and integration [128]. However,
in order to be promising for metro-area applications, VCSELs have to exhibit
properties such as broad modulation bandwidth and negligible frequency chirp.

Optically-injection-locked (OIL) VCSELs, which are locked, both in frequency and
phase, to a master laser by photon injection at a similar wavelength, have been
108
demonstrated to be effective for enhancing the small-signal modulation bandwidth
[129], as well as reducing the chirp of directly modulated lasers [130]. Hence, OIL-
VCSELs can be a promising candidate for future metro-area networks. Frequency
chirp reduction using OIL has been shown both theoretically and experimentally
[131]. However, little has been studied on the time-resolved chirp waveforms and
the chirp polarity, which are closely correlated to the link dispersion. Furthermore, it
would be valuable to be able to tune the chirp such that its magnitude can be
dynamically reconfigured according to the link for flexible dispersion compensation.

In this section, we demonstrate experimentally that the frequency chirp of OIL
VCSELs is not only reduced in magnitude but can also be switched in sign. We show
that the change of the chirp polarity from positive to negative is due to an interesting
phenomenon of data inversion in OIL VCSELs. Furthermore, by adjusting the
injection power ratio, the negative peak-to-peak chirp can be effectively controlled.
Chromatic dispersion compensation is investigated at 10-Gb/s, and more than 125
km standard single-mode fiber (SSMF) only transmission with negligible power
penalty at a BER of 10
-9
is achieved using OIL VCSELs. This shows a factor of 10
larger dispersion tolerance compared to that of a directly modulated VCSEL.

7.1.1 Concept and experimental setup
The experimental setup is shown in Fig. 7-1. A distributed feedback (DFB) laser
serves as the master laser to injection-lock a 1.55-mm VCSEL. An optical circulator
109
is placed in between the DFB and the VCSEL to achieve unidirectional locking. The
VCSEL current is directly modulated at 10-Gb/s, with a 2
15
-1 pseudorandom binary
sequence (PRBS). Both the VCSEL bias and the data driving voltage are optimized.
The DFB current is adjusted to control the power injecting into the VCSEL.
Chromatic dispersion is emulated using variable lengths of SSMF spools with
EDFAs in between. The fiber link is estimated to be linear with < 3.5-dB power into
the SSMF. A pre-amplified receiver and an error detector are used for BER
quantification of the signal quality with and without fiber transmission. The
Advantest Q7606B chirp-form analyzer is used together with a sampling
oscilloscope to obtain the time-resolved chirp waveforms and the intensity
waveforms at various injection ratio levels.

Fig. 7-1. Experimental setup. OIL VCSELs with tunable chirp for dispersion
compensation. Chirp form analyzer is used to investigate the polarity flipping of the
frequency chirp. Multiple spools of SSMF are used to study the effect of the flipped
chirp on chromatic dispersion.

7.1.2 Tunable chirp and dispersion compensation enhancement
The time-resolved intensity and chirp waveforms for a free-running VCSEL directly
modulated at 10-Gb/s are shown in Fig. 7-2 (a), with light and dark lines
110
respectively. The device is biased at 5.5 mA and the driving voltage is 1-Vpp. The
adiabatic chirp depends strongly on the optical intensity and appears as a frequency
shift according to the ON/OFF signal. The transient chirp appears at the rising and
falling edges of the signal as spikes. This is defined as the “positive chirp” due to the
positive frequency deviation on the rising edge and negative frequency deviation on
the falling edge. Positive chirp speeds up pulse broadening when transmitting
through standard positive dispersion fiber, thus increases power penalty [132]. It is
obvious that for the free-running case, the adiabatic chirp dominates and the peak-to-
peak chirp is > 25 GHz.

Fig. 7-2. Experimental measurement of time-resolved chirp and intensity waveforms
at 10-Gb/s for (a) free-running VCSEL, (b-d) OIL VCSEL with injection ratios of (b)
6.21 dB (c) 8.58 dB (d) 11.12 dB.
111
Fig. 7-2 (b-d) shows the intensity and chirp waveform when the VCSEL is injection-
locked at various injection ratios, which are defined as the power ratios of the
injected light to the VCSEL emission. Chirp reduction is evident compared to the
free-running case while the transient chirp now becomes the dominant part. By
adjusting the power of the DFB laser and the coupling to the VCSEL, one can
control the injection ratio. When the injection ratio is increased from 6.21 dB to 8.58
dB and to 11.12 dB, the peak-to-peak chirp is reduced from 3.1 GHz to 2.7 GHz and
then to 1.55 GHz, respectively, as shown in Fig. 7-2 (b, c, d). This can be understood
from the fact that strong injection reduces the carrier density change and thus the
index variation during the same transition time, as compared to weak injection.

Fig. 7-3. Peak-to-peak chirp and
extinction ratio at 10-Gb/s as functions
of injection ratio.
Fig. 7-4. Optical spectra of free-running
and OIL VCSEL with 8.58-dB injection
ratio, both modulated at 10 Gbit/s.
Figure 7-3 quantifies the peak-to-peak chirp tunability as a function of the power
injection ratio. The chirp can be reduced to half of its original value by increasing the
injection ratio from 6.21 dB to 12.07 dB. However, a tradeoff exists between the
chirp and the extinction ratio of the signal. The degradation of the extinction ratio is
inevitable at strong injection conditions due to the surface normal geometry of the
112
VCSEL. Therefore, the injection ratio needs to be optimized. Fig. 7-4 shows the
optical spectra of both free running and OIL VCSEL with an 8.58-dB injection ratio
under 10-Gb/s large signal modulation. The much broader and asymmetric free-
running spectrum indicates the dominant adiabatic chirp and the unbalanced transient
chirp. With injection locking, the spectrum is greatly narrowed because of the chirp
reduction. The locked wavelength is also blue-shifted to the master wavelength.

One remarkable difference between the chirp waveforms of a free running and an
injection-locked VCSEL shown in Fig. 7-2 is the polarity flipping of the transient
chirp from “positive” to “negative”, which manifests itself as negative frequency
deviation on the rising edge and positive deviation on the falling edge. This presents
a significant advantage for transmission over SSMF due to the narrowing rather than
the broadening of the pulse in its initial stage of propagation. We found that the
reason for the negative chirp from directly-modulated OIL VCSEL is data pattern
inversion. This phenomenon is repeatedly observed on different devices when the
coupling lensed-fiber is spatially adjusted. The VCSELs used in the experiment have
an aperture size of 5 mm [133]. The pattern inversion occurs when the lensed-fiber is
slightly off the center of the laser aperture, where the fundamental transverse mode
emission is the strongest. We attribute this phenomenon to modal competition, as
discussed in [134], where optical data inversion was achieved by injecting a
modulated master laser to lock onto a higher order transverse mode of a slave
VCSEL. However, in our case, the VCSEL is directly modulated by a large signal
113
and the locking is on the fundamental mode. The modulation is thus transferred to
the injection ratio (P
master
/ P
slave
) with an inverted pattern, because bit “1” gives a
large P
slave
. With the 5-mm aperture, the VCSEL waveguide actually supports higher
order transverse modes, although it emits a single fundamental mode under free-
running condition due to a larger match of the gain and the modal profile. However,
if the lensed fiber is moderately tuned away from the center of the aperture, the
external light injection will possibly excite a higher order transverse mode of the
device. A higher order transverse mode usually possesses a wavelength 5-nm shorter
than that of the fundamental mode. The wavelength of the external injection light,
however, is usually close to the fundamental mode with the aim of locking the lasing
mode of a free-running laser. When the current applied to the VCSEL is a bit “0”,
the injection ratio is high, and the fundamental mode is locked due to the wavelength
alignment, despite the spatial preference of the higher order mode. Therefore, the
output is relatively high in intensity (output bit “1”). Whereas if the current applied
to the VCSEL is a bit “1”, the injection ratio is low, the spatial coupling may be
more effective such that it excites some of the higher order transverse modes. Thus,
the fundamental mode output power, which is still the locked output, is reduced,
leading to a bit “0”. This results in the inversion of the data pattern.

In order to demonstrate the benefit of the adjustable negative chirp, we perform
chromatic dispersion tolerance comparison between free running and OIL VCSELs
by transmitting 10-Gb/s signals through SSMF with variable lengths. Fig. 7-5 shows
114
the BER measurements of the same OIL VCSEL at 10-Gb/s. After 25-km SSMF, the
power penalty reduction reaches its maximum and a 4-dB penalty improvement is
achieved at a BER of 10
-9
. Even 100-km SSMF transmission shows no penalty for a
BER of 10
-9
. These results can be explained by the fact that negative frequency
chirping interacts beneficially inside the SSMF. The pulse initially narrows as it
propagates inside the fiber and reaches a minimum width at a certain distance (25-
km in this case). After that, the pulse starts to broaden due to the onwards dispersion.
The three inset eye diagrams in Fig. 7-5 clearly show pulse narrowing after 25-km
transmission and broadening after 100 km.

Fig. 7-5. BER measurements and error-free eye diagrams of an OIL VCSEL with
back-to-back, 25-km and 100-km SSMF transmission.
Figure 7-6 quantifies the power penalty with increased SSMF distance. Due to the
large positive adiabatic chirp, the 10-Gb/s free-running VCSEL can transmit no more
than 5 km with more than 4-dB power penalty. Even for a 10-Gb/s commercial DFB
115
directly modulated laser (DML) with standard smaller positive chirp, the
transmission distance is still limited to be less than 20 km for a 4-dB power penalty.
For OIL VCSELs, even though there is some back-to-back penalty (due to extinction
ratio degradation), the signal is actually regenerated because of the negative chirp,
and there is no observed penalty after 125-km of uncompensated SSMF
transmission. This performance is more than 10 times better than that of a free-
running VCSEL or a DFB DML [135].

Fig. 7-6. Power penalty vs. SSMF transmission distance for free-running VCSEL,
commercial DFB DML and OIL VCSEL.

7.2 Multifunctional generation of ultra-wideband (UWB) signals,
format conversion, and data-clock recovery using OIL-VCSELs
116
A desirable hallmark of optical subsystems is the ability to perform various types of
functions by simply adjusting one of the control parameters of a device. As a simple
example, the basic Mach-Zehnder interferometer (MZI) structure has functional
utility as an amplitude modulator, phase modulator or optical filter, depending on the
bias and structural conditions [136]. Such ability to reconfigure the functionality of
an optical module greatly increases its cost-effectiveness. Moreover, performing any
function at high speed beyond 10-Gb/s enhances its value in high-capacity systems.

Ultra-wideband (UWB) has attracted considerable interest for short-range, high-
throughput wireless and sensor networks due to its intrinsic immunity to multipath
fading, high data capacity and low power consumption. UWB-over-fiber, which
offers undisrupted and high-rate service across different networks, has ignited
research interests in generating UWB in the optical domain. Photonic generation of
UWB signals has been demonstrated using either external phase modulators or
semiconductor optical amplifiers via phase-to-intensity conversion [137]. On the
other hand, optical data-format conversion and clock recovery have been considered
as indispensable functions for interfacing networks, and are realized using various
nonlinear elements [138]. However, the above three functions have not been shown
using the same basic structure in a single device that can be readily reconfigured.

In this section, we propose and demonstrate multifunctional operation of an
injection-locked VCSEL, showing UWB-monocycle generation, data-format
117
conversion, and clock recovery. Both single-mode and multi-mode VCSELs are
shown to be capable of functional reconfiguration. The key mechanism is using a 10-
GHz tunable interferometer to selectively filter out the distinctive time-resolved
frequency chirp after optical injection locking. Polarity-switchable UWB
monocycles are generated with a 5.1 GHz center frequency and a fractional
bandwidth of 129%. NRZ to pseudo-RZ (PRZ) format conversion is generated from
either the rising or falling edge detection. A 10-GHz clock tone with a 35 dB
suppression ratio is also generated from a 10-Gb/s NRZ input.

7.2.1 Concept and working principle
As shown in section 7.1, The OIL-VCSEL features significantly reduced frequency
chirp compared to a directly modulated VCSEL, as well as controllable chirp
polarity and magnitude. By passing the OIL-VCSEL through a delay-line
interferometer (DLI), we propose in Fig. 7-7 the concept of generating multiple
functions by simply reconfiguring the detuned positions of the DLI which selectively
filters one or more of the blue-chirped, the red-chirped or the center frequency
components. If either the blue chirp or the red chirp is selected while the center
frequency component is maintained, polarity-switchable UWB monocycles can be
generated, which can find value in access networks where UWB-over-fiber and
wireless/optical convergence is emerging. If either the blue chirp or the red chirp is
selected but the center frequency component is suppressed, either rising or falling
edges of the original data signal are detected and thus NRZ-to-PRZ format
118
conversion can be realized. If both the blue chirp and the red chirp are selected but
the center frequency component is suppressed, a strong clock at the data rate can be
recovered from the original data signal, which can be used for 3R regeneration, clock
and data recovery, or even optical logic gates applications.

Fig. 7-7. Concept of multifunctional generator using OIL-VCSEL followed by a
delay-line interferometer (DLI). Three unique and reconfigurable functions are
achieved by utilizing the adjustable-chirp from the OIL-VCSEL and subsequent
tunable filtering.

119
7.2.2 Experimental setup and time-resolved chirp measurement
The experimental setup is shown in Fig. 7-8. A distributed feedback (DFB) laser
serves as the master to injection-lock a 1.55-mm VCSEL. Both single-mode (SM)
and multi-mode (MM) BTJ-LW VCSELs, with optimized high-speed design [139],
are used. An optical circulator is used for unidirectional locking. The VCSEL is
directly modulated at 10-Gb/s, with a 2
15
-1 PRBS NRZ-data or programmable
pattern. The DFB current is adjusted to control the power into the VCSEL. A 10-
GHz all-fiber delay-line interferometer is place after the OIL-VCSEL to serve as a
tunable filter. The Advantest interferometric-based chirp-form analyzer together with
a digital sampling oscilloscope is used to obtain the time-resolved chirp and intensity
waveforms. A 10-GHz photodiode followed by a radio frequency spectrum analyzer
(RFSA) is used to measure the RF spectrum for various functions.

Fig. 7-8. Experimental setup of multifunctional generator using a chirp adjustable
injection-locked VCSEL followed by a tunable interferometer.
120
We show in [125] the “data inversion” state, which is essential to achieve dispersion
tolerance enhancement. By further increasing the power injection ratio and adjusting
the detuning value so that the VCSEL carrier density is in between the gain and loss
regime [140], we are able to achieve a “transition state” as shown in the intensity
axis of Fig. 7-9. The peak-to-peak chirp is reduced to ~ 1 GHz compared with that of
the data inversion state, yet with unchanged polarity of the chirp [125], even though
a bit of asymmetry exists.

Fig. 7-9. Time-resolved frequency chirp measurement of OIL single mode VCSEL
under the transition state, which has residual IM.

7.2.3 Polarity-switchable UWB-monocycle generation
The transition state, which manifests itself as having small residual intensity
modulation and reduced extinction ratio, is essential for the generation of UWB-
monocycles. Fig. 7-10 (a) and (b) are the input 10-Gb/s NRZ data signal and the OIL
121
transition state, respectively. By detuning the DLI in such a way that the OIL signal
is sitting on either the positive or negative linear slopes of the filter and selecting
either the blue chirp or red chirp and attenuates the other, polarity switchable optical
temporal differentiators [141] corresponding to the input data signal are generated as
shown in Fig. 7-10 (c) and (d).

Fig. 7-10. Polarity-switchable differentiator from positive or negative slope of DLI
using a single mode VCSEL with injection locking.
Realizing that multi-mode VCSELs become single mode after OIL [142], we choose
to use a multi-mode VCSEL with 10 mm aperture and three existing transverse
modes to demonstrate UWB-monocycle generation, in order to show the cost-
effectiveness with multi-mode VCSELs as well as the promising UWB-over-multi-
mode-fiber access network applications [143]. After programming the input data
pattern to be “1000000000000000” (one “1” per 16 bits), we obtain one polarity of
122
UWB-monocycle waveform in Fig. 7-11 (a) when the DLI is blue shifted by 0.04 nm
relative to the center frequency of the OIL data signal. The upper FWHM is 87 ps
while the lower is 83 ps. Fig. 7-11 (b) shows the other polarity of the UWB-
monocycle when the DLI is red shifted by 0.04nm. The 93 ps upper FWHM and 78
ps lower FWHM also exhibit a bit of asymmetry which is mainly due to the
asymmetric chirp from the OIL signal.

Fig. 7-11. Measured UWB signals using OIL multi-mode VCSEL.
Figure 7-12 shows the RF spectrum of the monocycle in Fig. 7-11 (a). The center
frequency is measured to be 5.1 GHz and the 10 dB bandwidth is about 6.6 GHz
(from 0.8 GHz to 7.4 GHz). This means that the generated monocycle pulse has a
fractional bandwidth of 129%, which well suits the FCC definition of UWB signals.
In addition, the frequency tone spacing is 0.625 GHz, which equals the repetition
rate of the input pulse train.

123

Fig. 7-12. RF spectrum of the UWB-monocycle of Fig. 5 (a), showing 129%
fractional bandwidth at 5.1 GHz.

7.2.4 NRZ-PRZ format conversion and NRZ-data clock recovery
By further detuning either side of the DLI by 0.06nm from the center frequency of
the OIL data signal, we are able to suppress the center frequency components of the
original transition state signal, and further enhance the desired chirped components.
Fig. 7-13 (a) and (b) show the detection of either the rising or the falling edge of the
original signal, respectively. The detected edge signal behaves like RZ format, as
compared to the original NRZ signal. Fig. 7-13 (c) shows the original NRZ eye
diagram and the rising-edge detected PRZ eye diagram, demonstrating the capability
of our proposed multifunctional generator for NRZ-to-PRZ data format conversion,
which is useful for clock tone detection and retiming.
124

Fig. 7-13. (a) Rising-edge detection. (b) Falling-edge detection. (c) Eye diagrams of
NRZ and format converted RZ from the rising-edge detection.
Due to the spectral periodicity of the DLI, if the signal is placed at the notch of the
DLI spectrum, both the blue and red-chirped components are enhanced while the
center frequency is notched out. In this way, the detection of both rising and falling
edges of the original 10-Gb/s NRZ data is realized and shown in Fig. 7-14 (a). The
corresponding RF spectrum is shown in Fig. 7-14 (b), featuring a 10-GHz recovered
clock with > 35 dB suppression ratio and 0.3 MHz tone spacing, corresponding to
the original 10-Gb/s data with 215-1 PRBS.

Fig. 7-14. (a) Edge detection of both rising and falling edges. (b) RF spectrum
showing the recovered 10-GHz clock and the 0.3-MHz tone spacing.

125
7.3 Dynamic bandwidth allocation using a bandwidth-tunable
MEMS-actuated micro-disk resonator filter
Wavelength-selective devices are crucial building blocks for many types of
wavelength-division-multiplexed (WDM) optical communication systems. Since
wavelength determines the routing in a typical WDM network, the ability to
manipulate the spectral characteristics of in-line devices can be quite advantageous.
These components are commonly optical filters, wavelength (de)-multiplexers and
add/drop modules. The often-reported optical spectral manipulation is to tune the
center wavelength of a device, such that a given wavelength data channel will either
be added, dropped or passed.

Fig. 7-15. Conceptual diagram of system-level applications of a tunable bandwidth
optical filter for dynamic bandwidth allocation: (i) Efficient allocation for variable
bit-rate systems; (ii) Optimization of OSNR using matched optical filtering for a
specific data-rate; (iii) Reconfigurable channel banding for common routing, signal
processing of data channels.
126
However, tuning the spectral width of the device pass-band has been quite a
challenge for device researchers. The highly laudable systems application of a
bandwidth tunable filter would include any type of dynamic bandwidth allocation for
optimal spectral efficiency, as conceptually shown in Fig. 7-15. (i) Variable bit-rate
channels: Coexistence of hybrid bit-rates and data-formats is highly likely in
heterogeneous optical systems. A bandwidth-tunable filter will enable efficient
allocation according to incoming data-rates and formats [144], (ii) Matched optical
filtering: for a static system that runs at a specific bit-rate, one would like the ability
to optimally filter this single channel to minimize the power penalty without wasting
excess bandwidth [145], and (iii) Reconfigurable channel banding: the ability to
dynamically route either a single data channel or a contiguous set of data channels to
a specific destination will enable advanced network routing and signal processing
functionalities [146]. Reconfiguration granularity determines the highest banding
resolution and is thus essential for efficient channel banding. To date, there have
been a few published reports of devices that are tunable in bandwidth and center
wavelength [147-150]. These reports showed the spectral static-tuning
characteristics. However, there has been little report of system performance
evaluation for actual data traffic being transmitted through the unique devices under
different bandwidth and wavelength conditions.

In this section, we experimentally demonstrate dynamic bandwidth allocation of
matched optical filtering, tunable channel banding and wavelength de-multiplexing
127
using a novel add/drop optical filter based on a MEMS-actuated microdisk resonator.
The filter bandwidth can be dynamically adjusted by voltage tuning the gap spacing
between the microdisk and the two waveguides. Error-free (10
-9
BER) data
transmission for matched optical filtering of a 5-Gb/s non-return-to-zero (NRZ) data
channel is demonstrated. Reconfigurable channel banding of three 2.5-Gb/s NRZ
data channels is achieved by either routing a single or a group of data channels. De-
multiplexing of three WDM channels under the worst-case scenario shows more than
14.5 dB suppression ratio with error-free operation.

7.3.1 Theory of bandwidth-tunable filter

Fig. 7-16. Principle of the MEMS-actuated microdisk resonator filter. The
bandwidth of the filter can be tuned by controlling the gap spacing, which results in
changing the power coupling ratio.
128
The bandwidth-tunable filter consists of a high-Q microdisk resonator (R=20 mm),
an input and an output deformable waveguide whose cross section is 0.8mm by
0.25mm. The waveguide is suspended around the microdisk and the gap spacing is
defined as the distance from the waveguide to the edge of the microdisk, as shown in
Fig. 7-16. Upon MEMS actuation, the waveguide is deformed and attracted towards
the microdisk. The gap spacing is thus reduced and the power coupling ratio κ
1
and
κ
2
is changed accordingly. Therefore, the device operation from under- to over-
coupling is achieved. Correspondingly, the resonant wavelength is switched from the
through port to the drop port. Device details can be found in [151].

According to the time-domain coupling theory [152], the amplitude transfer function
of the drop port is expressed as,
[7.1]
where w
0
is the resonant frequency, T is the round-trip time and g is the round-trip
loss. By biasing with different voltages, the MEMS actuators can independently
control the two gap spacing, and thus the coupling ratio κ
1
and κ
2
, between the
waveguides and the microdisk. In general, as both κ
1
and κ
2
are much larger than the
resonator loss g, the filter bandwidth and extinction ratio increase with coupling ratio
if κ
1
matches κ
2
, which is known as wide-band operation. On the other hand, for
narrow-band operation, to achieve maximum extinction in the through port, κ
1

(input) should be equal to the sum of κ
2
(output) and γ. This can be verified by the
129
time-domain coupling theory. Based on the equation, the lower limit of the
bandwidth is bounded by the intrinsic micro-resonator loss whereas the maximum
achievable bandwidth is limited by the phase matching between the microdisk and
the waveguide. The filter center wavelength can be changed independently by
temperature tuning (0.1 nm/°C).

7.3.2 Experimental results of dynamic bandwidth allocation

Fig. 7-17. Experimental setup of both single and WDM channel systems for the
demonstration of dynamic bandwidth allocation functions.
The experimental setup of both single and WDM channel system is shown in Fig. 7-
17. For the single channel case, one tunable laser source (TLS) is externally
modulated by 5-Gb/s NRZ 2
23
-1 PRBS data signals. For the WDM case, three
tunable laser sources are modulated by 2.5-Gb/s 2
23
-1 PRBS NRZ signals. RF delay
lines and single mode fibers (SMF) are used for de-correlation among channels. The
input signals are controlled to be TE polarized by a polarization controller and a
130
polarizer followed by a quarter wave plate (QWP). Spherical lensed fibers with spot
size of 2.5 mm are used as the input and output fibers. For this specific experiment,
the sample dependent micro-resonator filter has a tunable bandwidth range from 5 to
12-GHz. Wider tuning ranges from 12 to 41-GHz [149] and from 2.8 to 78.4-GHz
[150] can be utilized for higher-bit-rate operation. The pre-amplified receiver is used
for bit-error-rate (BER) characterization.

Fig. 7-18. Matched optical filtering: One 5-Gb/s NRZ data signal is passed through
the MEMS-actuated microdisk resonator filter. The filter bandwidth is tuned so that
the system power penalty is minimized.
Matched optical filtering is demonstrated on a single 5-Gb/s NRZ data signal. By
bandwidth tuning the MEMS-actuated microdisk resonator filter, we investigate the
system power penalty at 10
-9
BER as a function of the tunable pass-band (Fig. 7-18).
The optimum bandwidth (corresponds to minimized power penalty) is found to be
131
10-GHz. A smaller bandwidth cuts down higher frequency components and leads to
inter-symbol interference due to pulse broadening. For wider bandwidth, the small
penalty comes from the additional amplified spontaneous emission (ASE) noise.
Furthermore, the nonlinear phase response determines the dispersive properties of
these filters [151], and might distort the signal and lead to system degradation [153].
This limitation will likely prevent the filter from being an optimal matched filter.

Fig. 7-19. Reconfigurable channel banding: The filter is adjusted to either route a
single data channel (when the bandwidth is 6.5 GHz), or a group of two data
channels (when the bandwidth is opened up to 9.5 GHz).
Reconfigurable channel banding is demonstrated on a WDM system consists of three
2.5-Gb/s NRZ data signals at a fixed channel spacing of 7.5 GHz, as shown in the
experimental setup of Fig. 7-17. The bandwidth-tunable filter is adjusted to either re-
route a single channel (“Band 1”) or a group of data channels (“Band 2”), with the
bandwidth tuned to be either 6.5 GHz or 9.5 GHz, respectively (Fig. 7-19). When
only one channel is selected (“Band 1”), the extinction ratio is 14.5 dB with respect
to the adjacent channels. When two channels out of three are selected and routed
132
(“Band 2”), the filter bandwidth needs to be opened up to 9.5 GHz and the center
wavelength is tuned to the middle of the two channels. The extinction ratio shown in
the spectrum of Fig. 7-19 is 13.9 dB. Note that wider bandwidth tuning ranges [149-
150] will allow higher-speed operation and accommodate more flexible channel
banding situations.

Fig. 7-20. Error-free wavelength de-multiplexing: Spectrum on the left shows 14.5
dB suppression ratio under the worst-case scenario. BER measurement shows error-
free operation.

De-multiplexing three 2.5-Gb/s WDM channels is demonstrated under the same
condition as in the above channel banding experiment. Fig. 7-20 (a) and (b) show the
spectrum of the 3 channels before and after de-multiplexing. By adjusting the filter
bandwidth to be 6.5 GHz and temperature tuning the center wavelength, we are able
to effectively select and detect the middle channel, which corresponds to the worst-
case scenario due to the most channel crosstalk from its neighborhood. The
suppression ratio between the middle and the adjacent channels is 14.5 dB. Error-
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free de-multiplexing is achieved and the BER results are shown in Fig. 7-20, even
for this worst-case scenario.

As a final remark of this chapter, novel optoelectronic devices prove themselves to
be valuable in achieving some advanced and novel functions, which are not easily
reconfigurable in traditional optoelectronic devices. One of the goals for system
engineers to always keep in mind is the realization of multiple functions in a single
device, which can find great potential in future functional integration for optical
networks and versatile optical signal processing.

134
Chapter 8
Design and demonstration of novel polarization-based
optical components and instruments
Polarization is one of the fundamental yet unique properties of a transverse wave
such as light. Polarization is used in areas of science and technology dealing with
wave propagation, such as photonics, seismology, and fiber-optic
telecommunications. For electromagnetic waves, polarization is described by
specifying the direction of the wave’s electric field. According to the Maxwell
equations, the direction of the magnetic field is uniquely determined for a specific
electric field distribution and polarization.

When considering polarization in the field of photonics and fiber-optic
communication systems, it can find pretty interesting applications such as
polarization-based optical signal processing for the design of novel optical
components and photonic measurement instruments.

This chapter summarizes two research projects mainly done during my internship
experience at General Photonics Corp. Section 8.1 describes the first project which
utilizes unique polarization information for the design of a novel polarimeter-based
optical spectrum analyzer, which is capable of measuring fast-swept laser sources.
Section 8.2 shows a novel all-optical method to automatically de-multiplex
135
polarization-division-multiplexed (PDM) optical systems. By using this technique,
we experimentally demonstrate the transmission of 1.12-Tb/s (14 channels at 40-
Gb/s with doubled capacity) systems over more than 60 km of transmission distance.

8.1 Novel polarization-based fast-swept optical spectrum analyzer
Traditional optical spectrum analyzers (OSAs) are usually realized using one of the
following three methods: 1) a spatially dispersive element, such as a diffractive
grating, 2) a tunable narrow-band filter, such as a Fabry-Perot (F-P) resonator or a
tunable fiber Bragg grating, and 3) path-length-difference varying interferometer
(Michelson or Mach-Zehnder) followed by FFT analysis [154-156]. However, design
tradeoffs exist among the resolution, the spectral range, and the measurement speed
[157], and therefore it is difficult to achieve all three parameters simultaneously. For
example, the spectral resolution and the measurement range (free spectral range) of
an F-P filter based OSA are inversely proportional to each other. In order to achieve
fine resolution, the spectral range tends to be sacrificed. Improved resolution and
dynamic range are possible with coherent analysis techniques, yet it requires an
advanced swept local oscillator with polarization control [158]. Furthermore, for fast
swept tunable lasers with a scanning range of > 160 nm and a sweeping rate of tens
of kHz, it is desirable to measure the changing wavelength as a function of time.
Unfortunately, none of the method described above can simultaneously meet the
speed, resolution, and range requirements for characterizing such a swept tunable
laser. For example a diffraction grating based spectrum analyzer with a CCD can be
136
sufficiently fast, however, its resolution or range is not sufficient due to limitations
imposed by the size of the CCD and the appearance of higher diffraction orders from
the grating when the spectrum range is too large or when the grating period is too
small.

In this section, we propose and demonstrate a novel polarimeter-enabled optical
spectrum analyzer (P-OSA). Our method is based on analyzing both the state of
polarization (SOP) as well as the degree of polarization (DOP) information of the
light source after it passes through a variable differential group delay (DGD) module.
Thanks to the high-speed polarimeter [159], our proposed P-OSA can readily
achieve a measurement speed on the order of MHz, and is therefore capable of
measuring the center wavelength of a fast scanning laser as a function of time. The
measurement speed is limited only by the bandwidth of the photo-detectors, the RF
amplifiers, and digital processing electronics, and can be up to tens of GHz in
principle [160].

Another unique and attractive feature of the P-OSA is that it can determine the
direction of the frequency change, a capability unobtainable with most of the
conventional spectrum analysis methods. Consequently, the P-OSA is capable of
having arbitrarily high frequency resolution, yet, with arbitrarily large spectral range,
provided that the measurement speed is sufficiently fast compared with the rate of
the SOP change caused by the spectral change of the light source and that the signal-
137
to-noise ratio in P-OSA’s detection circuit is sufficiently high for accurate SOP
measurement. Such a feature opens a wide door for many spectral related
measurements not imaginable with conventional spectrum analysis methods.

Finally, we show that the P-OSA can measure the spectral shape (power vs.
frequency) of a swept-wavelength light source. With this unique capability, we
report the generation of a 3-D plot of the spectral shape of a modulated light signal
as a function of center wavelength of a wavelength-scanned light source. This
capability enables detailed spectral characterization of a fast swept-wavelength
source that cannot be obtained with other conventional methods.

8.1.1 Swept-Frequency (Wavelength) Measurement
The basic concept of the P-OSA for measuring the instantaneous wavelength of a
swept laser source is shown in Fig. 8-1(a), where the input light source first enters a
fixed differential group delay (DGD) element (e.g. a birefringent crystal) before
being analyzed by a high-speed polarimeter. It is known that when a tunable light
source passes through a DGD element, its SOP will trace a circle on the Poincare
sphere when the wavelength of the light source is tuned [157, 161], as shown in Fig.
8-1(b). The rate of the SOP change as a function of frequency is determined by the
value of the DGD element. Therefore, one can obtain the DGD value from the SOP
trace on the Poincare Sphere.

138
If we choose a precisely known DGD element, by using the reverse effect, the
frequency of the light source can be determined from the SOP trace on the Poincare
sphere. Let τ be the value of the DGD element, the complex amplitude of the
electrical field of the light after the DGD element can be expressed as,
[8.1]

where and are the amplitudes of the electrical field along the x and y
directions of the chosen coordinate system, and are the unit vectors along the x
and y directions, and is the common phase term.

Fig. 8-1. Concept of the proposed real-time polarimeter-based optical spectrum
analyzer used for a swept-wavelength source.
If , the SOP will trace a largest circle on the Poincare sphere, as shown in
Fig. 1(c), resulting in the highest frequency measurement resolution or sensitivity.
When considering two specific frequency values, f
1
and f
2
, during a wavelength
139
sweep, the angular difference, denoted as Δθ, between the two polarization states of
these two different frequencies is simply the phase difference in Eq. [8.1], which can
be expressed as,

[8.2]
For a known differential delay , the frequency difference can be calculated from
the SOP angular difference on Poincare Sphere as,

[8.3]
Figure 8-1(d) shows the working principle of the swept-wavelength operation mode.
The high-speed polarimeter collects the time-resolved SOP traces, which carries the
detailed polarization evolution information. Based on the known DGD value, one
can translate the SOP traces into the instantaneous wavelength evolution by
calculating the polarization rotation angle on the Poincare sphere using Eq. [8.3].
For conventional OSAs, such as those based on F-P interferometer, free spectral
range (FSR) is defined as the spacing between the periodic passbands. The FSR
usually determines the spectral measurement range of the analyzer. One of the major
tradeoffs for the conventional OSAs is that the FSR is always inversely proportional
to the spectral resolution. This means that the high spectral resolution will always
result in limited measurement range.

For our proposed P-OSA, if we consider that the SOP resolution is 0.36 degree, we
can have 360/0.36 = 1000 points resolved in a full circle (one-cycle) on the Poincare
Sphere. From Eq. [8.3], we can see that for a given τ, the resolution for measuring
140
the center frequency and the one-cycle measurement range of the polarimeter based
spectrum analyzer are,
Frequency Resolution: [8.4]
One-Cycle measurement range: [8.5]
As an example, for a DGD value of 1000 ps, the frequency resolution will be 1 MHz,
and the one-cycle measurement range will be 1 GHz. The tradeoff between the
resolution and the range still exists if we consider only one-cycle on the Poincare
sphere. However, since the SOP circle will be able to repeat itself on the sphere if the
frequency variation range is larger than , we can utilize the valuable
information of the direction of the SOP evolution. By combining Eq. [8.5] with the
SOP direction information, we obtain the following equation as the total
measurement range by the multiplication of the SOP cycle number,
Total measurement range: [8.6]
where N can be any arbitrarily large integer number.

This results in the unique feature of arbitrarily large spectral range, without any
compromise to the spectral resolution. Since only the value of the fixed DGD
element determines the spectral resolution, one can simply improve the resolution by
introducing arbitrarily large DGD element without sacrificing the measurement
range. The proposed P-OSA is thus not limited by the traditional tradeoff between
the spectral range and frequency resolution.

141
As shown in Fig. 8-2, we choose two representatives as the swept input source. The
first one is a spectral spliced ASE source using a high speed Fabry-Perot tunable
filter [162] (up to 40 KHz sweeping speed). The second swept source is the HP
8164A tunable laser source (TLS) with a sweep step size of 0.05 nm and a dwell
time of 0.1 second. A 5.7-ps birefringent crystal is applied as a fixed DGD element,
with input adjusted by a polarization controller for equal power splitting between
two eigen polarization states. The output port of the DGD element is directed to the
General Photonics’ high-speed DSP in-line polarimeter (POD-101D) for real-time
Poincare sphere display and SOP trace recording at a sampling rate ~1 MHz [159].

Fig. 8-2. P-OSA experimental setup for analyzing two types of swept sources. Note
that only one source is connected at a time. The SOP of the input light is adjusted to
45 degrees with respect to the birefringent axis of the DGD
Figure 8-3 and Fig. 8-4 show the results of the swept-wavelength input using a high
speed F-P filter based spectral-slicing source. A high power EDFA with output of
~15 dBm is used as the ASE source. The sweeping wavelength range of the high-
speed tunable filter is properly adjusted using a function generator, with frequency,
amplitude and offset matched to the EDFA gain bandwidth. Fig. 8-3(a) shows the
142
modulation of one (S1) of the recorded Stokes parameters from the polarimeter when
the tunable filter is swept at 1 KHz rate. The amplitude and the offset from the
sinusoidal function generator are set to be 10 V and 3.5 V, respectively. By utilizing
the directional SOP evolution, we obtain the accumulated polarization rotation angle,
as shown in the right Y-axis of Fig. 8-3(b). Note that the multiple full circle of the
SOP modulation can be correctly interpreted to the accumulated rotation angle. From
Eq. [8.3], we further derive the swept wavelength as a function of time (in the left Y
axis of Fig. 8-3(b)) from the accumulated polarization angle. The starting wavelength
is determined using a spectrum analyzer. In practice, we can utilize a tunable DGD
element and obtain the reference wavelength using the method described later. We
can see that the swept wavelength curve resembles well with the sinusoidal sweeping
function and the time period is determined by the swept frequency of 1 KHz.

Fig. 8-3. 1-KHz tuning F-P filter (a): SOP (S1) trace. (b): swept wavelength. Note
that the starting wavelength is obtained from a commercial spectrum analyzer,
although the P-OSA can also determine the absolute starting wavelength directly, as
described in the next section.
Figure 8-4 (a) shows one of the recorded Stokes parameters from DSP polarimeter
when the tunable filter is swept at a higher rate of 10 KHz. The amplitude and the
offset of the function generator are 5 V and 4.5 V, respectively. Fig. 8-4 (b) shows
143
the derived swept wavelength as a function of time. A period of 100 ms proves the
swept frequency of 10 KHz. Due to the limited sampling rate of the DSP
polarimeter, the recovered SOP trace can not be as smooth as that of the 1-KHz case.
Improved results are expected if the sampling rate of the polarimeter is increased.
The reduced SOP modulation cycle, and thus the reduced swept wavelength range, is
due to the smaller amplitude swing applied to the F-P filter.

Fig. 8-4. 10-KHz tuning F-P filter (a): SOP (S1) trace. (b): swept wavelength. Note
that the starting wavelength is obtained with a commercial spectrum analyzer,
although the P-OSA can also determine the absolute starting wavelength directly, as
described in the next section.

Fig. 8-5. POD-101D oscilloscope mode. SOP evolutions are recorded when the input
is swept at a speed of 0.1 sec.
144
Figure 8-5 and Fig. 8-6 show the results of the swept-wavelength input using HP
8164A. Fig. 8-5 shows the screen shots of the oscilloscope mode of the POD-101D,
where the SOP traces (S0, S1, S2, S3) are recorded. Remarkably, the SOPs not only
describe the sinusoidal behavior when the input HP 8164A light source is 0.05 nm
step swept, but also the “spiky” details when the wavelength is stepped from one
value to the next.

Fig. 8-6. Instantaneous wavelength and power as the input light source is swept at a
speed of 0.1 sec. The starting wavelength is from the setting of the commercial
tunable laser. Note that the transient dynamics of the swept laser source can be
clearly revealed, as shown in the inset.
Based on the sampled SOP traces, we post-process the recorded SOP data by
calculating the accumulated polarization rotation angle, taking into account the
direction of the rotation. The polarization rotation angle can be further translated into
the time-resolved swept frequency, as shown in Fig. 8-6, where the instantaneous
145
wavelength is obtained from 1540 to 1560 nm using the periodic nature of the SOP
traces in Fig. 8-5. The starting wavelength is the setting of the tunable laser and its
value is not obtained from the analysis, although the P-OSA is capable of
determining the absolute wavelength as described in the next section. Note that
recording more SOP evolution circles can further increase the range. A zoom in of
the curve in Fig. 8-6 proves that a relatively low speed (0.1 second) swept source
actually has a fast transition time on the order of millisecond. This reveals that when
the light source is stepped from one wavelength to the next, it experiences a fast
initialization stage in which the wavelength is oscillating. It then quickly jumps to
the desired value within several tens of milliseconds. However, most of the time is
then used for wavelength locking and stabilization. From Fig. 8-5 and 8-6, we can
see that P-OSA exhibits the powerful capability of capturing the transient dynamics
of a swept source. This capability greatly surpasses those of the conventional OSAs.
The instantaneous power evolution is also measured from the time-resolved S
0
trace.

The direction of the SOP traces has another interesting usage for determining the
direction of the wavelength change. As can be seen from the inset of Fig. 8-6, the
fast oscillation (on the order of millisecond) occurred during wavelength
transitioning can be resolved in terms of the direction of the instantaneous frequency
changing, which can be well correlated to the SOP evolutions shown in Fig. 8-5.
This unique feature is also unobtainable with traditional OSAs, and can find
interesting applications in the field of swept spectral analysis.
146
8.1.2 Spectral Shape Analysis
Figure 8-7 shows the concept and principle of the proposed P-OSA used for
analyzing the spectrum of a fixed wavelength source. In this spectrum analysis
mode, a variable DGD element is applied and the spectrum of the light source is
analyzed by post-processing the recorded SOP and DOP information from the
polarimeter as the DGD is tuned. For a fixed wavelength input source, the
polarization rotation angle is a linear function of the DGD (τ) value. By curve fitting
the measurement data using Eq. [8.7], one can readily obtain the center frequency of
the light source.
[8.7]

Fig. 8-7. Concept and principle of the proposed real-time polarimeter-based optical
spectrum analyzer used for spectral shape analysis. Curve fitting of (A) determines
the center frequency while Fourier transform of (B) yields the spectral shape and
width. The spectral resolution is inversely proportional to the range of the variable
DGD.
147
In order to determine the spectral shape and width of the input source, we utilize the
DOP information of the light as the DGD value is varied from zero to well beyond
the coherence length of the source. Since the DOP is well correlated with the self-
correlation function of the light source [161], which in turn relates to the power
spectrum by the Fourier transform, we obtain the following expression of the power
spectrum for the case of equal power splitting between two principle polarization
states of the DGD element.
[8.8]
where S
0
is the total received power and w is the relative angular frequency. From
Eq. [8.7] and [8.8], one can conclude that for a fixed wavelength input, the spectrum
of the source can be obtained accurately by measuring both the SOP and the DOP as
a function of DGD, as shown in Fig. 8-7.

The experimental setup for the spectrum analysis of a fixed wavelength source is
shown in Fig. 8-8. In order to verify the capability of the proposed P-OSA, we
generate two interesting spectral features by modulating a narrowband tunable laser
using two on-off-keying (OOK) modulation formats (non-return-to-zero (NRZ) and
return-to-zero (RZ)) at 40-Gbit/s. The variable DGD module consists of a 2x2
polarization beam splitter (PBS) for splitting the input light into two orthogonal
polarization states (port 1  port 2 and 3) and combining them again at the output
(port 2 and 3  port 4). One motorized delay line (MDL), with a tuning range of 560
ps, is inserted in one of the arms. Both arms are path length matched when the MDL
148
is set at its origin. Two Faraday rotating mirror (FRM) are placed at the end of both
arms for ensuring polarization orthogonality and stability of the light in the two arms
when they recombine at the PBS. The output port of the PBS is directed to the DSP
in-line polarimeter. A polarization controller is placed at the input of the polarimetric
interferometer to ensure equal power splitting of the two arms when they recombine
at the PBS, and thus the largest SOP circle (shown in the inset) on the Poincare
sphere, resulting in the highest frequency resolution.

Fig. 8-8. Experimental setup for spectrum analysis of fixed wavelength source.
Figure 8-9 shows the experimental results of the spectra analysis operation of the P-
OSA. DOP of both the 40-Gb/s NRZ-OOK and RZ-OOK are recorded as the MDL
values are increased from 0 to 500 ps. This corresponds to 1000 ps DGD tuning
range due to the double pass configuration of the experimental setup. We can see
from the DOP vs. DGD curve that the NRZ-OOK curve remains almost constant
around 60% when the DGD is beyond 25 ps, while the RZ-OOK curve exhibits
149
periodic DOP natures due to the fact that it has pronounced 40-GHz tones and some
residual 20-GHz tones. By using conventional OSAs, Fig. 8-9 (b) shows the
measured spectra of both NRZ-OOK and RZ-OOK, which exhibits dominant 40-
GHz spaced tones and much wider spectrum width. Based on Eq. [8.7] and [8.8], we
obtain the spectra for the two different formats by processing the rotation angle for
center frequency as well as the DOP curve for spectral shape and width. Fig. 8-9 (c)
shows the derived spectra using our P-OSA method. For the same horizontal and
vertical scales, we can see that the P-OSA provides very similar spectra width and
shapes, with a much better spectral resolution due to the 1000-ps DGD tuning range,
which corresponds to a line-width resolution of less than 1 GHz.

Fig. 8-9. (a) Experimental results of DOP values when the DGD is changed from 0 to
1000 ps for both 40-Gb/s NRZ-OOK and RZ-OOK signals. (b) The measured OSA
spectra. (c) The derived P-OSA spectra for comparison.
The spectral shape and the width of a swept-wavelength source at each wavelength is
an important parameter, since it contains the coherence length information of such
sources for optical coherence tomography (OCT) applications [163]. However, they
150
cannot be directly measured with conventional OSAs [164]. In this subsection, we
demonstrate that the P-OSA can directly measure the spectral shape of a fast swept-
wavelength source, in addition to the measurement of the spectral shape (power vs.
frequency) of a fixed wavelength source, as described earlier. With such a
capability, we report a unique 3-D plot of the spectral shape of a wavelength-swept
light source with feature-rich spectrum as a function of its center wavelength.

Fig. 8-10. A 3-D plot using the proposed P-OSA. Swept wavelength is the added
dimension compared to the conventional OSAs. Note that the absolute wavelengths
are directly obtained with P-OSA via curving fitting.
Figure 8-10 shows the unprecedented 3-D display of our proposed P-OSA with an
added dimension of the swept wavelength or time. For the swept-frequency input,
every time the DGD module is tuned to a specific value, the SOP and DOP
information are recorded when the wavelength of the source is swept a full cycle. By
tuning the DGD element gradually from minimum to maximum value, we obtain the
whole set of SOP and DOP as two dimensional matrices with respect to both swept
151
wavelength values as well as tuned DGD points. By rearranging the two dimensional
matrices, one can display each spectrum at every swept wavelength using equation
[8.7] and [8.8]. For Fig. 8-10, during each wavelength scan ranging from 1540 to
1560 nm, we generate alternative 40-Gb/s NRZ-OOK or 40-Gb/s RZ-OOK
modulation formats so as to obtain feature-rich yet contrasting spectra. The RZ-OOK
spectrum shows a better distinguishable and equally spaced carrier tones, as well as a
much wider spectrum. This capability enables detailed spectral characterization of a
fast swept-wavelength source that cannot be obtained with any conventional
methods.

In summary, we have proposed and experimentally demonstrated a novel
polarimeter-based optical spectrum analyzer, which utilizes both the state of
polarization as well as the degree of polarization information of the light source after
it passes through a variable DGD element. The speed, measurement range and the
frequency resolution of the proposed P-OSA greatly surpass those of the
conventional OSAs. The high-speed capability is enabled by the fast sampling
polarimeter and is thus ideal for measuring the spectrum of fast sweeping laser
sources. This will find broad application in swept-source OCT imaging [164], as
well as in the measurement of time-resolved frequency chirping [165]. The large
measurement range and high-resolution capability are realized by utilizing the
unique information of the directional SOP evolution. This will be very useful for
measuring the spectra drift of ultra-narrow line width lasers. Finally, we have also
152
demonstrated a unique 3-D plot, which displays the spectral shape of a swept-
wavelength light source at each instantaneous wavelength.

8.2 All-optical automatic de-multiplexing of polarization multiplexed
1.12-Tb/s (14 channel x 40-Gb/s x 2) systems

Fig. 8-11. Illustration of a polarization division multiplexing (PDM) system.
Increasing the transmission capacity or spectral efficiency of an existing fiber system
without having to change any part of transmission hardware or software is an
attractive proposition for carriers or system operators, because it can significantly
reduce the system “down” time and minimize the equipment and installation cost for
system upgrade. One method for doubling the system capacity or spectral efficiency
is polarization-division-multiplexing (PDM), in which two independently modulated
data channels with the same wavelength, but orthogonal polarization states are
simultaneously transmitted in a single fiber [166-177]. At the receiver end, the two
polarization channels are separated and detected independently. Ideally, the operator
only needs to add a transceiver (identical to the existing ones in the system) and an
153
associated polarization multiplexer/de-multiplexer at each end of the fiber link, while
leaving the rest of the system, including fibers, amplifiers, repeaters, wavelength
MUX/DEMUX, optical add/drop multiplexers (OADM), switching optics, and even
the network management software, unchanged, as shown in Fig. 8-11, or with
minimal modification. Other methods of increasing system spectral efficiency, such
as reducing the channel wavelength spacing or increasing transceiver bit rate, require
significant system re-design, and are therefore not suitable for the upgrade of
existing systems, although they may be feasible for the implementation of new
systems.

Significant challenges remain for the practical deployment of PDM systems,
including finding an effective polarization de-multiplexing solution and overcoming
polarization crosstalk between the two polarization channels induced by polarization-
mode-dispersion (PMD) and polarization-dependent-loss (PDL). In this section, we
will concentrate on a cost-effective polarization de-multiplexing solution, assuming
that the PMD and PDL of the system are sufficiently low for polarization-
multiplexed transmission.

Polarization multiplexing is straightforward, requiring only a polarization beam
combiner (PBC) to combine two channels with orthogonal polarizations, as shown in
Fig. 8-11. However, separating the two channels with acceptable crosstalk at the
receiving end is nontrivial, because the polarization states of the two channels are no
154
longer linear, and change rapidly with time. It is possible to monitor the crosstalk of
the two channels in real time and then use the monitored information to dynamically
control the states of polarization (SOP) of the two polarization channels in order to
separate them with a polarization beam splitter. So far, no good method has been
found to monitor the crosstalk optically; therefore, one must rely on the detected
electronic signal in the receiver to monitor crosstalk. Previously proposed schemes
include (i) monitoring of clock tone or pilot tones [170-173] (ii) multi-level
electronic detection [174-175], and (iii) cross-correlation detection of the two de-
multiplexed channels [176]. Each of these schemes has one or more of the following
drawbacks: (i) it requires high-speed electronics, thereby making it bit-rate
dependent; and more importantly, (ii) it requires modification or even significant re-
design of existing transceivers, making it more difficult to upgrade existing systems.

In this section, we propose and demonstrate a simple all optical de-multiplexing
scheme to automatically separate the two polarization channels in PDM systems, as
shown in Fig. 8-12. Our approach requires only two low-speed photo-detectors, a
polarization controller, and the associated low-speed control circuits, making it bit-
rate and modulation-format independent. Specifically, we launch slightly different
amount of optical power into the two polarization channels. Using the detected
power difference between the two channels as the feedback signal to control the
dynamic polarization controller, the two polarization channels at the same
wavelength can be readily separated and then detected by two identical receivers.
155
This scheme requires no modification of the existing transmitter, receiver, or
transmission link. Even high-speed electronics are not required. All that a system
operator needs to do to double the transmission capacity of the link is to add a
transmitter card and a polarization beam combiner at the transmitting end, before the
wavelength multiplexer, and a receiver card and the polarization channel separator
described in this section after the wavelength de-multiplexer.

In the following, we first describe theoretically the new polarization de-multiplexing
scheme based on channel power imbalance. We then show our experimental
validation of the scheme by separating two polarization-multiplexed channels with a
power imbalance of just above 0.5 dB. Finally, we show the results of a successful
system demonstration of the scheme by doubling the transmission capacity of a
DWDM system containing 14 WDM channels at 40-Gb/s per channel over 62-km
LS (LEAF-Submarine by Corning Inc.) fiber transmission.

8.2.1 Concept and working principle
The conceptual diagram of the automated detection scheme for a PDM system is
shown in Fig. 8-12 [178]. Optical data streams with orthogonal SOPs (TX1 and
TX2) are generated from the same or different light sources at the same wavelength,
and are then multiplexed through a polarization beam combiner (PBC). During
signal transmission over a fiber link, the two linear SOPs evolve into elliptical SOPs
but still maintain their relative orthogonality, assuming that the fiber link has no PDL
156
and PMD. A dynamic polarization controller (DPC) followed by a polarization
beam splitter (PBS) is used to de-multiplex the two data streams of orthogonal SOPs.
Choosing the transmission axes of the PBS as reference coordinates x and y for
convenience, the corresponding Mueller matrix of the PBS can be expressed as,
[8.9]
[8.10]

Optical data stream with an arbitrary SOP can be expressed in Stokes space as,
[8.11]
where is the optical power, is the ellipticity angle, and is the orientation
angle of the ith optical data stream. After passing through the PBS, the Stokes
vectors along the x and y directions are and , respectively, where the first
row of each Stokes vector represents the optical power along the corresponding
direction. In particular,
157

Fig. 8-12. Conceptual diagram of proposed Polarization DEMUX using automated
feedback control (solid-line: optical path; dotted-line: electronic control). PBC:
polarization combiner, PBS: polarization splitter, BS: beamsplitter, DPC: dynamic
polarization controller, G1 & G2: electrical amplifiers, PD1 & PD2: photodetectors.

[8.12]
[8.13]
Since the two data streams are incoherent with each other (they are either generated
using two independent laser sources or are rendered incoherent by other means), the
optical powers emerging along the x and y-axes of the PBS are
[8.14]
[8.15]
For the two optical data streams with orthogonal SOPs and , the following
relationships hold,
[8.16]
[8.17]
Substituting Eq. [8.12] and [8.13] into Eq. [8.14] and [8.15] yields,
158
[8.18]
[8.19]
To automatically and effectively separate the two orthogonal data channels, we
monitor the relative optical power levels of the two channels by coupling a small
amount of the signal power into two low-speed photodetectors (PD1 and PD2).
Through low-noise electronic circuits (G1 and G2), the power difference between the
two polarization states ( ) is translated into the voltage difference ( ),
expressed as,
[8.20]
where α1 and α2 are the response coefficients of the two photo-detectors and their
corresponding amplification circuits. Through electronic gain balancing or software
calibration, they can be adjusted to be equal (α1 = α2 = α) and therefore the voltage
difference of Eq. [8.20] becomes
[8.21]
As long as there is a power difference between the two channels , the
voltage difference between the two power monitors depends on the orientation angle
θ and the ellipticity angle ε, which can be changed by the dynamic polarization
controller. Therefore, by maximizing the calibrated voltage difference ΔV, we can
effectively minimize the crosstalk and readily separate the two orthogonal channels
by forcing either a positive maximum [(θ = 0°, ε = 0°) or (θ = ±90°, ε = ±90°)] or a
negative maximum [(θ = ±90°, ε = 0°) or (θ = 0°, ε = ±90°)]. The positive maximum
159
corresponds to a Stokes vector of (1,0,0) while the negative maximum corresponds
to a Stokes vector of (-1,0,0).

8.2.2 Experimental Verification
We implemented this simple yet novel de-multiplexing scheme with a digital signal
processor (DSP) based circuit, a fiber squeezer polarization controller, a polarization
beam splitter, and two monitoring photo-detectors, as shown in Fig. 8-12. The two
monitoring photo-detectors obtain the voltage difference defined in Eq. [8.21] and
feed it back to the DSP circuit. Our DSP firmware then automatically instructs the
polarization controller to control the SOP to maximize the voltage difference (either
a positive or a negative maximum). The two polarization channels are considered
separated when the maximum voltage difference is reached and maintained.

Fig. 8-13. Concept proof using two static wavelength channels with different power
levels: here the power difference is ~ 0.5 dB (before Pol. DEMUX), and an ER of ~
28 dB is achieved with the proposed polarization de-multiplexing scheme (after Pol.
DEMUX). > 35 dB ER is possible as the power difference increases.
160
First we evaluate the concept using two static wavelength channels (~ 1-nm
separation) launched at two orthogonal polarization states with different power
levels. The reason for the use of different wavelengths is to distinguish the two
polarization channels with an optical spectrum analyzer (OSA). This does not affect
the result because the scheme is wavelength independent. After the polarization de-
multiplexer, we measure the extinction ratio (ER) using an optical spectrum
analyzer, as shown in Fig. 8-13. A stable ER of >28-dB can be achieved when the
power difference between the two channels is higher than 0.5 dB. For higher power
differences (e.g. >1-dB), a stable ER >35 dB is possible. The remaining crosstalk is
mainly due to electronic noise and the limits of the feedback accuracy, with the
upper limit determined by the ER of the PBS inside the polarization demultiplexer
(>40-dB).

Fig. 8-14. Evaluation of proposed polarization demultiplexing scheme in a single-
channel 10-Gb/s RZ back-to-back transmission setup. (a) Power penalties of both
polarization channels (PDM_H and PDM_V) as a function of power difference
between them. (b) Bit-error-rate (BER) curves as the power difference between two
orthogonal channels is set to 0.5 dB (i.e. the power of PDM_V is 0.5-dB higher than
that of PDM_H); the corresponding power penalties for the two orthogonal channels
compared to the case without PDM are ~ 0.25 dB and 0.75 dB, respectively. Square:
back-to-back without PDM. Circle: PDM-V. Triangle: PDM-H.
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We next use this polarization de-multiplexing scheme in a single-channel 10-Gb/s
back- to-back (i.e. no transmission fiber) transmission setup. The data signal is RZ
modulated from a short pulse laser source with a wavelength of ~ 1550–nm,
separated into two arms with orthogonal polarization states, and then combined into
one transmission port (fiber) using a PBC. Fig. 8-14(a) shows the power penalty of
the de-multiplexed signals as a function of the power difference between the two
orthogonal channels (PDM_V and PDM_H). As can be seen from the figure, the
power penalties of both polarization channels are less than 0.5 dB when the power
difference between the channels is larger than 1 dB. Even when the power difference
is 0.5 dB, the additional power penalties are only 0.25 and 0.75 dB for two
orthogonal channels. As an example, the comparisons of bit-error-rate (BER) curves
are shown in Fig. 8-14(b), with typical eye diagrams also inserted. The slight
deviation of BER curves below 10
-9
is mainly due to the response of the 10-GHz
receiver to the short-pulse laser source and to possible measurement instabilities.

8.2.3 PDM Transmission Systems with 1.12-Tb/s Capacity
To further evaluate the effectiveness of the proposed automated polarization de-
multiplexing scheme, we demonstrate a 1.12-Tb/s (14×2×40-Gb/s) PDM
transmission system over 62-km LS fiber with the experimental setup shown in Fig.
8-15(a). For this particular demonstration, we used 14 WDM channels with a
spacing of 0.8-nm (from 1546.8 nm to 1557.2 nm) operating at 40 Gb/s. In a
practical system, each wavelength channel should be comprised of two DFB lasers,
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two modulators, and a polarization beam combiner to multiplex the two polarization
channels into a single fiber before the combined signal enters the wavelength
division multiplexer (WDM) [170], as shown in Fig. 8-11. Alternatively, for
demonstration purposes, all 14 multiplexed channels can be separated into two
orthogonal polarizations by a PBS and then modulated by two independent
modulators, before finally being combined by a PBC. However, due to equipment
limitations, we further simplified the demonstration without losing generality as
follows: all fourteen channels are modulated at 40-Gb/s PRBS (2
11
-1) using a single
modulator (the spectra of all fourteen channels are shown in Fig. 8-15(b)) because
we only have one 40-Gb/s modulator in the lab. Each channel is separated into two
orthogonal polarization states (PDM_V and PDM_H with powers P1 and P2,
respectively) and multiplexed through the PBC with ~ 35 dB extinction ratio. One of
the arms incorporates a 1-km SMF to make sure that the two polarization channels
are incoherent with each other; this is sufficient because the coherence lengths of
transmission lasers are less than 1 km. The power difference is fixed at 1.0 dB (P
1
is
higher than P
2
). The input optical power into the 62-km LS fiber is set to be 4 dBm.
An optical filter with a bandwidth ~ 0.35 nm is used to select one of the channels.
Either of the two orthogonal data streams is chosen for bit-error detection at the
receiver end by activating the proposed Pol. DeMux via the feedback control of the
dynamic polarization controller. Although the Pol. DeMux module has two outputs,
we only need to measure the performance at one port by switching the control
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parameter (maximizing V1-V2 or V2-V1). The total 62-km LS fiber link has ~ 0.6-
ps PMD and ~ 0.15 dB PDL on average.

Fig. 8-15. Experimental demonstration of 14-channel 1.12-Tb/s WDM-PDM
transmission: (a) experimental setup; (b) optical spectrum of all 14 channels.
The performances of all 14 channels after the 62-km LS fiber are compared in Fig. 8-
16(a), for both polarization channels (PDM_V and PDM_H). The power penalties
are compared to the best channel receiver sensitivity measured at 10
-9
BER for the
back-to-back PDM transmission (~ 0.8 dB additional penalty compared to the back-
to-back transmission without PDM). Since the optical power of PDM_V is 1.0-dB
higher than PDM_H, with the contributions of both optical-signal-to-noise-ratio
(OSNR) and possible chromatic dispersion, the performance of PDM_V is better
than PDM_H by about 1 dB for all of the channels: the power penalties for PDM_V
ranges from 1.8 to 3.1 dB, while the power penalties of PDM_H range from 2.8 dB
to 4.2 dB. As a reference, the penalty for a regular WDM transmission over the
same 62-km link with the same setup is ~ 1.0-dB (40-Gb/s data rate). The relatively
high power penalties in the PDM transmission system may be due to the following
reasons: (i) intrinsic crosstalk between the two polarization states; (ii) imperfection
164
of the polarization tracking after transmission links; and (iii) link sensitivity (PMD,
PDL, etc.) of the PDM scheme itself. In addition, typical BER curves for one of the
fourteen channels are shown in Fig. 8-16(b).

Fig. 8-16. Transmission results (a) Power penalties of both polarization channels
(PDM_V and PDM_H) for all 14 wavelength channels compared to the back-to-back
PDM system sensitivity measured at 10-9 BER. (b) Typical BER curves of one
wavelength channel with eye diagrams inserted: bk_bk (back-to-back case without
PDM transmitter); PDM bk_bk (back-to-back case with PDM transmitter).
In addition to experimental demonstrations, several key issues remain: (i) the
sensitivity to power difference: As described in the concept, due to the limitation of
the electronics, as the power difference decreases (< 0.5 dB), the effectiveness of the
feedback control decreases (i.e. lower ER); (ii) the effect of PDL and PMD: PDL
along the link may degrade the power difference set at the transmitters and invalidate
the de-multiplexing. Under the worst-case scenario, PDL may totally wipe out the
power difference. On the other hand, the effect of the PDL also includes the OSNR
improvement or degradation along the transmission link. The tradeoff between
power difference and PDL should be considered for system optimization. Since this
scheme does not target PMD immunization, the effects of PMD are expected to be
165
similar to those of other approaches that have been studied in the literature [179-
181]. Related issues (e.g. PMD impairments and mitigation) and optimization are
under further investigation.

In summary, we have described a new polarization de-multiplexing scheme for
separating two polarization-multiplexed channels based on channel power
imbalance. We validated the scheme with a power imbalance of just above 0.5 dB in
a system containing a single wavelength channel. Finally, we successfully
demonstrated the scheme in a DWDM system containing 14 WDM channels of 40-
Gb/s per channel over 62-km LS fiber transmission.

166
Chapter 9
Design and evaluation of a re-circulating fiber loop test-bed
for 40-Gb/s WDM long-haul transmission
In order to develop an ultra-long distance optical fiber communication system for
emulating straight-line transmission of transoceanic, terrestrial, or metropolitan
reach, extensive resources, including people, optical components and equipment, are
needed [182]. A re-circulating fiber loop test-bed [183] attempts to simulate the
transmission performance of an ultra-long haul system by circulating the optical
signal through fewer EDFAs and a modest length of optical fiber ranging from tens
to hundreds of kilometers (Fig. 9-1), which not only save quite a few optical
components, but also make the space and management effort much more efficient.

Fig. 9-1. A comparison of implementing 2000 km transmission (a) A real straight-
line optical link. (b) A re-circulating loop test-bed.
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9.1 Fundamentals of a Re-circulating Fiber Loop
The re-circulating loop test-bed (Fig. 9-2) contains most of the elements typically
found in a conventional long-haul system, such as an optical data transmitter and
receiver pair, a chain of optical amplifiers and fibers, and diagnostic equipments
such as bit error ratio test set (BERTS), sampling oscilloscopes, and OSAs. Critical
for the loop test-bed, one optical switch is used to load data into the loop, while the
other allows data to circulate inside the loop. Loop control electronics is also needed
to synchronize the two optical switches as well as all the measurement equipments.

Fig. 9-2. Block diagram of a typical re-circulating loop transmission test-bed.
The working principle of the re-circulating fiber loop test-bed is to (1) load the loop
with a pseudo-random stream of optical data bits, (2) allow these data bits to re-
circulate around the loop a finite number of times corresponding to some desired
transmission distance, and (3) couple out these data streams from the loop after
circulating for various measurements. The details are as follows. The experiment
starts with the load-switch on (or transmitting light) and loop-switch off (or blocking
light) (Fig. 9-3(a)). The two switches are held in this load state for more than one
168
loop time (closed loop round trip time τ
loop
) to fill the loop with enough data patterns.
Once the loop is fully loaded with data, the two switches change state to the loop
state (Fig. 9-3(b)), and the data is allowed to circulate around the loop for some pre-
determined number of revolutions. After that, a portion of the data signal is
passively coupled out to the receiver for signal quality analysis. The data signal is
received and re-timed and then compared to the transmitted signal in the BERTS for
error detection. The BERTS needs to be properly gated using loop control
electronics so that only the errors in the circulation of interest (usually the last
circulation) are counted. The measurement continues, switching between the load
and loop states so that the errors can be accumulated over long intervals of time. Fig.
9-4 shows the proper timing diagrams of all the critical control signals.

Fig. 9-3. Optical Switches operating at the (a) load and (b) loop states.
The key to perform successful bit error rate measurement is the synchronization of
the two optical switches and the BERTS. For conventional bit error counters, the
frame synchronization time can be as long as several milliseconds. Therefore, in
order to maintain the proper frame alignment in the error detector, it is necessary that
the receiver see an unbroken data pattern so that the detector can acquire the frame
and count the errors. This puts a stringent requirement that an integer number of
169
patterns be in the loop at any given time. Synchronization is achieved by counting
the number of data patterns transmitted from the pulse pattern generator. The
relationship among the clock frequency f, the loop time τ
loop
, the number of patterns
in the loop N, and the number of bits per pattern M, can be stated as follows [183]:
[9.1]
When the condition of Equation [9.1] is satisfied, the circulating data pattern returns
to the 3-dB coupler with the same phase as the previous circulation, and the receiver
sees a continuous data pattern. However, thermal and mechanical perturbations of
the transmission fiber cause τ
loop
to drift with time, making it mandatory to
dynamically control the bit rate so that long-term stability is ensured. One nontrivial
method of accomplishing this is to detect the phase of the recovered clock and feed it
back to the master clock at the transmitter to readjust the bit rate.

The long-term stability of the re-circulating loop test-bed is greatly improved
through the use of the BERTS with a much faster frame synchronization time
(usually referred to as “burst-mode”). Because the frame synchronization time of
modern detectors is much shorter than the loop propagation time, they simplify error
counting by decoupling the strict relationship between the clock frequency and the
looping time τ
loop
, thus allowing the transmitter to run asynchronously to the loop.

As shown in Fig. 9-4, the timing control of the load switch and the loop switch can
be easily understood as complementary to each other. The critical control signal is
170
the “Error Gate” which is associated with the error bursts at the boundaries between
each loop time. The error bursts are caused by the finite speed of the optical
switches. During the switch transition from the load to the loop state, both switches
are still transmitting some amount of residual signals, which will interfere with the
optical pulses originating from the transmitter due to the same wavelength and
random phase. This interference process corrupts the data bits and causes the BERTS
to detect errors at these transitions. Since the same signal will circulate around the
loop, the error bursts are repeated at regular intervals of τ
loop
. The width of the error
gate thus needs to be made smaller than one loop time (a rule of thumb for this
number is usually 60-70%) to avoid the error bursts that occur on the seams of the
revolution (bottom of Fig. 4).

Fig. 9-4. Loop timing scheme of the control signals [183]. The error-gating signal
needs to be carefully designed in order to avoid the error bursts on the seams of the
revolutions, which is mainly caused by the finite speed of the optical switches.
171
9.2 Design Guidelines for a 40-Gb/s Re-circulating Fiber Loop
The previous section introduces the fundamental principles of a re-circulating fiber
loop test-bed for the general purpose of emulating long-haul transmission systems.
As the bandwidth demands are exponentially increasing during the past few years,
40-Gb/s data rate and beyond are attracting more and more attention and are
predicted to be deployed in the very near future to replace the current 10-Gb/s data
rates. This section is specifically devoted to the discussion of practical design
guidelines for a re-circulating fiber loop capable of running at 40-Gb/s. Experimental
implementation considerations of critical optical and electronic components and
subsystems are documented in detail.

Fig. 9-5. A typical experimental setup of a re-circulating loop test-bed designed for
40-Gb/s WDM systems.
Figure 9-5 shows a typical setup of a 40-Gb/s re-circulating fiber loop. The
transmitter consists of multiple laser diode (LD) channels, which are polarization
controlled, multiplexed and modulated with 40-Gb/s pseudo-random bit sequence
(PRBS). The modulation format can be either conventional on-off-keying (OOK) or
172
advanced phase-shift-keying (PSK) signals, depending on the bias and driving
voltage of the Mach-Zehnder modulator (MZM), with the added choice of return-to-
zero (RZ) format using a separate pulse carver MZM. Two acoustic-optic modulators
are used as load and loop switches for properly filling and circulating the data signal
inside the loop. The fiber loop span usually consists of a chain of single mode fiber
(SMF) as well as the dispersion compensating fiber (DCF), with erbium doped fiber
amplifiers (EDFAs) in between for loss compensation. The residual dispersion of the
fiber loop needs to be well determined, since the chromatic dispersion tolerance at
40-Gb/s is 16 times less than that of 10-Gb/s. The last EDFA in the loop link is used
for compensating loop-specific losses, which stem from the gain flattening filter (or
gain equalizer), the loop synchronous polarization scrambler (LSPS), and the power-
balancing attenuator. The gain equalizer is mainly used for flattening out the much-
narrowed gain bandwidth after long cascaded EDFAs over circulations, so that more
wavelength channels can be equally supported. In order for the re-circulating loop
test-bed to emulate true polarization evolution in a real straight-line optical link, the
LSPS is mandatory so that the periodic polarization states artificially introduced by
the loop test-bed can be synchronously scrambled and thus randomized. This is
especially important at 40-Gb/s systems since the accumulated polarization mode
dispersion has a 4-time bigger impact on 40-Gb/s than on 10-Gb/s. After certain
numbers of circulation, the data signal is routed out towards the receiver side where a
tunable dispersion compensation module (TDCM) is indispensible at 40-Gb/s so as
to clean up the residual chromatic dispersion. The compensated signal is then sent to
173
either a single-ended receiver or a delay-line interferometer followed by a balanced
receiver, depending upon the modulation format being OOK or DPSK. Electrical de-
multiplexing as well as the clock and data recovery is needed at 40-Gb/s for taking
the final bit-error rate at 10-Gb/s, which is the data rate most of the conventional
BERTS are operating at. As is also noticed in Fig. 9-5, loop control electronics send
out designed gating signals to the following three parts of the re-circulating fiber
loop test-bed,
1. Optical switches (two acoustic-optic modulators for loading and looping)
2. In-line loop components (LSPS, PMD emulator, etc.)
3. Measurement equipments (BERTS, OSAs, oscilloscopes, etc.)

The following subsections discuss the working principles and detailed experimental
implementations of all the critical optical and electrical components inside the 40-
Gb/s re-circulating fiber loop test-bed.

9.2.1 40-Gb/s Transmitters and Receivers
Modulation formats have been a hot research topic over the entire history of optical-
fiber communications. Early fiber-optic transmission demonstrations used the
conventional NRZ format because it was easy to generate and detect. Many research
institutes in the 1980s studied coherent optical communication techniques (including
phase-based modulation) to increase receiver sensitivity [4]. Work on coherent
optical communications slowed down dramatically in the early 1990s because of the
174
discovery of optical amplifiers. EDFA-based long haul systems started with the
NRZ format. Later, formats such as RZ and chirped RZ (C-RZ) took off for 10-Gb/s
systems. Starting from early 2000, due to the demand of high-capacity and high-
performance systems and networks, phase-based modulation formats, such as DPSK
and DQPSK, hold promise thanks to their advantageous 3-dB receiver sensitivity,
spectral efficiency and tolerance to various fiber-degrading effects. In this
subsection, we introduce the basic experimental setup of 40-Gb/s transmitters and
receivers, with the consideration of different modulation formats.

Fig. 9-6. Experimental configuration of a typical 40-Gb/s WDM transmitter, with
various modulation formats enabled.
Fig. 9-6 shows a typical experimental setup of a 40-Gb/s transmitter with multiple
wavelengths and reconfigurable modulation formats. As can be seen in the
experimental configuration, the optical part of the transmitter consists of two
cascaded 40-GHz bandwidth Mach-Zehnder modulators (MZMs) with an EDFA
booster and an optical tunable delay line (OTDL) in between. The light source can be
either a single channel tunable laser source (TLS) or multiple channels, depending on
175
the specific experimental needs. The first MZM serves as a data modulator, which is
biased at either quadrature point or null point on the cosine square transfer function,
so that regular NRZ-OOK or NRZ-DPSK format can be generated, respectively [4].
The second MZM serves as a pulse carver modulator for RZ generation. Different
flavors of RZ formats, such as 33% RZ, 50% RZ, or 67% RZ, also known as carrier
suppressed RZ (CSRZ), can be generated, depending upon the rate of the input
driving clock and driving voltage as well as the bias point [4]. Other advanced
modulation formats, such as DQPSK and polarization multiplexing, can also be
generated with the necessary optical hardware, like a nested MZM, a cascaded phase
modulator and polarization beam splitters and combiners [4]. One OTDL is used for
accurate time synchronization for pulse carving in the optical domain. RF delay lines
can also be used in the electrical domain, yet generally suffers from smaller tuning
range and limited bandwidth operation. The booster EDFA is usually needed for
compensating the insertion loss of MZMs and OTDL. The input power to the EDFA
needs to be high enough to saturate the booster so that the optical signal to noise
ratio (OSNR) right after the transmitter can be as high as possible, since this OSNR
dictates the launching OSNR into the transmission link. When WDM systems are
considered, one needs to be careful about the optical power of the individual channel
and the overall power. The individual power and total power follows a logarithm
relationship in dB unit and should be comprehensively considered when hitting the
booster EDFA. The PRBS generator provides a 40-Gb/s electrical signal as well as a
half rate (20 G) clock or a full rate (40 G) clock, depending on whether an internal or
176
external synthesizer is used. Fig. 9-6 shows the configuration where the PRBS
generator is internally clocked with a 20 G source, which is a cheaper solution for
40-Gb/s transmitters. A 20 G clock is provided at the output to drive the pulse carver
modulator for 33% or 67% RZ generation. This 20G clock is also split to drive the
precision time base for eye mode display on the high-speed digital sampling
oscilloscope. The pattern/bit mode is enabled with the low rate clock pattern trigger
also provided by the PRBS generator.

Fig. 9-7. Experimental configuration of a typical 40-Gb/s DPSK receiver, with
electronic clock recovery and de-multiplexer for bit error rate measurement.
At the receiver side, depending on the transmitted modulation format, different
receiver designs are needed. Fig. 9-7 illustrates a typical receiver configuration for
40-Gb/s DPSK reception and bit-error-rate measurement. At the front end, a one-bit
delay line interferometer (DLI) followed by a balanced receiver is needed for
demodulation of the DPSK signals to intensity-modulated signals, so that direct
177
detection can be applied. From an experimental consideration, the DLI needs to be
phase stable and the two optical path lengths needs to be exactly matched to ensure
both the constructive and destructive ports of the DLI are well time aligned to the
front end of the balanced receiver. For the two balanced receivers, important
parameters, such as the responsivity of the photodiodes, the gain of the trans-
impedance amplifiers (TIA) and the limiting amplifiers, should all be well matched
to produce almost identical performance. Commercial balanced receivers with high
integration usually address these issues.

Since most of the modern BERTS are operating at a bandwidth not exceeding 12.5-
Gb/s, one has to electrically de-multiplex the 40-Gb/s signals down to 10-Gb/s, with
properly recovered 10 GHz clock, for bit error rate measurement. Fig. 9-7 shows the
interplay configuration of the clock recovery unit (CRU) and the electrical de-
multiplexer (DeMux). The detected 40-Gb/s electrical signals will need to be fed into
both the CRU and the DeMux, with appropriate peak-to-peak voltage to drive both
units. The CRU will then recover both the 10G clock and 20G clock, which is
needed to drive the DeMux for proper synchronization and de-multiplexing. The
electrical power of the 20G clock fed into the DeMux should be well controlled to
accurately drive the high-speed D flip-flop and logic gates circuitry. The de-
multiplexed four 10-Gb/s data tributaries, together with the 10G recovered clock
from the CRU, are finally sent into the BERT for error rate measurement. For
178
training sequence purposes, a low speed (e.g. 2.5G) reference clock is sometimes
needed for the CRU in order to lock the clock with the actual data.

For re-circulating fiber loop applications, the abovementioned static operation might
require some modification, especially for the synchronization and gating part. One
thing to note is that the frame synchronization time of both the CRU and the DeMux
need to be taken into consideration, where a longer loop span setup (means longer
loop propagation time) is usually beneficial. Depending on the specific configuration
of the CRU, additional gating of its reference clock might be needed when one
particular circulation of interest is measured.

As coherent detection with digital signal processing, as well as some advance
electrical equalization techniques (such as FFE, DFE, MLSE, turbo equalizer), are
becoming the research of interests during the past few years [160], more and more
activities are expected in this particular field for the application of metro to long-haul
transmission. One thing to keep in mind is that for re-circulating loop experiments,
the frame synchronization time of involved specific high-speed chips, such as the
analog-to-digital converters (ADC), should be well understood before such advanced
test-beds are designed. A word of caution is that the interplay between these high-
speed chips with the conventional gating signals might fall out of the expectation of
a traditional re-circulating loop designer.

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9.2.2 Acousto-Optic (AO) Switches
Acousto-optic components are typically used internal or external to laser equipment
for the electronic control of the intensity modulation and/or position deflection of the
laser beam. Interaction of acoustic waves and light occur in optical materials when
the acoustic wave generates a refractive index wave, which acts as a sinusoidal
grating in the optical material. An incident laser beam passing through this grating
will be diffracted into several orders. With appropriate design of the modulator and
proper adjustment of the incident angle between the laser light and the axis of
acoustic propagation in the optical material, the first order beam can be made to have
the highest efficiency. The angle, also known as the Bragg angle, the light is
diffracted is defined by the equation:
[9.2]
where λ is the optical wavelength in air, V
a
is the acoustic velocity of the material, f
a

is the acoustic frequency and θ
b
is the Bragg angle. θ is the angle between the
incident laser beam and the diffracted laser beam, with the acoustic wave direction
propagating at the base of the triangle formed by the three vectors. A diagram of the
relationship between the acoustic wave and the laser beam is shown in Fig. 9-8.

Once the acousto-optic material is selected, optically polish is needed. The side of
the material that the acoustic energy is to originate from usually has a Lithium
Niobate transducer metal vacuum bonded to the modulator medium. The transducer
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converts RF energy applied to it into acoustic energy. The RF driver is typically a
fixed frequency oscillator and usually consists of a crystal oscillator, an amplitude
modulator with an interface, which accepts input modulation, digital or analog, and a
RF amplifier, which supplies the AO modulator with the level of RF power needed
to achieve the highest diffraction efficiency, as shown conceptually in Fig. 9-8.

Fig. 9-8. Acousto-optic modulator (AOM) system configuration and principle [184].
For application of simulating and testing long distance fiber-optic communication
systems, a fiber-pigtailed AO modulator system, consisting of two AO switches and
their corresponding RF drivers, is usually used [185]. The load switch, which is
placed outside the loop, is used to define the transmitted streams of bit patterns. A
high extinction ratio, usually above 60 dB, is required for the load switch, since this
will prevent the unwanted leaking of the bit streams into the loop and thus coherently
interfering with the already looping bit streams. The loop switch, which is placed
181
inside the loop span, is used to define the desired transmission distance by
controlling its ON state for a certain multiples of integers of a single circulation time
over the loop. The loop switch can have a moderate extinction ratio (~40-50 dB), but
the tens of MHz acoustic frequency shift deserves careful attention. One thought is
that by cascading two AOMs with opposite acoustic frequency change, shift-free
optical switches can be designed. However, there are two issues associated with it.
First, two cascaded AOMs will double the insertion loss of the loop switch by 2-3
dB, which is considered as additional loop-specific losses and with worsen the
overall OSNR. Second, from a practical point of view for 40-Gb/s systems, long-haul
transmission distances we are considering are usually in the range of 1000 km to
3000 km. For a 200 km loop span configuration, this translates into up to 15
circulations, which means that the accumulated acoustic frequency shift is less than
600 MHz, considering a 40 MHz acoustic frequency shift. The accumulated shift
introduces negligible power penalty when the transmitted signal bandwidth is
considered [183]. A rule of thumb for the design of the loop switch would be to
avoid the use of cascaded AOM structure and build a loop span as long as possible
so that less number of circulations is required for a specific distance.

As discussed earlier, the extinction ratio (ER) of the AOM is a critical parameter
when selecting optical switches. This is especially true when dynamic RF frequency
driving of the AOM is considered. Fig. 9-9 describes a useful method for measuring
the dynamic ER of the AOMs. The two cascaded AOMs (AOM1 and AOM2) are
182
placed right before the device under test (DUT), AOM3, in order to generate high
ER (>80 dB) pulses for testing. Pulse generator (Gen) #1 serves as the master
generator to drive the DUT, and slave pulse Gen #2, which is externally triggered by
the master, is split, amplified and delayed properly to drive the AOM1 and AOM2.
The timing diagram for both the Gen #1, #2 and the delayed copy of #2 is also
shown in Fig. 9-9. Gen #2 and its delayed copy measures ON and OFF levels of the
DUT with > 80 dB ER thanks to the cascaded configuration. An optical spectrum
analyzer (OSA) then reads the optical power level corresponding to both the ON and
OFF states. Preliminary testing indicates that an ER of 40-45 dB is possible with a
RF frequency rate of 1.5 MHz. One thing to note here is that the OSA reading of the
OFF state changes with its reference level because the OSA will adjust its internal
gain level when the reference is changed, especially for the case of measuring very
small (< -50 dBm) optical power.

Fig. 9-9. Dynamic extinction ratio measurement of the AOM switch.
183
9.2.3 Loop Control Electronics
Loop control electronics are at the heart of the accurate operation of the re-
circulating loop. One critical parameter governing the design of loop control
electronics is the loop propagation time, also known as the round trip time. For a
200-km re-circulating loop, since the unit fiber propagation time is 4.89 µs/km, the
total round trip time is 978 µs. This loop propagation time, also defined as τ
loop
, is
the fundamental parameter for the design of all the gating signals.

Before designing or choosing the digital control board or pulse delay generator, the
following important parameters need to be considered,
1. Number of channel outputs: One should keep in mind that not only the two
AO switches needs to be controlled, several measurement equipments (such
as BERT, OSA, oscilloscope, chirp form analyzer), as well as some loop in-
line components (such as LSPS, PMD emulator or compensator) also require
proper gating. A rule of thumb would be to have at least 4 channels and up to
8 channels is preferred.
2. Delay range and resolution: The delay range on each channel should meet the
requirement of the maximum possible transmission distance, and the delay
resolution should be fine enough so that less than 1% of the loop propagation
time can be controlled.
184
3. Pulse width control: This is extremely important when the loop span distance
is changed or adjusted for various purposes. It is also useful when one would
like to diagnose the impact of the error bursts on the actual data quality.
4. Signal output level: This is sometimes ignored yet might cause trouble when
the gating voltage criterion of some specific measurement equipments is
unconventional. For example, most of the modern BERT and OSA accept
TTL (0/5V) input, while some older versions require SCFL (0/-1V) input.

After designing or choosing the versatile digital control board, which can meet the
above parameter requirements, one can go ahead and design the timing gating signals
for the AOMs and the measurement equipments. Fig. 9-4 has already shown a typical
timing diagram for the load and loop switch, as well as the error-gating signal for the
measurement equipment. One thing to note is that the ON state for the load switch is
chosen to be more than one round trip time (usually 2*τ
loop
for convenience), which
is to avoid any unexpected transient responses of the optical loop components and to
ensure that the loop is fully loaded with a complete set of data stream before looping.
Various measurement equipments can commonly share the error-gating signals, as
long as their acceptable gating input and the circulation of interest to be measured
are the same. As a rule of thumb of the duty cycle of the error-gating signal, 60-70%
of the loop propagation time is usually sufficient to avoid the error bursts on the
seams of the loop transition. Specific gating signals for the inline components, such
185
as LSPS or PMD emulator, need to take into consideration their unique driving
method.

9.2.4 Cascaded EDFA Design and OSNR analysis
Since the invention of optical amplifiers in the early 1990’s, optical
telecommunications industry has experienced an enormous bandwidth demand and
capacity boost. Erbium doped fiber amplifiers (EDFAs) are at the heart of the fiber
transmission link for compensating the loss of fibers as well as supporting densely
spaced wavelength channels. Therefore, the cascaded EDFAs in the re-circulating
loop need to be well designed in terms of the maintaining the accumulated gain
spectrum and the noise figure.

Fig. 9-10. Non-uniform EDFA gain accumulation and spectrum narrowing.
186
Figure 9-10 shows a typical measured result of the gain spectrum after a single
EDFA and after a cascade of 13 EDFAs. Due to the non-uniform erbium gain shape,
the cascaded EDFAs exhibits a sharply narrowing gain spectrum compared with a
single EDFA. This is certainly an unwanted effect and requires the search of some
gain flattening techniques. Fig. 9-11 provides two methods of flattening the EDFA
gain, with the common idea of designing a gain flattening filter (GFF) with an
inverse gain shape. Individual equalization (GFF after each EDFA) or block
equalization (GFF after a certain cascades of EDFAs) can be selectively applied,
depending on the particular shape of a single EDFA as well as the loss control the
GFF resources. Typical GFFs are designed with long period grating filters, thin-film
based filters, or Mach-Zehnder filters. The thin-film based filters usually can only
provide less than two gain peaks, while the long period grating filter can be
engineered to exhibit multiple gain peaks, which is more suitable for block
equalization. The critical parameter of a GFF is the peak-to-peak error function,
which is defined as the maximum deviation away from the ideal filter shape in dB. A
peak-to-peak error down to 0.3 dB is usually required for re-circulating loop
applications.

Realizing that the EDFA gain is not only provided to the optical signal but to the
noise as well, one has to carefully consider a very important parameter of the EDFA,
the noise figure (NF), which is defined as the ratio of the input OSNR to the output
187
degraded OSNR in dB. The measurement of the EDFA NF is mandatory before
choosing the cascaded EDFAs. The following methods are usually applied [157],

Fig. 9-11. Gain flattening methods: individual equalization and block equalization
with customized broadband filter.
1. Source subtraction method
2. Time domain extinction method (considering the slow gain dynamics)
3. Polarization extinction method
4. Signal substitution method
5. Reduced channel method (for DWDM applications)
Among the above techniques, the source subtraction method is easy to implement
and exhibits relatively accurate results, and is thus recommended. The main idea is to
measure the OSNR before and after the introduction of the EDFA using a calibrated
OSA. By reading the signal power level as well as interpolate the noise power level
on the OSA, one can easily subtract the source spontaneous emission power and
188
derive the noise figure value from the definition of input and output OSNR. When
considering a chain of cascaded EDFAs for re-circulating fiber loop transmission,
the noise figure of the first EDFA in the link is the dominant NF for the total
accumulated NF. Therefore, the EDFA with the smallest NF should be placed in the
front of a cascade of EDFAs in the loop span.

For long-haul transmissions, the EDFAs alongside the fiber link are all operated
under the saturation condition [183]. This is particularly beneficial when we consider
automatic gain control in the link [183]. The saturation operation of the EDFA also
provides better OSNR performances especially when a long chain of EDFAs is
considered. A very useful OSNR equation to keep in mind is as follows,
[9.3]
where P
in
is the launching power of the individual channel of interest, the NF
amp
is
the noise figure of the EDFA, assuming all are the same, L
span
is the loss of each
single mode fiber span, and N
span
is the number of single mode fiber spans. One can
see from the equation that the OSNR sensitivity is not only determined by the noise
figure of the EDFA, but is also dictated by the loss of each span as well as the
launching optical power of the transmitted channel. For instance, 1 dB of additional
fiber loss (e.g. connector loss) or 1 dB of additional launching power loss will
directly translate into 1 dB worse of received OSNR.

189
9.2.5 CD and PMD Management
Standard fiber plants of a re-circulating loop usually consist of several spans of
single mode fibers (SMFs) and dispersion compensating fibers (DCFs). The
minimum length of the total loop span, as discussed in both 9.1 and 9.2.1, is
constrained by the frame synchronization time of the error detector, CDR, DeMux
and other advanced electronic signal processors. Propagation delay measurement of
the total loop span needs to be taken in order to verify with the predicted round trip
time, τ
loop
. Modern re-circulating loop test-beds usually consists of at least 200 km
length and can be up to 400-500 km lengths for emulating ultra-long-haul undersea
transmission links.

After the length of the loop span is determined, the chromatic dispersion of both the
SMF and DCF needs to be accurately measured in order to calculate the residual
dispersion at a specific wavelength channel, which is crucial especially for 40-Gb/s
systems. Phase shift method and differential phase shift methods [157] are available
with a network analyzer. Time-of-flight method is also a practical way to determine
the dispersion when the experienced delay of a 10-Gb/s PRBS signal is monitored on
a digital sampling oscilloscope if the source wavelength is changed exactly by 1 nm.
Dispersion slopes of either the SMF or DCF are also very important parameters to
measure if more than 10 nm of channel capacity and longer than 1000 km distance
are considered.
190
At 40-Gb/s and beyond, DCFs mainly serve as coarse dispersion compensation
modules, and tunable and fine dispersion compensating elements are required right
before the receiver to clean up the residual chromatic dispersion on a per channel
basis. Fiber Bragg grating (FBG) and virtual imaged phase array (VIPA)
technologies are mainly used for realizing tunable dispersion compensation modules
(TDCM). Tuning resolution, tuning range and channel spacing are the three most
important parameters to consider when selecting a TDCM. One thing to note here is
that the dispersion map, considering both the pre- and post-compensation with in-
line compensation, needs to be designed carefully at 40-Gb/s, taking into account the
interplay between the chromatic dispersion and the dominant fiber intra-channel
nonlinearity, which will be discussed in the next sub-section.

Polarization mode dispersion (PMD) is typically caused by the asymmetry of the
fiber core and is considered as a time-varying effect due to temperature or
mechanical vibration. The first-order PMD, also known as the differential group
delay (DGD), follows a Maxwellian distribution. Its average value can be predicted
and measured by one of the following methods [157].
1. Broadband interferometric technique
2. Fixed analyzer and wavelength scanning technique
3. Jones Matrix Eigen-analysis (JME) technique
191
The first two methods are easier to implement but is not as accurate as the third
method, which can also measure higher-order PMD and polarization dependent loss
(PDL) of the fiber plant. The effect of the 2
nd
order PMD should not be neglected
especially when considering DWDM systems at 40-Gb/s and beyond.

For re-circulating loop applications, one critical difference compared with a real
straight-line optical link is that the loop exhibits periodic polarization evolution
nature, which is not true and realistic for a real link. One idea to bridge this
difference is to randomize the polarization state alongside the fiber and its
scrambling should also be in sync with the loop circulation. Loop synchronous
polarization scrambler (LSPS) is thus designed [186] and its implementation is
meant to emulate practical PMD accumulation as well as PDL accumulation for a
real fiber link. LSPS is usually a TTL-signal gated polarization scrambler. Fig. 9-12
shows a typical experimental comparison result of the impact of the LSPS on the
distributions of the DGD. One piece of polarization maintaining fiber (PMF) is
placed inside the loop for simulating large fiber DGD. When no LSPS is used, the
statistics for either a one section PMF or a 15-section of PMD emulator substantially
deviates away from the Maxwellian distribution. However, when LSPS is applied
along with a one section PMF, after 8 round trips of circulation, the statistics follows
well with the desired distribution, which proves the effectiveness of the LSPS for re-
circulating loop applications. One thing to note here is that the speed of the LSPS
192
should ideally be much faster than the frame synchronization time of the receiver
electronics in order to accurately measure the bit-error-rate performance.

Fig. 9-12. The impact of LSPS on the statistical distribution of first-order PMD.
Other advanced polarization components can also be placed inside the loop for either
polarization measurement or PMD compensation. Polarization measurement
instrument, such as the polarimeter, can monitor the degree of polarization (DOP)
information as well as the Stokes parameter of the looping signal, which is a useful
monitoring technique to analyze the polarization evolution. Polarization mode
dispersion compensators (PMDCs) can be applied with either a one-stage or two-
stage implementation, depending upon whether only the compensation of 1
st
order
PMD or higher-order PMD is concerned. For both polarimeters and PMDCs to be
effective, proper gating signals as well as the measurement of the response time of
the components need to be designed and understood in advance.
193
9.2.6 Fiber Nonlinearity Management
Inter-channel nonlinearities, such as cross phase modulation (XPM), four-wave-
mixing (FWM), are dominant effects at 10-Gb/s or lower, which is happening
between adjacent channels. However, at 40-Gb/s or higher, due to the reduced time
slot between adjacent bits, intra-channel nonlinearities, such as intra-channel cross
phase modulation (IXPM) and intra-channel four wave mixing (IFWM) start to
become dominant degrading effects. When pulses overlap due to dispersion,
frequency shift is introduced due to IXPM, while new frequencies are generated due
to IFWM. IXPM manifests itself as timing jitter and IFWM exhibit itself as
amplitude variations. The other thing to note is that IXPM dominates in low
dispersion fibers while IFWM is more significant in high dispersion fiber. Both
impairments can be minimized by correct dispersion map and advanced formats.

For phase-based modulation formats, such as DPSK or DQPSK, the signal quality is
also degraded by the Gordon-Mollenauer nonlinear phase noise [187], which is
introduced from the ASE noise-induced signal amplitude fluctuations through the
SPM and/or the XPM effect. In general, the effect of nonlinear phase noise is the
largest when the signal waveform evolution is slow during propagation (e.g., when
the symbol rate is low) or when fibers with low values of CD are used. Formats with
a large number of phase levels (i.e., multi-level formats) are also generally more
sensitive to nonlinear phase noise. One should also point out that nonlinear phase
noise depends on both the signal and noise power levels. Therefore, systems with
194
identical signal power evolution but different noise power evolution (different
delivered OSNRs) will generally have different OSNR penalties if they are affected
by nonlinear phase noise. Constellation diagrams or phasor diagrams are considered
useful tools for the analysis of phase noise for phase-modulated formats.

9.3 Experimental Results
Having discussed in detail the design guidelines of building the critical components
for a re-circulating loop test-bed, we will present in this section some typical
experimental results achieved at both 10-Gb/s and 40-Gb/s.

9.3.1 10-Gb/s, 8 channels, 3,000 km error-free transmission
As shown in Fig. 9-13, the 10-Gb/s re-circulating loop consists of one spool of 80
km SMF, 14 km of DCF and three EDFAs inside the link. The modulation format
used is conventional OOK with RZ options at eight different wavelength channels.

Fig. 9-13 Experimental setup of a 10-Gb/s WDM re-circulating loop.
195
The booster EDFA has an input power of -3 dBm and an output of 8 dBm. The three-
cascaded EDFAs inside the link have -7.8 dBm, -12.5 dBm and -10.5 dBm of input
power, and 7 dBm, 0.3dBm, and -3.5 dBm of output power, respectively. The three
EDFAs are operated at 7.5 dB, 4.5 dB and 7.5 dB under saturation for automatic gain
control. Both the simulation and experimental results of OSNR evolution of the
cascaded EDFA analysis are shown in Fig. 9-14. Up to 30 round trips, corresponding
to roughly 3,000 km of transmission and 90-cascaded EDFAs is simulated and
measured.
Fig. 9-14 Simulation and experimental results of OSNR evolution up to 3,000 km.
As can be seen from Fig. 9-14, both the simulation and experimental results match
quite well with each other under the same EDFA saturation conditions. One needs to
note here that, due to the relatively shallow saturation condition of the 2
nd
EDFA
compared with the 1
st
and 3
rd
EDFA (insets of Fig. 9-14), the OSNR gets a hit after
196
the first round and accumulates to the further round trips. One expects that the
received OSNR would be improved had we replaced the 2
nd
EDFA with a better
operating one. Even under the current condition, the received OSNR can still achieve
error free with proper FEC correction.

Fig. 9-15. Eye diagrams of RZ-OOK and NRZ-OOK up to 3,000 km loop
transmission.
After understanding the cascaded EDFA performance, we send into the loop both
RZ-OOK and NRZ-OOK signals for comparison. Fig. 9-15 shows the eye diagrams
of both formats up to 3,000 km transmission with 100 km loop span. For the same
launching power into the fiber, RZ-OOK exhibits much better nonlinearity tolerance
compared with NRZ-OOK, which mainly suffers from vertical eye closure. After
3,000 km transmission, corresponding to 30 round trip times, RZ-OOK still has a
relatively open eye, even though it’s becoming NRZ like, mainly due to the
197
accumulated residual dispersion and small fiber nonlinearity. Bit error rate
measurements are shown in Fig. 9-16. In back to back configuration, RZ-OOK
performs 1.5 dB better than NRZ-OOK. After 1,500 km transmission, NRZ-OOK
already exhibits ~7 dB power penalty. RZ-OOK only shows less than 5 dB penalty at
10
-9
BER even after 2,000 km transmission, which can be mainly attributed to better
nonlinearity tolerance for RZ formats.

Fig. 9-16. BER measurement of 10-Gb/s RZ-OOK and NRZ-OOK transmission.

9.3.2 40-Gb/s, 8 channels, 800 km error-free transmission
The experimental setup of 40-Gb/s re-circulating loop is shown in Fig. 9-5. This
time, the loop span length is increased from 100 km to 200 km, with 5 newly
designed EDFAs. The residual dispersion of the whole span at 1550 nm wavelength
is measured to be around -30 ps/nm/span. Realizing that RZ format is better than
198
NRZ, we implement 67% RZ-OOK and RZ-DPSK from the 40-Gb/s transmitter. 8
channels with 200-GHz spacing from 1547 nm to 1558 nm are launched. Two GFFs
are incorporated in the link in order to block equalize the gain bandwidth of the
cascaded EDFAs. Loop synchronous polarization scramblers with proper gating
signal is setup to randomize the artificial periodic polarization states. 4:1 de-
multiplexer and clock recovery unit are used to measure the bit-error-rate of a 40-
Gb/s signal down at 10-Gb/s. Fig. 9-17 shows the eye diagrams of back to back, 1, 2
and 4 round trips (r.t.) of a 200 km loop. With accurate dispersion compensation, the
eye is still widely open and error free is achieved after 800 km transmission.

Fig. 9-17. Eye diagrams of 40-Gb/s RZ-OOK up to 800 km loop transmission.

Last, but not the least, we show in Fig. 9-18, the BER measurement of transmission
of RZ-DPSK format up to 400 km at 40-Gb/s. Eye diagrams of balance-detected RZ-
DPSK signals are shown at 10
-9
BER, which manifests itself as a 4.5 dB power
penalty after 400 km transmission. The back-to-back RZ-DPSK eye diagram is also
199
shown in the inset, which exhibits some non-idealities in the 40-Gb/s RZ-DPSK
pulse trains. We expect that by replacing the bandwidth-limited electro-optic data
modulator as well as increasing the driving voltage of the pulse-carver modulator
driver, the transmission performance of RZ-DPSK should be 1-2 dB better.

Fig. 9-18. BER measurement of 40-Gb/s RZ-DPSK transmission.

200
Chapter 10
Conclusions
Optical signal processing technologies are envisioned to play vital role for future
optical networks. Two key enabling elements, namely tunable optical delay lines and
high-speed wavelength converters, are discussed in the first part of the dissertation.
Slow light tunable delay lines with phase preservation and spectral efficiency are
proposed and experimentally demonstrated using advanced modulation formats.
Novel and functional optical modules, such as multi-channel synchronizer and
variable-bit-rate optical time division multiplexer are designed and demonstrated
using slow-light tunable delay lines. Additionally, deleterious degrading effects on
SOA-based differential mode high-speed wavelength converters are experimentally
identified and techniques to combat these degrading effects are proposed.

Enabling technologies for enhancing the system performance or enriching the system
functionalities are discussed in the second part of the dissertation. System
applications of two novel optoelectronic devices are demonstrated for transmission
reach extension, multifunctional operation and dynamic bandwidth allocation. In
addition, polarization-based novel optical instruments, such as a polarimeter-enabled
optical spectrum analyzer and an all-optical polarization de-multiplexer, are designed
and experimentally demonstrated. Finally, a re-circulating loop test-bed capable of
40-Gb/s operations is designed and experimental results are discussed in detail.

201
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Abstract (if available)

Abstract The past decade has witnessed astounding boom in telecommunication network traffic. With the emergence of multimedia over Internet, the high-capacity optical transport systems have started to shift focus from the core network towards the end users. This trend leads to diverse optical networks with transparency and reconfigurability requirement. As single channel data rate continues to increase and channel spacing continues to shrink for high capacity, high spectral efficiency, the workload on conventional electronic signal processing elements in the router nodes continues to build up. Performing signal processing functions in the optical domain can potentially alleviate the speed bottleneck if the unique optical properties are efficiently leveraged to assist electronic processing methodologies. Ultra-high bandwidth capability along with the promise for multi-channel and format-transparent operation make optical signal processing an attractive technology which is expected to have great impact on future optical networks.

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Asset Metadata

Creator Zhang, Bo (author)

Core Title Nonlinear optical signal processing for high-speed, spectrally efficient fiber optic systems and networks

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 02/26/2009

Defense Date 12/01/2008

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag advanced modulation format,differential phase shift keying,differential quadrature phase shift keying,nonlinear optics,OAI-PMH Harvest,optical fiber communication,optical signal processing,slow light

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Willner, Alan E. (committee chair), Bickers, Nelson Eugene, Jr. (committee member), Steier, William H. (committee member)

Creator Email boz@usc.edu,bozbozboz@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1988

Unique identifier UC1315446

Identifier etd-Zhang-2575 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-152965 (legacy record id),usctheses-m1988 (legacy record id)

Legacy Identifier etd-Zhang-2575.pdf

Dmrecord 152965

Document Type Dissertation

Rights Zhang, Bo

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu