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Optical wave mixing for tunable delays and high‐speed signal processing

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Optical wave mixing for tunable delays and high‐speed signal processing

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OPTICAL WAVE MIXING FOR TUNABLE DELAYS AND
HIGH-SPEED SIGNAL PROCESSING

by
Ahmed Almaiman

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

May 2018

Copyright 2018 Ahmed Almaiman
ii

Dedication

To my parents, my grandparents my wife and my brothers
To my thesis advisor, OCLab members, and friends
for their encouragement and support.

iii

Acknowledgments
First and foremost, I would like to thank Allah (God) for giving me the strength,
knowledge, ability and opportunity to undertake this Ph.D. degree and to persevere
and complete it satisfactorily. Without his blessings, this achievement would not have
been possible.
I would like to acknowledge Prof. Alan E. Willner for his patience and support
from the first day I met him. The words cannot express the appreciation to him for
accepting me into his group. Prof. Willner has been a great advisor whose wisdom and
vision goes beyond the technical areas of science and engineering. I want to thank Prof.
Willner for all he has taught me throughout my graduate studies, from the most
straightforward lessons and short discussions to the most scholarly and technical, and
for his encouragement, inspiration, and valuable hints and advice.
I would like to thank my wife, Wejdan Almuqbil, who was on board with me
during the Ph.D. adventure. She took the risk coming with me from Saudi Arabia
within few weeks from our marriage and withdrew her college admission to support
me. Wejdan was the best partner a Ph.D. student could wish. She was encouraging,
helping, fun, patient. She did not save any effort in helping me and keep me standing
against the difficulties. I would like to say, Thank you! I love you!
I want to extend my appreciation to Prof. Alexander Sawchuk and Prof. Stephan
Haas, for serving on my dissertation committee. I wish to thank Prof. Wei Wu and
Prof. Joe Touch for their advice during the qualification exam. I would also like to
thank Prof. Moshe Tur for his guidance and support during his visits to USC. Also, I
iv

am grateful to Dr. Youichi Akasaka for his involved discussions and advice that went
beyond to scientific world to the professional environment and ethics.
It is with great pleasure that I also thank Prof. Habib Fathallah, Saleh Alshebili,
Abdulhameed Al-Sanie's, and Basil Assadhan, for their mentorship, guidance, and
insight during my last year as an undergraduate student in King Saud University,
which established the path for my Ph.D. in the field of optics. Moreover, I would like
to thank the government of Saudi Arabia and the Saudi Arabian Cultural Mission
(SACM) for their generous support.
My warmest thanks go to the many members of the Optical Communications
Lab (OCLab) at USC for all these years of insightful discussions and collaboration. I
would like to thank Dr. Scott Nuccio, Bishara Shamee, Dr. Yang Yue, Dr. Hao Huang,
Dr. Asher Voskoboinik, Dr. Salman Khaleghi, Dr. Mohammad Reza Chitgarha, Dr.
Yan Yan, Dr. Nisar Ahmed, Dr. Yongxiong Ren, Dr. Morteza Ziyadi, Wajih Daab,
Dr. Guodong Xie, and Dr. Changjing Bao, and Amirhossein Mohajerin-Ariaei for
valuable discussions and their help. Thank you all! I enjoyed all the days and sleepless
nights we spent in the lab, and I wish you all the best.
Speaking of OCLab members, I would like to particularly thank Yinwen Cao,
with whom I collaborated on most of the experiments in the lab over the past few years.
I also want to thank Peiching Liao, Fatemeh Alishahi, Ahmad Fallahpour, Zhe Zhao,
Long Li, Kai Pang, Haoqian Song, Cong Liu, Zhe Wang, Runzhou Zhang, Kaiheng
Zou, and Hao Song for all their helpful discussions.
v

I also want to thank the excellent staff of the electrical engineering department
at USC, Tim Boston, Diane Demetras, Corine Wang, and Gerrielyn Ramos, who have
been a phenomenal help during my Ph.D. years.
Finally, but very importantly, I want to thank my parents for their unconditional
love and support during these years. I am thankful to my father, Sami Almaiman and
my mother, Huda Alhumood, for her love, understanding, support, and dedication in
raising us to become who we are. I would also like to thank my brothers for their love
and support in all the ways they can. Thank you all!

vi

Table of Content
Dedication ................................................................................................................... ii
Acknowledgments ..................................................................................................... iii
Table of Content ........................................................................................................ vi
List of Figures ............................................................................................................ ix
Abstract ..................................................................................................................... xv
Chapter 1 Introduction ............................................................................................ 17
1.1 Nonlinear Wave Mixing Processes............................................................... 17
1.1.1 Four-Wave Mixing ............................................................................. 18
1.1.2 Three Wave Mixing ........................................................................... 19
1.1.3 Materials and Devices ........................................................................ 20
1.2 Enabling Technologies ................................................................................. 21
1.2.1 Encoding in Multiple Domains of Optical Wave ............................... 21
1.2.2 Coherent Detection............................................................................. 22
1.2.3 Optical Frequency Comb ................................................................... 23
1.3 Basic Enabling Operations ........................................................................... 24
1.3.1 Wavelength Multicasting ................................................................... 24
1.3.2 Active Optical Multiplexing .............................................................. 25
1.3.3 Generation of Higher-Order Harmonics ............................................ 26
1.4 Dissertation Outline ...................................................................................... 26
Chapter 2 Fine and Coarse Discrete Delay Line Using Chromatic Dispersion
and an Optical Frequency Comb ...................................................................... 28
2.1 Introduction .................................................................................................. 28
2.2 Concept ......................................................................................................... 29
2.3 Experimental Setup....................................................................................... 30
2.4 Results .......................................................................................................... 32
2.5 Characterization of Distortion in the PPLN Waveguide .............................. 34
2.6 Experiment and Results for Measuring the PPLN Waveguide Distortion ... 35
2.7 Conclusion .................................................................................................... 37
Chapter 3 Continuously Coarse and Fine Tunable Optical Delay Using the
Time-of-flight in Fiber Bragg Gratings and Wavelength Conversion .......... 39
3.1 Introduction .................................................................................................. 39
3.2 Concept ......................................................................................................... 39
3.3 Experimental Setup....................................................................................... 40
3.4 Results .......................................................................................................... 42
vii

3.5 Conclusion .................................................................................................... 43
Chapter 4 Multiple Access Delays using Fiber Bragg Gratings and Multicasting
with a Frequency Comb .................................................................................... 44
4.1 Introduction .................................................................................................. 44
4.2 Concept ......................................................................................................... 45
4.3 Experimental Setup....................................................................................... 45
4.4 Experimental Results .................................................................................... 46
4.5 Characterization of the Chirped FBGs ......................................................... 47
4.6 Conclusion .................................................................................................... 50
Chapter 5 Repeated Spatial-mode Shifting for Achieving Discrete Delays in a
Free-space Recirculating Loop ......................................................................... 51
5.1 Introduction .................................................................................................. 51
5.2 Background of OAM .................................................................................... 51
5.3 OAM Generation and Detection ................................................................... 52
5.4 Concept of Repeated Spatial-Mode Shifting for Achieving Discrete
Delays in a Free-Space Recirculating Loop ................................................. 53
5.5 Experimental Setup....................................................................................... 54
5.6 Experimental Results .................................................................................... 56
5.7 Discussion and Conclusion ........................................................................... 58
Chapter 6 Homodyne Detection of WDM and Dual-polarization PSK Channels
by Automatically Locking the Channels to a Local Pump Laser Using
Nonlinear Mixing ............................................................................................... 60
6.1 Introduction .................................................................................................. 60
6.2 Concept ......................................................................................................... 61
6.3 Experimental Setup of Dual-Polarization QPSK Detection ......................... 63
6.4 Results for Dual-Polarization QPSK Homodyne Detection ......................... 65
6.5 Experimental Setup for WDM Homodyne Detection .................................. 66
6.6 Results for WDM Homodyne Detection ...................................................... 68
6.7 Discussion and Conclusion ........................................................................... 70
Chapter 7 Phase-Sensitive Regeneration of a BPSK Channel without Phase-
Locked Loop Using Brillouin Amplification ................................................... 72
7.1 Introduction .................................................................................................. 72
7.2 Concept ......................................................................................................... 73
7.3 Experimental Setup....................................................................................... 74
7.3 Experimental Results .................................................................................... 77
7.4 Discussion and conclusion............................................................................ 81

viii

Chapter 8 QPSK Regeneration by Amplifying the Fourth-harmonic Idler Using
Counter-Propagating Brillouin Amplification ................................................ 82
8.1 Introduction .................................................................................................. 82
8.2 Theory ........................................................................................................... 83
8.3 Concept ......................................................................................................... 84
8.4 Experimental Setup....................................................................................... 85
8.5 Experimental Results .................................................................................... 88
8.6 Discussion and Conclusion ........................................................................... 91
References ................................................................................................................. 93

ix

List of Figures
Figure 1.1 (a) Degenerate and (b) Non-degenerate four-wave mixing (FWM)
schemes for generation of phase conjugate signal copy. ZDW: zero dispersion
wavelength. .......................................................................................................... 18
Figure 1.2 (a) Cascaded sum and difference frequency generations (cSFG-DFG) and
(b) Second harmonic generation and DFG (cSHF-DFG) for wavelength
conversion in a PPLN device. QPM: quasi-phase matching. .............................. 20
Figure 1.3 Advanced modulation formats using amplitude and phase domains, with
independent polarization and wavelength multiplexing ...................................... 22
Figure 1.4 Coherent signal detection using the coherent receiver. ................................ 23
Figure 1.5 An optical frequency comb in the frequency domain (a) and in the time
domain (b). .......................................................................................................... 24
Figure 1.6 Various configurations for N-fold signal multicasting using multi-pumps.
............................................................................................................................. 25
Figure 1.7 An example of coherent multiplexing in a nonlinear device to generate
higher order amplitude and phase formats. ......................................................... 25
Figure 1.8 Concept of generating the higher harmonics of a signal using nonlinear
materials and a pump. .......................................................................................... 26

Figure 2.1 The concept of an all-optical multiple-access, fine- and coarse-delay
system using a frequency comb. Pre-dispersion of DCF 1 is compensated by
phase conjugating the signal in a HNLF and propagating the multicast
conjugates later through DCF 2. The multicast conjugates are created in a
PPLN waveguide with frequency comb lines as pumps. The fine delay is
realized using GVD while the coarse-delay stage is created using a fiber bank.
............................................................................................................................. 29
Figure 2.2 (a) Experimental setup of the multiple-access fine- and coarse-delay
system using an optical frequency comb. (b) The optical spectrum of S*-D
generation at the output of HNLF 1. (c) 10x multicasting of S*-D at the output
of the PPLN waveguide. ...................................................................................... 31
Figure 2.3 The magnitude responses measured using the VNA for the: (a) B2B
signal, (b) signal after DCF 1, (c) copy 5 after DCF 2, and (d) copy 5 after the
DCM. (e) The dispersion compensation module setup to compensate for the
residual GVD. ...................................................................................................... 33
x

Figure 2.4 (a) Experimentally captured copies at the output of the fine-delay stage.
(b) Accessible delays when combining the coarse delay and fine delay. ............ 33
Figure 2.5 The BER performance of different delayed 10-Gb/s OOK copies. .............. 34
Figure 2.6 (a) Concept of SFDR measurements for the idler generated in a χ2 PPLN
waveguide. An optical carrier which is modulated with microwave tones is
combined with a pump laser and sent into the PPLN waveguide where they
mix in a SHG and a DFG manner to generate the idler. (b) Spurious-free
dynamic range measurement on the idler for both second and third harmonic
distortions (THD: Third-order harmonic, SHD: Second-order harmonic). ......... 35
Figure 2.7 The experimental setups showing different characterization scenarios
(with the added/changed components highlighted for every scenario). .............. 36
Figure 2.8 The experimentally measured SHD and THD for the various cases in
Figure 2.9............................................................................................................. 37
Figure 2.9 Summary of the measured SFDR-THD and SFDR-SHD. ........................... 37

Figure 3.1 Concept of coarse and fine-tuning delays using time-of-flight in cascaded
FBGs and wavelength conversion. ...................................................................... 40
Figure 3.2 (a) Experimental setup. (b) Reflection spectra from arrayed and
channelized FBGs. (c) Wavelength conversion output from PPLN-1 when the
coarse tuning of FBG1 is used along with the tuning range of P1. (d) Output
of PPLN-2 when FBG1 is used for the coarse tuning delay. (e) the case of
creating the largest delay using FBG10 and the largest delay from P1 after
PPLN-1. (f) The output of PPLN-2 when creating the largest delay. .................. 41
Figure 3.3 (a) Waveforms for some of the coarse-tuning stages delays at largest and
smallest fine-tuning range. (b) Accessible delays by combining the coarse and
fine-tuning stages up to 20.6 ns. (c) Samples of the recorded waveforms when
fine-tuning delays is carried within the coarse delay of FBG2. .......................... 42
Figure 3.4 (a) Constellations of the B2B signals and various delayed signals. (b) The
BER of the various delayed signals when transmitting 10 Gbaud QPSK data.
(c) VNA magnitude response of some delay samples. ........................................ 43

Figure 4.1 Concept of multiple coarse- and fine-tuning delays using a comb and
FBGs. ................................................................................................................... 45
Figure 4.2 (a) Experimental setup. (b) The output of HNLF1 along with the tuning
range of P 1. (c) The output of multicasting stage of PPLN-1. (d) Matched
reflection spectra from arrayed and sampled-and-chirped FBGs. (e,f)
converting the fast/slow signals to original wavelength after HNLF2. ............... 46
xi

Figure 4.3 (a) Waveforms for some of the signal delays. (b) Accessible delays by
combining the coarse- and fine-tuning stages up to 8.1 ns. (c) constellations
of the 10 Gbaud QPSK signal at different points of the system. (d) BER
performance of the 10 Gbaud signal before and after the delays system. ........... 47
Figure 4.4 (a) Chromatic dispersion measurement setup for the chirped FBGs. (b)
Chromatic dispersion curve of the chirped-and-sampled FBG, along the
values of dispersion for the linearly chirped FBG at 1535 nm and 1540 nm. ..... 48
Figure 4.5 (a) RF B2B system to generate and detect the chirp. (b) RF-detected chirp
in time and frequency domains. (c) The optical delay system setup to delay
microwave chirp pulse. ........................................................................................ 49
Figure 4.6 Compressed pulses for (a) RF B2B, (b) delayed pulse at 1528 nm. ............ 49

Figure 5.1 Different OAM modes corresponding to different 𝓵 ’s are orthogonal. ........ 52
Figure 5.2 (a) Generation, (b) detection, and (c) shifting an OAM beam by using a
spatial light modulator (SLM). ............................................................................ 53
Figure 5.3 Concept an optical recirculating delay loop based on the orthogonality of
spatial OAM modes. ............................................................................................ 54
Figure 5.4 Experimental setup of the OAM-shifting recirculating delay loop. ............. 55
Figure 5.5 (a,b) Detected power on the OAM modes when the loop is blocked (SLM-
2 is blocked) for the cases of transmitting ℓ𝑖𝑛 = 0 and when transmitting
ℓ𝑖𝑛 = 8, respectively. .......................................................................................... 56
Figure 5.6 (a) Power on the detected OAM delayed modes when the loop is enabled
when transmitting ℓ𝑖𝑛 = 0 and shifting by ℓ𝑠 ℎ𝑖𝑓𝑡 = −3. (b) Detected 1-ns
pulses to measure the delays. (c) The corresponding constellations when
transmitting 20 Gbaud QPSK. (d) The BER performance of detected
recirculations. (e-h) The results when sending ℓ𝑖𝑛 = 8 and shifting by
ℓ𝑠 ℎ𝑖𝑓𝑡 = −5, showing the performance of the delayed recirulations#0 to #3.
............................................................................................................................. 58

Figure 6.1 (a) Concept of homodyne detection of WDM DP-signals utilizing PPLN
waveguides inside polarization-diversity loops to coherently multiplex the
signals, conjugates, and LO. The generated multi-level eye diagrams at the
photodiode outputs correspond to multiplexing the in-phase and quadrature
data on both polarization states, respectively, of the two channels. (b)
Conjugates generation in Stage-1 using a dual-polarization LO in a PDL. (c)
Multiplexing of the DP-signals, conjugates and LO using a DP-pump (P(t)),
and PPLN waveguides inside two PDLs (for the in-phase and quadrature
paths) in Stage-2. ................................................................................................. 62
xii

Figure 6.2 (a) Experimental setup for a homodyne receiver for a DP-QPSK signal
using PPLNs inside a PDL. (b) Experimental spectrum after the first stage
(Stage-1). (c) Experimental multiplexing spectrum after Stage-2. ...................... 65
Figure 6.3 Experimentally recorded eyes the from homodyne detection of a DP-
QPSK signal showing the I/Q components under different conditions at (a) 32
Gbaud, and (b) 20 Gbaud. (c) BER performance of the homodyne detection
system and the BER measured using a coherent receiver. .................................. 66
Figure 6.4 (a) Experimental setup of homodyne detection for two SP-PSK signals
using nonlinearity. (b) Spectrum after conjugate generation in Stage-1. (c)
Spectrum of the multiplexing of both signals with LO after Stage-2. (d,e)
Multiplexing spectra when only one signal/conjugate pair is transmitted at the
LCoS filter while the other pair is blocked. ........................................................ 68
Figure 6.5 (a) Experimental homodyne detection eyes for the first BPSK signal. (b)
Detected eyes for the second BPSK signal. (c) The multiplexed four-level
eyes composed of two BPSK signals at 20 Gbaud. (d) BER performance of
the four-level multiplexed output. ....................................................................... 69
Figure 6.6 (a) Homodyne detection of the first QPSK signal in a system of two 20
Gbaud channels (in-phase component). (b) In-phase component of the second
QPSK signal. (c) Experimental homodyne detection of the multiplexed two
QPSK signals at 20 Gbaud showing noisy eyes with BER exceeding 3.8×10
-
3
due to power handling and conversion efficiencies limitations. ....................... 70

Figure 7.1 Concept of BPSK regeneration without a phase-locked loop using narrow
bandwidth Brillouin amplification (BA) to amplify the idler “in-line”. The
idler is generated in HNLF1 and exclusively amplified in an SMF using a
counter propagating Brillouin pump. Because the idler is amplified in the
same path in which the signal and the pump propagate, their phase
relationships remain fixed; avoiding the need for phase stabilization. ................ 74
Figure 7.2 (a) Experimental setup of BPSK regeneration using a BA. (b) SMF SBS
performance as a function of EDFA5 output power (BA pump power) to
illustrate the operating point. (c) Spectrum at the 500m SMF input. (d)
Spectrum at the 500m SMF output with idler amplification. (e) Spectrum of
the idler of a 20 Gb/s signal recorded at EDFA6 input using a 10 MHz
resolution OSA without loading the phase noise. (f) Spectrum after
regeneration at HNLF2 output. ............................................................................ 76
Figure 7.3 Constellations before and after the phase-sensitive regeneration system
at different bitrates ranging between 10-30 Gb/s with different phase noise
levels, different types of HNLF2, and different types of phase noise (1 GHz
tone or white noise) (a-e). (f) EVM percentage of improvement for the various
xiii

scenarios in (a-e). (g) Percentage of improvement in the φ noise for the different
scenarios. ............................................................................................................. 78
Figure 7.4 BER Performance and corresponding eyes before and after the
regeneration system when φ noise is 1 GHz tone for signals at: (a) 10 Gb/s, and
(b) 20 Gb/s (same cases (a) and (b) in Figure 7.3 for level-1 and level-2). ......... 79
Figure 7.5 Experimental Study of tuning various parameters on system performance
and its stability when regenerating a 10 Gb/s signal with φ noise of level-2: (a)
Effect of tuning the BA pump frequency from the optimal ν B and recording
the EVM and constellations of different frequency tunings cases. (b) Effect
of tuning the BA gain through tuning BA’s pump power (EDFA5 power) on
the EVM, showing the regeneration output constellations at different EDFA5
power levels. (c) Measurement of phase sensitive dynamic range (PSDR). (d)
System EVM performance over an hour while running the system without
PLL feedback. ..................................................................................................... 80

Figure 8.1 Constellations of an input QPSK signal with phase noise, and the
regeneration output (simulation). ........................................................................ 83
Figure 8.2 The concept of QPSK channel phase regeneration without a phase-locked
loop using Brillouin amplification. ...................................................................... 85
Figure 8.3 (a) Experimental setup. (b) The spectrum of generated idlers after HNLF 1.
(c) Applied delay in the LCoS filter to compensate for the dispersion-induced
walk-off in the 500 m SMF-28 between P, S, idler 3φS, and idler 4φS. (d) BA
operating point as a function of EDFA 5 output power. (e) Spectrum at the
SMF-28 output to show the amplification on idler 4φS. (f) Spectrum of the
amplified idler 4φS captured using a 10-MHz resolution optical spectrum
analyzer, showing that idler 4φS’s central component gains 40 dB, while the
5.5-GHz φ noise components are not amplified. (g) HNLF 2 output when the
system is regenerating the phase, and when S is blocked to observe the ∼10
dB power difference between e
(jφS)
and e
(−j3φS)
. .................................................... 87
Figure 8.4 (a) Constellations before and after the regeneration system at various
φ noise levels, (b) Percentages of improvement in the figures-of-merit
corresponding to input phase noise variance (∆Φ) levels. (c) BER
performance of the regeneration system. ............................................................. 89
Figure 8.5 (a) Impact of tuning the phase of idler 4φS on the regeneration system, (b)
Effect of tuning the frequency shifter of the BA on regeneration the output. ..... 90
Figure 8.6 (a) BA Gain with respect to tuning the BA pump frequency. (b) ON/OFF
ratio of the BA process for the idler 4φS. ............................................................... 90
xiv

Figure 8.7 (a) Histograms of input and regenerated 10-Gbaud output signal. (b,c)
Free-running stability test over an hour without a PLL. The performance is
characterized by (b) EVM and (c) ∆φ. ................................................................ 91

xv

Abstract
Optical communication systems have benefited from the tremendous bandwidth
of optical signals (beyond tera-hertz) to transmit information for a long time [1,2].
Through using the optical nonlinear wave mixing, this Ph.D. dissertation explores the
potential of developing tunable delay lines and processing high-speed signals in the
optical domain.
The first part of this dissertation studies tunable multiple-access optical delay lines.
Traditionally, optical delays have been created by sending a signal through a fixed optical path
which provides a fixed delay [48]. On the other hand, having tunable optical delays can create
possibilities of more optical signal processing functions capable of accommodating the
heterogeneous data traffic of future networks, as well as baud-rate-adjustable, reconfigurable
and tunable signal processing and arbitrary filter designs [3–5]. In the past, tunable optical
delays have been achieved using wavelength conversion and group-velocity dispersion
(GVD) [6,7]. However, for many signal-processing functions, accessing multiple delays at
the same time is needed [1,2]. In this dissertation, we first explore using nonlinear multicasting
with a frequency comb to create multiple delays. We next investigate reducing the latency
excess lengths of fibers in the delay system by replacing kilometers of dispersive fibers with
the time-of-flight in fiber Bragg gratings shorter than 100 meters. We also present a new
concept to access different delays at the same time by using orthogonal spatial modes in a
recirculating loop.
The second part of this dissertation is about using the wave mixing to enable
signal processing functions. We demonstrate all-optical signal processing functions
that bring together various nonlinear devices and processes, and different data
modulation formats. Our goal is to achieve high-speed signal processing functions that
can potentially operate at the line rate of fiber optic communications [8,9]. Therefore,
we employ the recent advances in the enabling technologies to demonstrate various
techniques that can process phase- and amplitude-encoded optical signals. We use
nonlinear media, such as highly nonlinear fiber, and periodically poled lithium niobate
for nonlinear mixing of optical signals. We propose and experimentally demonstrate
all-optical homodyne detection of dual-polarization and WDM phase modulated
xvi

channels. We also describe BPSK signal regeneration in the optical domain with
assistance from Brillouin amplification to reduce the requirements on the phase-locked
loop tracking. Finally, we extend our approach to regenerate a QPSK channel by
generating the signal’s higher harmonics and mixing them.

17

Chapter 1 Introduction
This chapter will introduce some basic concepts and devices for optical wave
mixing such as four-wave mixing and three wave mixing. Next, we will discuss the
technologies to enable the utilization of wave mixing, such as modulating the optical
wave, coherent detection, and optical frequency combs. Then, we will explain some
building block enabling operations to realize tunable delays and signal processing
functions, such as optical multicasting, coherent superposition, and higher-harmonics
generation. By the end of the chapter, we will explain the outline of this dissertation
and how we benefit from wave mixing processes to advance the area of tunable delays
and signal processing.
1.1 Nonlinear Wave Mixing Processes
To manipulate the beams and enable various functions, nonlinear wave mixing
will be utilized in optical nonlinear elements. For example, Kerr nonlinearities have
ultra-fast sub-ps response times and can mix and vary optical signals over bandwidths
beyond THz. Such nonlinearities, therefore, have been considered as an enabling
technology for all-optical signal processing [9,10].
In this section, some of the used nonlinear processes in this dissertation for
tunable delays and signal processing will be reviewed. In general, “wave mixing" is a
process that involves interaction among different optical waves at different
wavelengths to generate new waves at a new wavelength, in the process commonly
known by wavelength conversion [9]. These wave-mixing interactions are governed
by a set of rules such as: (i) conservation of energy, and (ii) phase matching conditions,
which is a form of conservation of momentum [9,11,12]. We will overview the χ
(2)

and χ
(3)
nonlinear processes. The third-order nonlinear process of four-wave mixing
(FWM) that is achieved in third-order susceptibility χ
(3)
materials [11]. χ
(2)

nonlinearities can also mix two waves and generate mixing terms such as second
18

harmonic generation (SHG), sum frequency generation (SFG), difference frequency
generation (DFG), and a cascading of such mixing products [9,13].
1.1.1 Four-Wave Mixing
Four-wave mixing (FWM) is the wave mixing process that can be observed in
χ
(3)
materials. In this process, three input waves mix under the phase-matching
conditions in a nonlinear medium to generate a fourth wave. Figure 1.1 depicts the
schematic spectra of two different types of FWM, namely degenerate and non-
degenerate FWM [9].

Figure 1.1 (a) Degenerate and (b) Non-degenerate four-wave mixing (FWM) schemes for generation
of phase conjugate signal copy. ZDW: zero dispersion wavelength.
In degenerate FWM (Figure 1.1 (a)), a continuous wave (CW) pump at frequency
fpump and a data signal at fsig are combined and sent into a χ
(3)
nonlinear material such
as highly nonlinear fiber (HNLF) [9]. If the pump is located around the zero-
dispersion-wavelength (ZDW) of the nonlinear device, the phase matching conditions
are then satisfied, and the frequency of the newly created wave follows:
𝑓 𝑐𝑜𝑛𝑣 = 2𝑓 𝑝𝑢𝑚𝑝 − 𝑓 𝑠𝑖𝑔 (1.1)
The converted signal is a “wavelength converted" and “phase-conjugate" copy
of the original optical data channel [9]. In this thesis, we tend to drop the time
dependency term for the CW pumps in order to emphasize and distinguish between
data-modulated signals and CW pumps [9]. In the degenerate FWM, if the data-
sig
f
conv
f
ZDW
pump
f
*
Degenerate FWM
sig
f
1 conv
f
1 pump
f
*
2 conv
f
2 pump
f
*
3 conv
f
Non-Degenerate FWM
ZDW
19

modulated signal is used as the pump, then the converted signal is proportional to the
square of the signal field. Therefore, it neither conserves the phase information of the
original signal, nor preserves the intensity shape [9]. In the non-degenerate FWM
scheme, shown in Figure 1.1(b), two pumps at fpump1 and fpump2 located around the
ZDW of the medium, and the input signal are combined and sent into the nonlinear
medium [9]. If the device has flat dispersion slope around the ZDW, phase-matching
conditions hold for FWM between these pumps and signals, resulting in the generation
of the following mixing products [9]:
𝑓 𝑐𝑜𝑛𝑣 1
= 2𝑓 𝑝𝑢𝑚𝑝 1
− 𝑓 𝑠𝑖𝑔 (1.2)
𝑓 𝑐𝑜𝑛𝑣 2
= 𝑓 𝑝𝑢𝑚𝑝 1
+ 𝑓 𝑝𝑢𝑚𝑝 2
− 𝑓 𝑠𝑖𝑔 (1.3)
𝑓 𝑐𝑜𝑛𝑣 3
= 𝑓 𝑠𝑖𝑔 + 𝑓 𝑝𝑢𝑚𝑝 2
− 𝑓 𝑝𝑢𝑚𝑝 1
(1.4)
Thus, multiple wave-mixing interactions occur simultaneously in the two-pump
scheme resulting in both phase-conjugating and non-phase-conjugating wavelength
conversions. It is worth mentioning that, because FWM involves two frequencies
being added and one subtracted, if the input pumps happen to be in the same frequency
band (e.g., C-band), then the generated wavelength converted signals also generally
tend to appear in the same band [9].
1.1.2 Three Wave Mixing
In a χ
(2)
nonlinear material, optical signals at two frequency (e.g., f1, f2 ) can mix
under phase-matching conditions and generate a new signal at the sum frequency
( fSFG= f1 + f2 ) and difference frequency ( fSFG= f1 - f2 ). In the case of one input pump,
instead of sum frequency, the second harmonic term (fSFG= 2f1 ) is generated. It is
worth mentioning that if the two input signals are in the same frequency band (e.g.,
~1550 nm), the SHG/SFG term is at ~775 nm, which is in a different frequency band.
In many nonlinear signal processing demonstrations, there has been an interest in
keeping the generated signals in the same frequency band as the input signals using
20

cascading SFG and DFG (cSFG-DFG) or SHG and DFG (cSHG-DFG), as shown in
Figures 1.2 (a) and (b), respectively

Figure 1.2 (a) Cascaded sum and difference frequency generations (cSFG-DFG) and (b) Second
harmonic generation and DFG (cSHF-DFG) for wavelength conversion in a PPLN device. QPM: quasi-
phase matching.
1.1.3 Materials and Devices
Different types of materials and devices can be utilized for nonlinear wave mixing,
and the choice of a nonlinear device is a trade-off between different figures of merit,
such as high nonlinear efficiency, wide bandwidth, low loss, data format transparency
in order to maintain phase and amplitude modulation, simultaneous wave mixings for
simultaneous operations, low dispersion for phase matching, low two-photon
absorption, and latency [9,14,15]. Materials such as silica, lithium niobate, silicon,
bismuth oxide, chalcogenide, semiconductors and multiple quantum wells are used to
create nonlinear optical devices suitable for signal processing [9].
Throughout this dissertation, the primarily used device for χ
(3)
mixing will be
highly nonlinear fibers (HNLFs). Optical fibers made of silica can become efficient
mixing devices when the core is designed to become very small to confine the beams,
as well as when dispersion engineering is incorporated in the design. For instance,
large bandwidth of conversion and simultaneous wave mixing in low-dispersion
HNLFs can be realized [9,16]; however, because of a wide phase-matching bandwidth,

(2)
SFG
f
dummy
f
pump
f
SFG
QPM

(2)
DFG
f
signal
f
idler
Cascaded SFG and DFG
QPM: Quasi-phase matching

(2)
SHG
f
pump f
SFG
QPM

(2)
DFG
f
signal
f
idler
*
Cascaded SHG and DFG
21

a lot of extra parasitic mixing terms may be generated in an HNLF that may (i) occupy
bandwidth, and (ii) create cross-talk on the desired signal.
Periodically poled lithium niobate (PPLN) devices will also be used as a medium
for χ
(2)
nonlinear mixing. PPLNs exhibit high nonlinear mixing efficiency, relatively
low propagation loss, ease of fabrication, and small size. These devices may allow the
implementation of some advanced signal-processing functions at bandwidths beyond
THz as demonstrated in [9,17]. It should be noted that the QPM wavelength in PPLN
devices is very similar to ZDW in HNLFs in the sense that pumps need to be placed
symmetrically around the QPM wavelength in order for the wave mixings to occur [9].
1.2 Enabling Technologies
So far, we reviewed the devices that are used for nonlinear wave mixing.
Nonlinear optical interactions in the form of FWM, SFG, DFG, and SHG were
reviewed from a systems point of view. Here, we overview optical signal modulation
techniques to harness multiple domains of the optical signal.
1.2.1 Encoding in Multiple Domains of Optical Wave
Different domains of the optical wave can be utilized to encode the
information [18]. Coherent systems including coherent detection can be used to
recover both amplitude and phase of an optical signal. In general, n bits of information
can form M = 2
n
states. Each of these M states can be mapped to an amplitude and
phase symbol in the complex plane, as depicted in Figure 1.3. In addition to the
amplitude and phase of an optical wave, we can utilize the polarization of the wave (X
and Y polarization) and multiplex the signal on both polarization states and generate
polarization multiplexed (PM) signals. Moreover, using different frequencies provides
the opportunity of wavelength division multiplexing technique (WDM). Using these
techniques, we can increase the number of transmitted bits per second per one Hertz
of bandwidth which is also called spectral efficiency.
22

Figure 1.3 Advanced modulation formats using amplitude and phase domains, with independent
polarization and wavelength multiplexing
As shown in the constellation diagrams in Figure 1.3, different carrier
wavelengths and polarizations are orthogonal to each other and one can choose
different constellations for different channels. Amplitude shift keying (ASK), phase
shift keying (PSK) and quadrate amplitude modulation (QAM) are the modulation
formats that could be utilized to encode the data on different phase and amplitude of
an optical wave. For example, on channel λ1 in Figure 1.3, a 16-QAM signal is encoded
on the X-polarization of the optical wave and an 8-PSK signal is encoded
independently on the Y-polarization. Or on channel λ1, quadrature-phase-shift-keying
(QPSK) modulation format is used for both X and Y polarization. Because these
symbols are in the complex domain, instead of using amplitude and phase, one can
alternatively define a symbol using real (Re) and imaginary (Im) parts of the symbol.
In communications theory, the former is known as the in-phase (I) and the latter as the
quadrature (Q) component of the data symbol.
1.2.2 Coherent Detection
To recover the I/Q modulated optical beam, a coherent receiver is needed. An
incoming signal would be mixed with a local oscillator (LO) in a 90° hybrid as shown
in Figure 1.4 and then detected using photodiodes for the I/Q information on the X-Y
polarizations. In the coherent receiver, digital signal processing (DSP) can be
Polarization-X
Polarization-Y
Re
Im
Im
Re
Wavelength
1
Re
Im
Im
Re
Wavelength
2
23

implemented to measure the error-vector magnitude (EVM) as a quality metric of the
optical signal [19].

Figure 1.4 Coherent signal detection using the coherent receiver.
1.2.3 Optical Frequency Comb
Optical frequency combs provide multiple-wavelength “fingers” or frequency
lines that are (a) coherent with each other, (b) equidistant in the frequency domain,
and (c) narrow linewidth. These enable the manipulation of the amplitude and phase
for each individual finger and then processing of multiple fingers together without
significant phase noise degradation. At extremely high rates, different comb fingers
can be combined/mixed in a nonlinear optical element [20].

90
o
Hybrid
Local
Oscillator
Signal In
I(t)
Q(t)
E
S
(t) = E
S
(t) e
j(ω
S
t + 
S
(t))
Analog-Digital
Converter
E
LO
Carrier Phase / Polarization
DSP Unit
Carrier Recovery
CD
-1
PMD
-1
PDL
-1
Nonlinearities
24

Figure 1.5 An optical frequency comb in the frequency domain (a) and in the time domain (b).
As shown in Figure 1.5, optical frequency combs feature multiple comb lines
that are equidistant in the frequency domain and are phase coherent with respect to
each other. In this thesis, we utilize multiple narrow-linewidth coherent comb lines
from optical comb source instead of separate lasers to generate and process multiple
signals and to reduce the complexity of using a bank of lasers.
1.3 Basic Enabling Operations
In this section, a few basic operations that embrace the fundamental blocks for
tunable delays and optical signal processing functions are reviewed. These functions
will frequently be used in the following chapters. We overview signal multicasting,
multiplexing and higher-order harmonics generation.
1.3.1 Wavelength Multicasting
Similar to wavelength conversion, optical wavelength multicasting could be
achieved using nonlinearities to create multiple copies of the input data signal at
different output wavelengths [21,22]. Various materials, nonlinear processes,
numbers of pumps and pump configurations can be exploited for multicasting [9].
Figure 1.6 depicts conceptual spectra for two multicasting techniques [9,23]. In Figure
1.6, to generate N signal copies, the input data signal is sent to a nonlinear device with
N discrete pumps to create N copies of the input signal in a degenerate FWM process.
In the literature there are many examples of optical multicasting. For instance, in [22],
the results of multicasting 16-QAM signals in a PPLN waveguide were reported. Also,
like the after-mentioned wavelength conversion, various configurations can provide
either phase conjugated or non-phase conjugated copies.
25

Figure 1.6 Various configurations for N-fold signal multicasting using multi-pumps.
1.3.2 Active Optical Multiplexing
There have been different techniques for optical multiplexing of WDM data
channels into a single channel. These include but not limited to the use of XPM in
HNLFs [24], FWM in HNLFs and waveguides [14,25], and cSFG-DFG in PPLN
devices [26] as in Figure 1.7, where active multiplexing of signals is demonstrated to
generate higher order amplitude and phase modulation formats.

Figure 1.7 An example of coherent multiplexing in a nonlinear device to generate higher order
amplitude and phase formats.
Requires N probe pumps for N-
fold multicasting
f
Signal
Requires (N+1)/2 pumps for N-
fold multicasting
Signal
f
Multi-Pump multicasting configurations
CW Lasers
f
QPSK
Modulated
f
Nonlinear
Device
(Phase
Coherent
Addition)
+

CW
Lasers
f
Modulated
Lasers
Pump
S
1
S
2
S
3
D
3
D
2
D
1
P QAM
+ + =
1
st
QPSK 2
nd
QPSK 3
rd
QPSK
64-QAM
1
st
QPSK=45º 2
nd
QPSK=135º 3
rd
QPSK=225º
•n QPSK signals
generate 4
n
-QAM
• Vector addition of
QAM symbols
Coherent
superposition
26

1.3.3 Generation of Higher-Order Harmonics
In a highly χ
(3)
nonlinear device, the generated mixing terms might mix with the
pump and signal if sufficient power is provided to the system. The newly generated
mixing will be proportional to the higher harmonics of the signal and pump. For
example, sending a QPSK signal with four equidistant phase states and a pump to the
nonlinear material could generate various idlers as shown in Figure 1.8. These idlers
have different spectra and preserve different components of the signal. For instance,
the second harmonic of the QPSK signal is a BPSK signal due to multiplying the phase
by 2. The fourth harmonic on the other hand becomes a CW wave due to multiplying
the phase by 4. However, the generated idlers with the higher harmonics usually suffer
from power penalty due to the limited conversions efficiency. These generated higher
harmonic idlers can be used for various signal processing functions such as optical
phase regeneration and de-aggregation [27–29].

Figure 1.8 Concept of generating the higher harmonics of a signal using nonlinear materials and a pump.
1.4 Dissertation Outline
In this dissertation, Chapters 2-5 will focus on realizing tunable delays with multiple
access using wave mixing and Chapters 6-8 will demonstrate using the wave mixing to enable
high-speed optical signal processing functions. Therefore, this dissertation is organized
with the following structure: Chapter 2 presents the experimental utilization of the
optical frequency comb along in tunable wavelength-conversion/chromatic-dispersion
Re
Im
Re
Im Im
Re
ZDW
sig
f
pump
f
𝑓 𝑖 1
𝑓 𝑖 2
𝑓 𝑖 3

QPSK
BPSK
CW
27

delay lines to provide multiple delays at the same time. The chapter also includes
analysis of the distortion caused by the PPLN waveguide. Chapter 3 demonstrates
utilizing time-of-flight in fiber Bragg gratings with wavelength conversion to realize
tunable delays without excess fiber lengths. Chapter 4 investigates using multicasting
with the comb source to provide tunable multiple delays along using fiber Bragg
gratings. Chapter 5 presents a novel concept of utilizing repeated spatial mode shifting
to achieve discrete delays in a recirculating loop. Chapter 6 demonstrates using the
wave mixing to achieve homodyne detection of WDM and pol-mux channels. Chapter
7 presents using wave mixing and Brillouin amplification to regenerate a BPSK
channel. Chapter 8 reports the experiment of regenerating the phase of a QPSK
channel by amplifying the fourth-harmonic idler using Brillouin amplification.

28

Chapter 2 Fine and Coarse Discrete Delay Line
Using Chromatic Dispersion and an Optical
Frequency Comb
2.1 Introduction
Delay lines have value in many signal processing applications, including
equalization [3], correlation [4], and buffers [5]. In the past, optical delays have been
achieved using several different techniques, including (i) choosing among fixed lengths of
fibers for coarse delays [30], or (ii) utilizing wavelength conversion to achieve wavelength-
dependent time delay based on group-velocity dispersion (GVD) [6,7]. In fact, these two
techniques have been combined to achieve tunable optical fine and coarse delays [31].
An optical frequency comb provides multiple phase-locked lines on a single device
which has been used for various applications, such as in spectroscopy [20] and multi-channel
transmission [32]. Combining the fine and coarse delays with an optical frequency comb
could be of interest to enable coherently accessing multiple delays simultaneously. The access
to multiple delays could be desirable for signal processing applications like filtering [33,34].
In this chapter, we demonstrate an all-optical multiple access, fine and coarse delay line
using a frequency comb. A χ
2
-based periodically poled lithium niobate (PPLN) waveguide
and ten comb lines are used for multicasting [35]. Ten generated multicast copies propagate
in a dispersion compensating fiber (DCF) spool to introduce 3.7-ns delay steps using the group
velocity dispersion (GVD). The GVD fine-delay line is followed by four fiber segments for
the coarse delays, with each fiber adding an increment of ~39 ns. A total of 40 accessible
delays are obtained and the system performance is characterized using a 10 Gb/s on-off keying
(OOK) signal.

29

2.2 Concept
The concept of the optical delay system is depicted in Figure 2.1. The system
can be divided into five stages, which are: (i) pre-dispersion, (ii) phase conjugation,
(iii) multicasting, (iv) fine delay, and (v) coarse delay. The first two stages of pre-
dispersion using DCF1 and phase conjugation in the highly nonlinear fiber (HNLF) are
needed to compensate the intra-channel GVD of the copies in the upcoming fine-delay
stage. The multicasting in the PPLN with the comb lines produces the conjugate copies
for the multiple access, where the number of created copies equals the used number of
comb lines. The fine-delay stage utilizes the GVD of DCF2 to introduce wavelength-
dependent fine delays between the multicast conjugate copies. Finally, the coarse
delays are achieved using a fiber bank.

Figure 2.1 The concept of an all-optical multiple-access, fine- and coarse-delay system using a
frequency comb. Pre-dispersion of DCF 1 is compensated by phase conjugating the signal in a HNLF
and propagating the multicast conjugates later through DCF 2. The multicast conjugates are created in a
PPLN waveguide with frequency comb lines as pumps. The fine delay is realized using GVD while the
coarse-delay stage is created using a fiber bank.
When an incoming optical signal (S) with a frequency ω S enters the system, it
gets first pre-dispersed in DCF1, and it accumulates chromatic dispersion of the
amount +D (the dispersed signal is shown as S+D in Figure 2.1). Next, S +D is phase-
conjugated in a HNLF, which is pumped with a pump1 (P1) at ωP1 to produce S
*
-D at
ωS* through four-wave mixing, as in equation (2.1):

DCF
1
PPLN
λ
S*
-D
DFG Mixing
SFG Mixing
HNLF
Multicast
S*
-D
Incoming
optical
signal
Multicasting
(Generate copies)
λ
S
+D S*
-D
Pre-dispersion
CL,
1…
CL,
i
λ
Fine delay
(Dispersion-based delay)
λ
λ
λ
λ
delay
Select
multicast
Select
conjugate
P2
P
1
λ
S
+D
Coarse delay
(Fiber-bank delay)
λ
P
1
λ
Comb lines
(CL)
λ
S*
-D
S*
S*
S*
S*
λ
S
DCF
2
λ
P
2
phase
conjugation
QPM ω
S ω
S
ω
S
ω
S* ω
p1
ω
p2
ω
S*
ω S*,1 ω S*,i ω CL,i ω CL,1
… …
Delay
splitter
DCF: dispersion compensating fiber; DFG: difference-frequency generation, HNLF: highly nonlinear fiber;
PPLN: periodically poled lithium niobate, QPM: quasi-phase matching, SFG: sum-frequency generation.
30

S
*
-D ∝ (P1)
2
×( S+D)
*

ωS*-D=2ωP1-ωS+D
(2.1)
Where: ωP1 is pump1’s frequency and ωS*-D is the generated signal conjugate’s
frequency. S
*
-D is then multicasted in a PPLN waveguide that is pumped with the
comb lines and pump2 (P2). The multicasting in the χ
2
PPLN waveguide is based on
the cascaded sum-frequency generation (SFG) and difference-frequency generation
(DFG) processes [36]. S
*
-D and P2 are set symmetrically around the PPLN’s quasi-
phase matching (QPM) frequency to maximize the efficiency of their SFG. The DFG,
using the comb lines (CL,i), then creates the copies (S
*
-D,i) with the frequencies in
equation (2.2):
S
*
-D,i ∝ (P2)×( S
*
-D)×(CL,i)
*

ωS*,i=ωP2+ωS*-D-ωCL,i
(2.2)
where ωS*,i is the created copy’s frequency, ωp2 is the frequency of pump2, ωCL,i
is the comb line frequency, and i is the index of the comb line or signal copy.
Afterward, the multicast conjugates propagate through DCF2 to introduce the
fine delays. DCF1 and DCF2 have similar chromatic dispersion. The intra-channel
GVD of all multicast copies caused by DCF2 will almost be compensated because of
the prior pre-dispersion and phase conjugation. In addition, due to the inter-channel
dispersion, the multicast copies will arrive at different times, resulting in multiple-
access fine delays. Finally, a splitter and fiber segments (fiber bank) are added to
provide coarse-delay offsets. Therefore, the signal copy with the desired delay can be
selected using a band-pass filter (BPF) that is tuned to the wavelength corresponding
to the fine delay at the output of the corresponding fiber segment.
2.3 Experimental Setup
The experimental setup is depicted in Figure 2.2(a). A laser at 1562 nm is
intensity modulated in a 40-GHz Mach–Zehnder modulator (MZM). The intensity
31

modulator is driven by (i) a vector network analyzer (VNA) waveform to analyze the
dispersion of the system, (ii) a pulse to evaluate the delay using a 50-GHz sampling
scope, or (iii) a 10 Gb/s 2
31
-1 pseudo-random bit sequence (PRBS) pattern.

Figure 2.2 (a) Experimental setup of the multiple-access fine- and coarse-delay system using an optical
frequency comb. (b) The optical spectrum of S*-D generation at the output of HNLF 1. (c) 10x
multicasting of S*-D at the output of the PPLN waveguide.
The modulated signal is pre-dispersed through DCF1 with a total GVD of ‒4
ns/nm to give S+D. In the phase-conjugation stage, S+D is amplified in erbium-doped
fiber amplifier (EDFA), and coupled with an amplified continuous-wave (CW) P1 at
ωP1=1556 nm. S+D and P1 are then sent together into a 450-m-long HNLF1 to create
S
*
-D at ωS*-D=1549 nm, as shown in Figure 2.2(b).
S
*
-D is next boosted by EDFA and coupled with a CW P 2 at ωP2=1552 nm in
addition to ten comb lines that are spaced 1-nm apart from a mode-locked laser (MLL).
In the PPLN waveguide, the SFG process takes place between S
*
-D and the P2
concurrently with the DFG processes using the other ten comb lines. These processes
generate ten copies of the signal’s conjugate, covering the spectrum from 1537.9 nm
to 1546.4 nm (Figure 2.2(c)).
The ten generated multicast copies are selected in a BPF and sent into DCF2 to
introduce the relative fine delays. The delayed copies are amplified, and the residual
coarse
delay
(Fiber
bank)
1535 1545 1555 1565
(a)
Power (20dB/div)
Power (20dB/div)
P
1
Dispersed
Signal
S
+D
Wavelength [nm]
(b)
Conjugate
S*
-D
(c)
Comb lines
10x Multicasting
of S*
-D
Conjugate
S*
-D
P
2
Copies
10 9 . . . . 3 2 1
Wavelength [nm]
Power (20dB/div)
14.8-dB
1562
nm
1nm
Modulator
450m
HNLF1
DCF
1
-4ns/nm
1nm
50/50
BPF4
1nm
RF input:
(i) VNA signal.
(ii) Digital pulse
(iii) 10Gb/s OOK
1nm
phase conjugation
Pre-amp 130mW
200mW PPLN
15nm 11nm
P2
1552nm
13nm
2nm
Pre-amp
145mW
50/50 50/50
(a)
Multicasting in PPLN
with comb pumps
500mW
PC
b c
Detection
system
DCF
2
-4ns/nm
DCM
Fine delay
(Dispersion-
based delay)
Pre-amp
0.3 nm 1 nm
photo-
diode
Pre-amp
RF output:
(i) VNA
(ii) Sampling
scope
(iii) 10 Gb/s
BERT
0m
6.6m
13.2m
19.8m
1535 1545 1555 1565
1nm
P1=1556nm
500mW
Pre-
dispersion
BPF: Band-pass filter, DCM: Dispersion compensation module, DLI: Delay-line interferometer,
MLL: Mode-locked laser, PC: Polarization controller.
Comb
Source
32

dispersion is compensated in a dispersion compensation module (DCM) with a tuning
range of ±400 ps/nm. The dispersion-based fine-delay system is followed by a 1×4
splitter and four fiber segments with lengths corresponding to 0, 6.6, 13.2, and 19.8 m
to add ~39-ns of coarse-delay offsets. At the system output, the desired delayed copy
is selected using a BPF connected to the corresponding fiber. A low-noise EDFA is
used to amplify the selected delayed copy, which is detected using a 32-GHz
photodiode.
2.4 Results
We start by characterizing the system by transmitting the VNA’s waveform and
recording the magnitude responses at different points of the system as illustrated in Figure 2.3
(a‒d). The back-to-back (B2B) signal’s response is characterized by connecting input signal
of DCF 1 directly to the detection system, which gives the flat magnitude response shown in
Figure 2.3(a). Figure 2.3(b) shows the response of the dispersed signal after DCF 1, with the
distorted magnitude response due to the accumulated dispersion. In Figure 2.3(c), the
magnitude response of copy 5 is presented after propagating through DCF 2, which indicates
dispersion compensation but with some residual dispersion that necessitates using the DCM.
The performance after the DCM is shown in Figure 2.3(d), where the flat response is
recovered. The amount of dispersion compensation for the different copies is depicted in
Figure 2.3(e). the residual dispersion ranged from -320 ps/nm to -400 ps/nm among the
multicast copies.
33

Figure 2.3 The magnitude responses measured using the VNA for the: (a) B2B signal, (b) signal after
DCF 1, (c) copy 5 after DCF 2, and (d) copy 5 after the DCM. (e) The dispersion compensation module
setup to compensate for the residual GVD.
The delays between the output multicast copies after the fine-delay stage are
characterized by transmitting a 10-ns pulse and detecting the copies using a sampling scope.
The waveforms of the ten delayed copies are shown in Figure 2.4(a). A differential delay of
∼3.7 ns is observed between any two adjacent copies. It is noted that the pulses also have
falling edges, which can be caused by low-frequency filtering in the system. The delays of all
40 copies when combining the fine and coarse stages are shown in Figure 2.4(b).

Figure 2.4 (a) Experimentally captured copies at the output of the fine-delay stage. (b) Accessible delays
when combining the coarse delay and fine delay.
Figure 2.5(a) depicts the BER performance of some delayed signals when
transmitting a 10-Gb/s OOK signal. The penalty between the optical B2B signal and
-420
-380
-340
-300
1 2 3 4 5 6 7 8 9 10
Multicast copy
DCM Setup
[ps/nm]
B2B signal
Multicast copy #5, after DCF
2
Multicast copy #5, after DCM
Frequency [GHz]
Power
(10dB/div)
(a)
Power
(10dB/div)
Power
(10dB/div)
(e)
Frequency [GHz]
Frequency [GHz]
Frequency [GHz]
Power
(10dB/div)
Signal after DCF
1
(b)
(c) (d)
0
0.045
0.09
0.135
0.18
0 5 10 15 20 25 30
Copy1, λ=1546.4 nm
Copy2, λ=1545.5 nm
Copy3, λ=1544.5 nm
Copy4, λ=1543.6 nm
Copy5, λ=1542.6 nm
Copy6, λ=1541.7 nm
Copy7, λ=1540.7 nm
Copy8, λ=1539.8 nm
Copy9, λ=1538.8 nm
Copy10, λ=1537.9 nm
Copy1
Copy2
Time [ns]
0 60
33.3ns
3.7ns
Multicast copies
and their relative
delays after the fine
delay stage
(a)
Copy3
Copy4
Copy5
Copy6
Copy7
Copy8
Copy9
Copy10
60 mv
0 mv
60 mv
0 mv
60 mv
0 mv
60 mv
0 mv
60 mv
0 mv
60 mv
0 mv
60 mv
0 mv
60 mv
0 mv
60 mv
0 mv
60 mv
0 mv
Fiber Segment Length [m]
(b)
0 10 20 30
Relative Delay [ns]
180
135
90
45
0
34

the shown delayed copies is ~2‒4 dB at a BER of 10
‒9
. We believe the penalty is
caused by the nonlinear phase conjugation, multicasting processes. For example, in
the experiment we observe that mixing in HNLF1 causes ~1-dB penalty. In addition,
the multicasting in the PPLN can cause ~0.6 dB penalty.

Figure 2.5 The BER performance of different delayed 10-Gb/s OOK copies.
2.5 Characterization of Distortion in the PPLN Waveguide
Spurious-free dynamic range (SFDR) is considered an important characteristic
that measures the second- and third-order distortions [37], which represent the
linearity of systems. In a PPLN waveguide, there is typically a cascaded χ
2
:χ
2
process,
in which second-harmonic generation (SHG) followed by difference-frequency-
generation (DFG) [13]. The impact of the χ
2
:χ
2
process on the system linearity will be
studied in this section.
The concept of the distortion measurement is depicted in Figure 2.6. In Figure
2.6 (a) An optical carrier at λs which is modulated with two microwave tones (f1 and
f2) is combined with a pump laser at λpump, and the combined microwave signal and
pump are sent into the PPLN waveguide to generate the idler. Idler could be generated
when the pump laser is set to be at the QPM wavelength of the PPLN (λ pump=λQPM)
such that a second harmonic generation process (SHG) of the pump occurs
simultaneously with DFG with the signal. Therefore, the idler is generated as
idler=(pump)
2
×(optical signal)* at λidler=2λpump- λs. Then, we filter the idler and
investigate its SFDR as in Figure 2.6(b) and compare the obtained SFDR to the
5
10
-34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22
B2B After HNLF
Copy5 after PPLN, Bypass DCFs copy2, 0-m
copy4, 6.6-m copy5, 0-m
copy6, 13.2-m copy10, 19.8-m
Received Power (dBm)
5
6
9
7
8
10
-Log10(BER)
35

signal’s itself. We measure and compare the SFDR performance for both the third-
order harmonic distortion and second-order harmonic.

Figure 2.6 (a) Concept of SFDR measurements for the idler generated in a χ2 PPLN waveguide. An
optical carrier which is modulated with microwave tones is combined with a pump laser and sent into
the PPLN waveguide where they mix in a SHG and a DFG manner to generate the idler. (b) Spurious-
free dynamic range measurement on the idler for both second and third harmonic distortions (THD:
Third-order harmonic, SHD: Second-order harmonic).
2.6 Experiment and Results for Measuring the PPLN Waveguide
Distortion
The experimental diagrams for each SFDR measurement is shown in Figure 2.7.
We started in Figure 2.7(a) by characterizing the RF B2B system by sending two tones
at 9.906 and 9.912 GHz into an SHF 807 linear amplifier and an HP 8565E spectrum
analyzer. Then, in Figure 2.7 (b), we build the simplest optical B2B system using a
laser at 1546nm and an optical modulator (EOSPACE 40GHz Vπ=2.25V) and
characterized the system. In Figure 2.7(c), we characterize the addition of the high
power amplifier which will be needed to generate the idler in the PPLN and the
attenuator used to fix low-noise pre-amplifier (LN-EDFA) input power at -15 dBm,
χ2-Based
PPLN Waveguide
λs
f
1
f
2
λpump
carrier
pump
f
1
f
2
carrier
pump
λs λpump
Optical
pump
Second
order
harmonic
Third
order
harmonic
f
1
f
2
carrier
pump
λs λpump
f
1
f
2
idler
2f
2
-f
1
2f
1
-f
2
2f
1
2f
2
(a)
SHD
SFDR-THD
Noise floor(1Hz)
THD
Input power
Output power
SFDR-
SHD
SFDR measurement
(b)
Optical carrier
modulated with
RF tones
SHG and DFG mixing
36

where LN-EDFA is used to deliver the PD with fixed +10dBm. Figure 2.7(d) shows
the setup when signal passes through a “passive” PPLN (without nonlinear interaction)
and in Figure 2.7(e) we added the pump at 1551 nm and characterized the idler’s
performance. Finally, in Figure 2.7(f) we tune the PPLN temperature by 1.3
o
C such
that QPM changes with 0.1 nm from the its position and conversation efficiency
degraded from 14.5 to 25 dB.

Figure 2.7 The experimental setups showing different characterization scenarios (with the
added/changed components highlighted for every scenario).
In Figure 2.8, the measured power of the THD and SHD for the various cases are
shown, and the summary of the SFDR measurements is shown in Figure 2.9. We
f1=9.906 GHz
f2=9.912 GHz
+
SHF 807
RF amplifier
HP 8565E
RF spectrum
analyzer
f1=9.906 GHz
HP 8565E RF
spectrum
analyzer
Filter
2nm
Laser
1546nm
EDFA1
200mw
f2=9.912 GHz
MZM PD
SHF 807
RF amplifier
+
(a) Characterization of
RF B2B system
(b) Characterization
of analog optical
signal in a B2B
system
LN-EDFA
10 dBm
f1=9.906 GHz
Filter
2nm
Laser
1546nm
EDFA1
200mw
f2=9.912 GHz
MZM
HP 8565E RF
spectrum
analyzer
PD
SHF 807
RF amplifier
+
EDFA2
400mw
Filter
2nm
attenuator
(c) Characterization
of analog optical
signal in a system
including EDFA
LN-EDFA
10 dBm
f1=9.906 GHz
Filter
2nm
Laser
1546nm
EDFA1
200mw
f2=9.912 GHz
MZM
HP 8565E RF
spectrum
analyzer
PD
SHF 807
RF amplifier
+
EDFA2
400mw
Filter
2nm
attenuator
(d) Characterization
of analog optical
signal in a system
including passive
PPLN
PPLN
T=49.3
o
C
QPM=
1551nm
LN-EDFA
10 dBm
f1=9.906 GHz
Filter
2nm
Laser
1546nm
EDFA1
200mw
f2=9.912 GHz
MZM
HP 8565E RF
spectrum
analyzer
PD
SHF 807
RF amplifier
+
EDFA2
400mw
Filter
2nm
attenuator
(e) Characterization
of the idler
generated using
PPLN
Pump
1551nm
PPLN
T=49.3
o
C
QPM=
1551 nm
LN-EDFA
10 dBm
f1=9.906 GHz
Filter
2nm
Laser
1546nm
EDFA1
200mw
f2=9.912 GHz
MZM
HP 8565E RF
spectrum
analyzer
PD
SHF 807
RF amplifier
+
EDFA2
400mw
Filter
2nm
attenuator
(f) Characterization
of idler when PPLN
temperature/QPM is
tuned
Pump
1551nm
PPLN
T=48
o
C
QPM=
1550 nm
Filter
2nm
Filter
2nm
Filter
2nm
Experimental Scenarios
37

conclude from the measurements that SFDR didn’t change significantly by including
the PPLN waveguide in the system.

Figure 2.8 The experimentally measured SHD and THD for the various cases in Figure 2.9.

Figure 2.9 Summary of the measured SFDR-THD and SFDR-SHD.
2.7 Conclusion
In conclusion, an all-optical fine and coarse delay line with access to multiple discrete
delays is experimentally demonstrated. There are several aspects to be noted about our
Corresponding SFDR plots
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
-200-160-120 -80 -40 0 40
Fundamental
THD
SHD
(a)
Output power [dBm]
RF Input power [dBm]
(b)
Output power [dBm]
RF Input power [dBm]
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
-200 -160 -120 -80 -40 0 40
Fundamental
THD
SHD
1-Hz noise 1-Hz noise
(c)
Output power [dBm]
RF Input power [dBm]
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
-200 -160 -120 -80 -40 0 40
Fundamental
THD
SHD
(d)
Output power [dBm]
RF Input power [dBm]
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
-200 -160 -120 -80 -40 0 40
Fundamental
THD
SHD
1-Hz noise
1-Hz noise
(e)
Output power [dBm]
RF Input power [dBm]
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
-200 -160 -120 -80 -40 0 40
Fundamental
THD
SHD
1-Hz noise 1-Hz noise
(f)
Output power [dBm]
RF Input power [dBm]
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
-200 -160 -120 -80 -40 0 40
Fundamental
THD
SHD
101.7 93.71
87.18 87.18
86.62
88.12
86.6
83.59
78.49 77.5
78.4 78.14
0
20
40
60
80
100
120
140
(a) (b) ( c) (d) (d) (f)
SFDR-THD
SFDR-SHD
Summary of SFDR measurements
Scenarios from Fig.2
Before PPLN
After PPLN
SFDR-THD(dB.Hz
2/3
)
SFDR-SHD(dB.Hz
1/2
)
38

experiment. Although we did not shift the copies back, one can translate one of the 10
accessible fine-delay output copies back to the original wavelength by using an additional all-
optical wavelength conversion stage [6,7,31]. In order to preserve the phase at the output, an
additional phase-conjugation stage for the incoming data signal before DCF 1 should be added.
Also, the relative fine delay between the adjacent copies is governed by the frequency spacing
between the comb lines and the GVD of the DCFs. One can tune the fine-delay stage by
changing the comb’s frequency spacing like in electro-optic combs [38] or by changing the
selected comb lines using a programmable filter. Furthermore, this system can be used as a
tunable and programmable all-optical delay line, where one can add a switch to select the
desired delay [39].

39

Chapter 3 Continuously Coarse and Fine Tunable
Optical Delay Using the Time-of-flight in Fiber
Bragg Gratings and Wavelength Conversion
3.1 Introduction
There are various applications for the ability to delay a data channel and choose among
different delay values. Applications include microwave photonics for analog signals and data
synchronization and network management for digital channels [39,40].
Desirable characteristics of delay lines include, low loss, low distortion, and low
latency [41,42]. A relatively straightforward approach to achieving delays is to vary the time
of flight of an optical beam. Previous approaches include varying free space paths and lengths
of fiber [43], and wavelength dependent reflections from an array of fiber Bragg gratings
(FBGs) [44–46]. It is also of interest to create continuously tunable delay systems that offer
coarse and fine tunability to achieve large delays with small and high-resolution steps [47].
In this chapter, we use FBG array to achieve coarse delays. Then, we use wavelength
conversion in PPLN waveguides with channelized FBG and a chirped FBG to realize tunable
continuous fine tuning delays [48]. We achieve 20.6 ns continuous delay tuning range with
OSNR penalty below 0.6 dB for a 10 Gbaud QPSK signal.
3.2 Concept
The concept of using the FBGs to continuously access coarse and fine-tuning delays
is depicted in Figure 3.1. A data signal (S) is first sent to arrayed FBGs and a
channelized FBG (phase-only sampled FBG [49]). The discrete FBGs add the coarse-
tuning delays depending on the time-of-flight. The channelized FBG adds a constant
delay to all wavelengths and is used to pre-equalize the signal. The pre-equalization is
needed for the upcoming continuous fine-tuning stage. Next, we send the signal to a
tunable wavelength conversion stage using a PPLN waveguide and two pumps (P1,
40

and P2). P2 is placed in symmetry with the signal around the quasi-phase matching
(QPM) wavelength, and P1 is tuned to choose the wavelength of generated signal copy
(S’). The created copy then enters the chirped FBG that adds fine-tuning delay. Finally,
we send the delayed signal with the same two pumps to PPLN2 to wavelength-convert
the signal back to the original wavelength. As a result, the fine-tuning stage can be
used to fill the gaps in between the discrete delays and to achieve a large continuous
tunable delay range.

Figure 3.1 Concept of coarse and fine-tuning delays using time-of-flight in cascaded FBGs and
wavelength conversion.
3.3 Experimental Setup
The experimental setup is depicted in Figure 3.2(a). A tunable laser source with
wavelength (λs) transmits a continuous-wave (CW) light which is modulated by: (i)
10Gb/s OOK pattern to characterize the delay, (ii) 10 Gbaud QPSK signal, or (iii) a
VNA waveform to characterize the magnitude response. We send the signal to the
arrayed FBGs and the channelized FBG. The arrayed FBGs are ~0.38nm wide each,
0.2 m distant apart and have 1.6 nm wavelength spacing. The channelized FBG pre-
equalized for group velocity dispersion equivalent to a 120 km SMF. The reflections
from the arrayed FBGs and channelized FBG are shown in Figure 3.2(b).
The signal is combined with two pumps (P1 and P2) and sent to PPLN-1 for
wavelength conversion. P2 is placed in symmetry with the signal around QPM. The
QPM is temperature tuned to 1549.6nm. P1 is tuned within a range of 1.5 nm which
PPLN-1
λ
S
+D
Input
S
’
+D
Tunable
Wavelength
Conversion
Chirped
FBG
λ
P1
P1
S
λ
P2
P2
QPM
λs
FBG
array
Channelized
FBG
P2 P1
PPLN-2
λ
S
’
λ
2
λ
P1
P1
λ
P2
P2
QPM
P2 P1
S
λ
s
λ
s λ
2
λ
1
λ
2
Tunable
Wavelength
Conversion
Output
S
λs
S
+D
S
’
+D
Delay
Fine
continuous
delay
Delay
Fine and coarse
tunable delay
Delay
Coarse
discrete delay
λ
S
Delay
Pre-
equalization
λ
S
Δ λ 0
λ
S
Δ λ
41

is used to choose the fine delay. The output of wavelength conversion in PPLN-1 is
shown in Figure 3.2(c) when the first FBG in the arrayed FBGs (FBG1) is used for the
coarse tuning delay, along with showing the maximum and minimum wavelengths for
the fine-tuning range by varying P1. We select the created copy and send it to the
chirped FBG which is fabricated to accumulate similar dispersion of a 120 km SMF.
Finally, the output of the chirped FBG is sent back to the original wavelength using
PPLN-2, as shown in Figure 3.2(d). The case of creating the largest delay by using
FBG10 and the longest delay by fine tuning P1 is shown for PPLN-1 in Figure 3.2(e)
and for PPLN-2 in Figure 3.2(f).

Figure 3.2 (a) Experimental setup. (b) Reflection spectra from arrayed and channelized FBGs. (c)
Wavelength conversion output from PPLN-1 when the coarse tuning of FBG1 is used along with the
tuning range of P1. (d) Output of PPLN-2 when FBG1 is used for the coarse tuning delay. (e) the case
of creating the largest delay using FBG10 and the largest delay from P1 after PPLN-1. (f) The output
of PPLN-2 when creating the largest delay.
Chirped
FBG
D=-120*16.8ps/nm
λ
s
Modulator
50/50
RF input:
(i) 10Gbaud OOK
(ii) 10Gbaud QPSK
(iii)VNA signal
PC
50/50
PPLN-1 PPLN-2
PC PC
PC PC
Optical output:
(i) Optical Sampling
scope
(ii) Coherent receiver
(iii)VNA
50/50
Pre-Amp
Pre-Amp
P
1
P
2
(a)
FBG10
FBG2
FBG1
FBG3
…
0.2m
…
Δλ=
1.6nm
FBG
array
Channelized
FBG
Ch
BW
0.8nm 10cm
D=120*16.8ps/nm
1535 1545 1555 1565
Wavelength (nm)
PC
(b)
S
P2
P1
S
’
S
’
S
P2
P1
1 2 3 4 5 6 7 8 9 10
FBG#
(c) (d)
1544 1550 1556
Wavelength(nm)
1535 1545 1555 1565
Wavelength (nm)
Power (20db/div)
Power (20db/div)
Power (20db/div)
Arrayed FBGs
Channelized FBG
FBG1,fast
FBG1,slow
FBG1,fast
FBG1,slow
Power (20db/div)
S
’
S
P2
P1
S
S
’
P2
P1
(e) (f)
1535 1545 1555 1565
Wavelength (nm)
1535 1545 1555 1565
Wavelength (nm)
Power (20db/div)
FBG10,slow
FBG10,slow
5m
42

3.4 Results
In Figure 3.3(a), we show the waveforms of a 10 Gb/s OOK for some coarse
tuning scenarios with the minimum (blue) and maximum (red) fine tuning delays. Each
of the discrete FBGs adds ~2 ns while the fine-tuning range by varying P1 could span
2.8-ns. Figure 3.3(b) shows the accessible delays by combining the coarse and fine-
tuning stages. A continuous tuning range could be accessed with overlapping of ~0.8
ns between the coarse tuning ranges. Also, a maximum delay of 20.6 ns could be
achieved. In Figure. 3.3(c), we show four samples of the captured waveforms when
fine tuning the delay by varying λP1 in steps of 0.1 nm, where each step changes the
delay by 185 ps.

Figure 3.3 (a) Waveforms for some of the coarse-tuning stages delays at largest and smallest fine-tuning range.
(b) Accessible delays by combining the coarse and fine-tuning stages up to 20.6 ns. (c) Samples of the recorded
waveforms when fine-tuning delays is carried within the coarse delay of FBG2.
Next, we transmit a 10-Gbaud QPSK signal into the delay system. In Figure
3.4(a), we show the constellation of the back-to-back (B2B) baseline and its EVM
along with some of the detected signals after the delay system. In Figure 3.4(b) we
measure the BER performance of the different delayed signals compared to the B2B
and the penalty at the forward error FEC can be observed to remain below 0.6 dB. The
signals with the larger coarse delays performed slightly worse and we believe this is
caused by the residual uncompensated dispersion. In Figure 3.4(c) we measure the
magnitude response of the delayed signals and observe that a dispersion notch appears
0
5
10
15
20
25
0.00E+00 1.00E+00 2.00E+00 3.00E+00 4.00E+00 5.00E+00 6.00E+00 7.00E+00 8.00E+00 9.00E+00 1.00E+01 1.10E+01 1.20E+01 1.30E+01 1.40E+01 1.50E+01 1.60E+01 1.70E+01 1.80E+01 1.90E+01 2.00E+01 2.10E+01 2.20E+01
Delay (ns)
λ
(P1 continious tuning over coarse segments)
Beginning of fine
tuning range
End of fine tuning
range
(b) (c) (a) λP1 fast λP1 slow
0 time (ns) 30 0 time (ns) 30
0 time (ns) 10
Fine tuning within FBG-2
FBG-1
0+0ns
FBG-2
1.99+0ns
FBG-8
13.8+0ns
FBG-10
17.7+0ns
FBG-1
0+2.84ns
FBG-2
1.99+2.84ns
FBG-8
13.8+2.84ns
FBG-10
17.7+2.84ns
1.99+1.33ns
1.99+1.52ns
1.99+1.71ns
1.99+1.91ns
FBG1
λP1
fast
λP1
slow
FBG5
λP1
fast
λP1
slow
FBG10
λP1
slow λP1
fast
43

at 21.6 GHz at the case of FBG10 (17.7+2.85 ns) due to the residual dispersion, which
corresponds to ~152ps/nm.

Figure 3.4 (a) Constellations of the B2B signals and various delayed signals. (b) The BER of the various
delayed signals when transmitting 10 Gbaud QPSK data. (c) VNA magnitude response of some delay
samples.
3.5 Conclusion
In conclusion, we demonstrated using the time-of-flight in arrayed, channelized
and chirped fiber Bragg gratings along with wavelength conversion in PPLN
waveguides to build continuously coarse- and fine-tunable delay line. More than 20 ns
continues tuning range is achieved with less-than-0.6dB OSNR penalty for a 10 Gbaud
QPSK signal. The short length of the FBGs could potentially enable low latency
continuously tunable delay line.

B2B
EVM=10.0%
FBG-1,
0+0ns
EVM=10.4%
FBG-3,
3.98+0.56ns
EVM=10.0%
FBG-5,
7.91+1.13ns
EVM=10.1%
FBG-7,
11.9+1.71ns
EVM=10.3%
FBG-10,
17.7+2.85ns
EVM=10.3%
-5
-4
-3
-2
-1
7 8 9 10 11 12
B2B
FBG-2, 2+0.37ns
FBG-1, 0+0ns
FBG-3, 3.98+0.56ns
FBG-4, 5.93+0.94ns
FBG-5, 7.91+1.13ns
FBG-6, 9.89+1.52ns
FBG-7, 11.9+17.71ns
FBG-8, 13.8+2.1ns
FBG-9, 15.6+2.47ns
FBG-10, 17.7+2.85ns
FEC
Log10(BER)
Magnitude response (20dB/div)
0 10 20 30
RF frequency (GHz)
(a)
(b) (c)
OSNR (dB)
~150ps/nm
residual
dispersion
FBG-1,
0+0ns
FBG-5,
7.91+1.13ns
FBG-10,
17.7+2.85ns
44

Chapter 4 Multiple Access Delays using Fiber
Bragg Gratings and Multicasting with a Frequency
Comb
4.1 Introduction
Tunable optical delays may have value in different signal processing functions,
including equalization, tapped-delay-line filters, beam steering, correlation, and data
buffering [39,50]. Such optical delays could benefit from the following performance
characteristics: (a) continuous tunability over the entire delay range to access all values, (b)
fine and coarse tenability to enable larger ranges of achievable delays, (c) relatively small
optical length that introduces relatively low overall excess latency generated beyond the base
delay range (e.g., not using long lengths of fiber), and (d) access one or more possible delay
values simultaneously for advanced signal processing functions. Moreover, the use of an
optical frequency comb (instead of multiple discrete laser pumps) to help achieve the above
characteristics would also be of benefit.
In this chapter, we experimentally demonstrate fine- and coarse-tunability over a
continuous 8.1-ns delay range with access to multiple possible delays using a frequency comb,
and without excess lengths of fibers by using short fiber Bragg gratings (FBGs). Wavelength
conversion and a linearly-chirped FBG are used for the continuous fine-tuning delay stage.
The coarse delays and multiple access are achieved by multicasting using a comb in a
periodically poled lithium niobate (PPLN) waveguide and passing the multicast signals
through an array of FBGs. We transmit 10 Gb/s OOK data to demonstrate the delays over the
8.1-ns range, and then transmit a 10 Gbaud QPSK channel and observe ~2 dB penalty at the
system output. We also convert one of the output delays to the original wavelength in another
HNLF stage, adding ~0.3 dB penalty.

45

4.2 Concept
The concept of using the comb and FBGs to continuously access multiple coarse- and
fine-tuning delays is depicted in Figure 4.1. A data signal (S) is first sent to a highly nonlinear
fiber (HNLF) along with a pump (P 1) to generate a conjugate copy (S
*
) and we send S
*
to a
linearly-chirped FBG, where we choose the fine-tuning delay by varying P1. Next, we
multicast S
*
in a PPLN waveguide with comb lines and a pump (P 2). We pass the generated
multicast through a chirped-and-sampled FBG to compensate the dispersion, and this FBG
adds the same group delay to all channels. Afterwards, the multicast is transmitted through an
array of FBGs, where the discrete FBGs add the coarse-tuning delays depending on the time-
of-flight.
At the output of the FBG array (green box), we can access multiple delays at the same
time with fine and coarse tunability. We then can add another HNLF stage to demonstrate the
possibility of selecting one of the delays and converting it to the original wavelength. As a
result, the fine-tuning stage can be used to fill the gaps in between the discrete coarse-delays
and to achieve a larger continuous tunable delay range.

Figure 4.1 Concept of multiple coarse- and fine-tuning delays using a comb and FBGs.
4.3 Experimental Setup
The experimental setup is depicted in Figure 4.2(a). We modulate a CW laser
with: (i) 10 Gb/s OOK pattern to characterize the delay, and (ii) 10 Gbaud QPSK signal.
We combine the signal with P1 and send them to an EDFA which is set to provide 190
mw and then send the EDFA output to a 520 m HNLF1. The output of HNLF1 is
shown in Figure 4.2(b). We select the output using a filter and send it the linearly-
PPLN-1
λ P1
Input
S
’
Multicasting using
PPLN waveguide
and a comb
λ
comb
S
λ
P2
P2
QPM
λs
FBG
array
Chirped-and-
sampled FBG
P2
S*
λ
s*
λ
2
Output
S
out
λs
Delay
Fine and coarse
tunable delay
Group Delay
Coarse
discrete delay
λ
Group Delay
Dispersion
compensation
λ
λ
S
Δ λ
λ
S
S
*
λ
P1
P1
P1
λ
s
Tunable
Wavelength
Conversion
HNLF1
λ
p1 λ
s*
Linearly-
chirped
FBG
Group Delay
Fine
continuous
delay
Δ λ 0
λ
S(t-T) S
*
(t-T)
λ
P2
P3
P3
λ
s
HNLF2
λ
p1 λ
s*
Multicast
Simultaneous
multiple
access delays
Tunable
Wavelength
Conversion
Select
delay
λ
fine-tuning
delay
delay
Comb
46

chirped FBG to impose the fine-tuning delay. We combine the delayed copy with four
comb lines and P2, and send them to PPLN-1 through an amplifier with 400 mw output
to generate the multicast copies as shown in Figure 4.2(b). We select the multicast
using an LCoS programmable filter and send them to the 10-cm chirped-and-sampled
FBG to compensate the dispersion, and send them to the FBG array to add the coarse
delays. The chirped-and-sampled FBG and array of FBGs are matched in the spectrum
as shown in Figure 4.2(d). Therefore, at the output of these two FBGs, we can access
4 copies at the same time, and with different coarse delays. We also can select one of
the outputs using a filter and convert it to the original wavelength in HNLF2 as
demonstrated in Figure 4.2(e,f) for the fastest and slowest coarse delay outputs.

Figure 4.2 (a) Experimental setup. (b) The output of HNLF1 along with the tuning range of P 1. (c) The
output of multicasting stage of PPLN-1. (d) Matched reflection spectra from arrayed and sampled-and-
chirped FBGs. (e,f) converting the fast/slow signals to original wavelength after HNLF2.
4.4 Experimental Results
In Figure 4.3(a), we show the waveforms of the 10 Gb/s OOK at the beginning
and end of the fine-tuning ranges at the output of FBG#1 (fast) and FBG#4 (slow).
Figure 4.3(b) shows the accessible delays by combining the coarse and fine-tuning
stages. Overall, A continuous tuning range of 8.1 ns could be accessed after HNLF2,
and four delays with ΔT=~2 ns can always be accessed.
Next, we transmit a 10-Gbaud QPSK signal into the delay system. In Figure
4.3(c), we show the constellation of the back-to-back (B2B) baseline and its EVM
λ
s
Modulator
3:1
RF input:
(i) 10Gbaud OOK
(ii) 10Gbaud QPSK
PC
50/50 PPLN-1
PC
HNLF1
Optical output:
(i) Optical Sampling
scope
(ii) Coherent receiver
50/50
Pre
Amp
P
2
(a)
ΔL=0.2m
FBG
array
P
1
PC
L=5m
D=
120*16.8ps/nm
Linearly
chirped
FBG
4 lines
from a
comb
Programmable
LCoS
-120*16.8ps/nm
Chirped-and-
sampled FBG
P
3
PC
HNLF2
190 mw 400 mw
160 mw
FBG4
FBG2
FBG1
FBG3 Δλ=
1.6nm
L=10cm
Ch
BW
0.8nm
PC
(d)
S
P1
S*
S*
comb
P2
Multicast
S*
1 2 3 4
FBG#
S
*
(fast)
S
out
P3
(b) (c) (e) (f)
1553 1556 1559
Wavelength(nm)
1535 1545 1555 1565
Wavelength (nm)
1535 1545 1555 1565
Wavelength (nm)
1535 1545 1555 1565
Wavelength (nm)
1535 1545 1555 1565
Wavelength (nm)
Power (20db/div)
fast
slow
Arrayed FBGs
Channelized FBG
fast
slow
S
out
P3
QPM
Power (20db/div)
Power (20db/div)
Power (20db/div)
Power (20db/div)
//
Simultaneous
multiple
access delays
S
*
(slow)
Select a
delay
(fast) (Slow)
47

along with the constellations after HNLF1, after the FBG array (the multiple access
delays), and after HNLF2. In Figure 4.3(d) we measure the BER performance of the
delayed signals compared to the B2B. The penalty at the FEC can be observed to be
~2 dB after the FBG array and ~ 2.3 dB after converting the signal back. We believe
this penalty is caused by OSNR reduction after multicasting as well as because of the
filtering effect from the FBGs.

Figure 4.3 (a) Waveforms for some of the signal delays. (b) Accessible delays by combining the coarse- and fine-
tuning stages up to 8.1 ns. (c) constellations of the 10 Gbaud QPSK signal at different points of the system. (d)
BER performance of the 10 Gbaud signal before and after the delays system.
4.5 Characterization of the Chirped FBGs
We characterize the chirped FBGs of our system in this section. Figure 4.4(a)
shows the experimental setup to characterize the chromatic dispersion measurement
for linearly chirped, and chirped-and-sampled FBGs. The measurement is conducted
through measuring the phase shift of 1-GHz tone using the VNA and by varying the
input laser wavelength. Figure 4.4(b) shows the measurement results, where the
0
3
6
9
Delay (ns)
Beginning of fine-tuning range
End of fine-tuning range
λ
(P1 continuous tuning over coarse segments)
FBG#2
output
FBG#1
output
FBG#3
output
FBG#4
output
FBG#1 fast
FBG#4 fast
FBG#4 slow
0 10ns
0 10ns
0 Time 10ns
FBG#1 slow
0 10ns
(a)
(b)
(c)
B2B
EVM=10.2%
After HNLF1
EVM=11.3%
FBG#1 fast
After FBG array
EVM=14.8%
FBG#4 slow
After FBG array
EVM=15.1%
FBG#1 fast
After HNLF2
EVM=15.4%
FBG#4 slow
After HNLF2
EVM=15.6%
FEC
Log10(BER)
OSNR (0.1nm) (dB)
(d)
-5
-4
-3
-2
-1
7 8 9 10 11 12 13 14
B2B
After HNLF1
FBG#1 fast, After
FBG array
FBG#4 slow, After
FBG array
FBG#1 fast, After
HNLF2
FBG#4 slow, After
HNLF2
48

chirped-and-sampled FBG had a dispersion profile similar to 120 km of single-mode
fiber, while the linearly chirped FBG had a dispersion value of 1870 ps/nm at 1535
nm and 1900 ps/nm at 1540 nm. By choosing the fine and coarse delay wavelengths,
the residual dispersion can be thus estimated.

Figure 4.4 (a) Chromatic dispersion measurement setup for the chirped FBGs. (b) Chromatic dispersion
curve of the chirped-and-sampled FBG, along the values of dispersion for the linearly chirped FBG at
1535 nm and 1540 nm.
Moreover, we characterize the distortion of the FBGs by sending a microwave
chirp pulse and measuring the extinction ratio [51]. Figure 4.5(a) shows our back-to-
back (B2B) RF system for generating the microwave chirp and detecting it using an
80 Gsample/sec real-time scope. Figure 4.5(b) shows the detected chirp in time and
frequency domains. We then send the chirp pulse into the FBGs, as seen in Figure
4.5(c). We drive the optical modulator with the chirp pulse from the waveform
generator and detect the signal using a photodiode and oscilloscope.

Intensity
Modulator
Vector network analyzer (VNA) ( 1-GHz tone for phase measurement)
Output
Bias
Tee
Power
Supply
Device
under test
Wavelength meter
Photodiode
Input
SHF 806
0-50 GHz
RF amplifier
(a)
-2150
-2100
-2050
-2000
-1950
-1900
-1850
-1800
1520 1530 1540 1550 1560 1570
Dispersion (ps/nm)
Wavelength (nm)
Chirped-and-sampled
(-D) of linearly
chirped at 1535
(-D) of linearly
chirped at 1540
49

Figure 4.5 (a) RF B2B system to generate and detect the chirp. (b) RF-detected chirp in time and
frequency domains. (c) The optical delay system setup to delay microwave chirp pulse.
Figure 4.6 shows the results of the delayed chirp after pulse compression. We
characterize the compressed RF chirp in Figure 4.6(a). Figure 4.6(b) shows the delayed
chirp when the laser is set at 1528 nm. The results show that we can delay the pulses
with an extinction ratio > 35 dB.

Figure 4.6 Compressed pulses for (a) RF B2B, (b) delayed pulse at 1528 nm.

Keysight AWG
M8196A
Fc=10 GHz
BW= 1 GHz
3 us duration
Keysight
80 Gsample
oscilloscope
Time
Voltage
Frequency
Power
(a)
(b)
50 G MZM
Linearly chirped
FBG
Power
Supply
photodiode
SHF 806
0-50GHz
RF amplifier
Chirped and
sampled FBG
EDFA
Keysight
80Gsample
oscilloscope
Keysight AWG
M8196A
Fc=10 GHz
BW= 1 GHz
3 us duration
(c)
EDFA: Erbium doped fiber amplifier
AWG: Arbitrary waveform generator
(a) RF Back-to-back
(b) Delayed 1528 nm
50

4.6 Conclusion
In conclusion, a continuous delay range of 8.1 ns is achieved with simultaneous access
to four different delays. Our system’s penalty is ~2 dB for a 10 Gbaud QPSK signal. We also
add an HNLF to convert one of the delays to the original wavelength, adding ~ 0.3 dB penalty.
Moreover, the chromatic dispersion of the FBGs is characterized, along with the distortion of
the chirped FBGs. Results showed that chirped FBGs can be used without adding significant
distortion to the signal.

51

Chapter 5 Repeated Spatial-mode Shifting for
Achieving Discrete Delays in a Free-space
Recirculating Loop
5.1 Introduction
Optical delays have been achieved using different techniques, including: (a) propagation
through free space or lengths of fiber [30], and (b) wavelength conversion and chromatic
dispersion [52], (c) multiple passes through a recirculating optical loop [53,54]. The delay in
a recirculating loop is the delay of one loop multiplied by the number of passes.
A key challenge with achieving delays using a recirculating loop is the ability to delay
the data without overlapping between the beginning and end of a data packet, such that the
loop delay should always be greater than the packet duration. This challenge has been solved
using wavelength (or frequency) conversion such that a signal is wavelength (or frequency)
up-or-down converted after each circulation, whereupon the delay becomes wavelength (or
frequency) dependent [55,56].
A domain that has not been significantly explored for enabling delays in recirculating
loops is the spatial domain. An interesting goal could be to explore the ability to achieve
discrete delays in a spatial domain.
In this chapter, we experimentally utilize repeated spatial-mode shifting for achieving
discrete delays in a free-space orbital-angular momentum (OAM) recirculating delay loop.
We send a 20 Gbaud QPSK signal into the loop and generate 3 recirculations, each with added
loop delay of 2.2 ns. The first two circulations have negligible penalty, and the third
recirculation observes ~2dB penalty due to the accumulated loss.
5.2 Background of OAM
Les Allen reported in 1992 that beams of light, and indeed all EM beams, with a
spiral phase front can carry orbital angular momentum (OAM) [57]. Such that, any
52

wave (or photon) with azimuthal phase dependence 𝑒 𝑗 ℓ𝜃 carries OAM of ℓℏ per
photon (ℓ is an unbounded integer and ℏ is the reduced Plank constant), and its
wavefront twists along the propagation axis. Different amounts of phase twists can
form a set of orthogonal beams (i.e., modes) as shown in Figure 5.1. Therefore, OAM
enables (de)multiplexing and allows us to simultaneously send multiple independent
beams over the same space and in the same frequency band.

Figure 5.1 Different OAM modes corresponding to different 𝓵 ’s are orthogonal.
5.3 OAM Generation and Detection
One could generate an OAM beam by converting a fundamental Gaussian beam
into an OAM beam. The converter could be a programmable spatial light modulator
(SLM), spiral phase plate, or metamaterial. For example, when we shine a Gaussian
beam with planar phase front on a reflective-type SLM loaded with a spiral phase mask
with a charge of 𝓵 , this phase mask adds an azimuthal phase term 𝑒 𝑗 ℓ𝜃 to the beam
and converts it them into OAM𝓵 . As an example, using the SLM to generate an OAM3
beam is shown in Figure 5.2(a).
To detect one of the OAM beams, another SLM loaded with the opposite spiral
phase mask can then be used to convert the OAM beam back to a Gaussian beam with
-10 -8 -6 -4 -2 0 2 4 6 8
x 10 -4
-10
-8
-6
-4
-2
0
2
4
6
8
x 10 -4
[m]
[m]
-10 -8 -6 -4 -2 0 2 4 6 8
x 10
-4
-10
-8
-6
-4
-2
0
2
4
6
8
x 10
-4
[m]
[m]
-10 -8 -6 -4 -2 0 2 4 6 8
x 10
-4
-10
-8
-6
-4
-2
0
2
4
6
8
x 10
-4
-10 -8 -6 -4 -2 0 2 4 6 8
x 10
-4
-10
-8
-6
-4
-2
0
2
4
6
8
x 10
-4
= 0 = 1
= 2
= 3
= …. -3, -2, -1 ,0 ,+1, +2, +3 ….
‘No OAM’
0
2π
Intensity Intensity
Intensity Intensity
Phase
Phase
Phase
Phase
=1
=3
=0
=2
53

planar phase front. For instance, detecting an OAM3 beam can be done by passing
through a SLM with ℓ = -3, as shown in Figure 5.2(b). An incoming OAM beam also
can be easily shifted to another OAM mode by passing through the SLM with a spiral
phase mask. For example, in Figure 5.2(c), OAM1 is converted into OAM3 by passing
through a SLM with 𝓵 =2.

Figure 5.2 (a) Generation, (b) detection, and (c) shifting an OAM beam by using a spatial light
modulator (SLM).
5.4 Concept of Repeated Spatial-Mode Shifting for Achieving
Discrete Delays in a Free-Space Recirculating Loop
The concept of the method is shown in Figure 5.3. First, we convert an input
signal into an OAM beam with mode ℓ
𝑖𝑛
and send it into the OAM-shifting
recirculating loop. The loop consists of a beam combiner/splitter and an OAM-mode
shifter. Inside the loop, part of the incoming beam with the OAM mode ℓ
𝑖𝑛
is directed
Incoming
Gaussian beam
Incoming OAM3
Re-converted into Gaussian
Converted into OAM3 beam
= 3
= -3
(a)
(b)
Spatial light modulator
(SLM)
Incoming OAM1
Shifted into OAM3
= 2
(c)
Incoming OAM1
54

to the OAM-mode shifter, where the OAM value gets shifted to ℓ
𝑖𝑛
+ ℓ
𝑠 ℎ𝑖𝑓𝑡 and then
delayed by the loop length. The delayed beam will again reach the beam
combiner/splitter, in which a portion of its power will get transmitted towards the loop
output while the rest will get shifted to a new OAM mode inside the loop and
additionally delayed.
Therefore, at the loop output, we can access different delays by selecting and
detecting the OAM modes. Detecting a delayed OAM beam can be done by converting
it back to a Gaussian beam and collimating the beam. For convenience, we assign the
term recirculation#0 to the output beam that traversed the combiner/splitter without
entering the loop.

Figure 5.3 Concept an optical recirculating delay loop based on the orthogonality of spatial OAM modes.
5.5 Experimental Setup
The experimental setup is depicted in Figure 5.4. We use three spatial-light
modulators (SLMs) in the system as: (i) SLM-1 with ℓ = ℓ
𝑖𝑛
to generate an OAM
beam that enters the loop. (ii) SLM-2 with ℓ = ℓ
𝑠 ℎ𝑖𝑓𝑡 to shift the modes of the OAM
beams which are already inside the loop by ℓ
𝑠 ℎ𝑖𝑓𝑡 amount. (iii) SLM-3 with ℓ =− ℓ
𝑜𝑢𝑡
to detect one of the OAM modes by converting the beam into Gaussian (the value of
−ℓ
𝑜𝑢𝑡 is dictated by the delayed version we want to detect).
Convert one
OAM back to
Gaussian
Input
signal
S(t)
λs
Loop input Convert to
an OAM
beam ( in)
Multiple OAM beams
with different delays
One OAM beam
Delay
S(t)
Number of
re-circulations
0
S(t+T)
S(t+2T)
S(t+nT)
…
Loop output
Delay
S(t)
OAM
mode
+
…
+ +
Recirculation#0
Delay
S(t)
OAM
mode
S(t+T)
S(t+2T)
S(t+nT)
Recirculation#1
Recirculation#2
Recirc.#n
+
…
+ +
Beam
combiner
/splitter
OAM-mode
shifter
( shift)
OAM-shifting
recirculating
delay loop
55

Figure 5.4 Experimental setup of the OAM-shifting recirculating delay loop.
The loop delay can be controlled by changing the distances between the mirrors:
M1, M2 and M3. Moreover, every reflection on a mirror flips the sign of any OAM
mode from ℓ to −ℓ . Thus, after SLM-2, the number of reflections should be even to
receive the same beam back into SLM-2 after a full cycle. In our system, three
reflections happen in the three mirrors M1, M2, and M3. The fourth reflection happens
in the 50:50 beam splitter when exiting the loop or in SLM-2 if the signal is kept inside
the loop.
In the transmitter, we modulate a narrow linewidth (10-kHz) laser at 1550.7 nm
with 1-ns intensity modulated pulse at 62.5MHz repetition rate for characterization
purposes, and then with 20-Gbaud QPSK signal from an IQ-modulator. The signal is
amplified and ~ +10 dBm is transmitted from collimator#1. The beam gets
transformed into an OAM beam with charge ℓ
𝑖𝑛
and enters the loop through a 50:50
splitter. Inside the loop, the beam’s OAM mode gets shifted to ℓ = ℓ
𝑖𝑛
+ 𝑛 ℓ
𝑠 ℎ𝑖𝑓𝑡 in
every recirculation using SLM-2, where n is the number of recirculations, and the loop
length is ~63 cm (2.2 ns). The loop’s output delayed beams are directed into SLM-3.
In SLM-3, we apply the conjugate pattern of the desired delayed beam and convert it
into a Gaussian beam. The beam then can be coupled to a SMF-28 fiber using two
lenses with focal lengths F= -100mm and F=200mm and a collimator with F=3mm.
Optical
Transmitter
BPF
PC
EDFA
SLM-1
Collimator-1
Collimator-2
Lens-1
F=200mm
Lens-2
F=-100mm
Generate
OAM with
in
Detect one
delayed OAM
beam
out
8cm
19cm
5cm
20cm
Loop
length
~63cm
11cm
OAM-shifting
recirculating delay loop
16cm
11cm
20cm
15cm
20cm
28cm
8cm 12cm
12cm
Pre-amp
50:50
splitter
M1
M2
M3
Shift the
OAM value
by
shift
Optical
receiver
Loop
Loop
input
Loop
output
56

We amplify the collimated light using a low-noise EDFA that has 4.5 dB noise figure
for an input of -35 dBm, then we detect and demodulate the signal using an optical
receiver.
5.6 Experimental Results
We first analyze the modal purity of the OAM beams when the loop is blocked (SLM-
2 is blocked) so that only recirculation# 0 appears at the loop output in Figure 5.5(a,b). When
SLM-1 is set to transmit OAM with ℓ
𝑖𝑛
= 0 (Gaussian beam) into the loop, the peak
detected power in Figure 5.5(a) using SLM-3 becomes ~ -2 dBm and the power leakage into
OAM -3 (𝛥 ℓ = 3) becomes ~33 dB down from the signal’s power. The collimated power
decreases when we transmit ℓ
𝑖𝑛
= +8 to ~-13 dBm. Also, the power leakage into OAM +5
(𝛥 ℓ = 3) becomes 25 dB lower than the signal’s. This can happen because higher OAM
modes diverge faster while the collimation and alignment is optimized in our system to
maximize the power coupling based on the divergence of a received OAM with ℓ = 0. The
total loss from the two SLMs and a 50:50 coupler is ~12 dB when collimating the beam of
ℓ
𝑖𝑛
= 0. Therefore, every SLM has ~4.5 dB loss.

Figure 5.5 (a,b) Detected power on the OAM modes when the loop is blocked (SLM-2 is blocked) for
the cases of transmitting ℓ
𝑖𝑛
= 0 and when transmitting ℓ
𝑖𝑛
= 8, respectively.
In Figure 5.6(a), we activate the loop and transmit ℓ
𝑖𝑛
= 0 from SLM-1 and shift by
ℓ
𝑖𝑛
= −3 in SLM-2, and we show the OAM spectrum by scanning SLM-3. Results in Figure
OAM value on SLM-3 ( )
Δpower=33dB
For Δ =3
Loop is blocked;
Only recirculation#0 exists.
SLM-1: =0
Detected power (dBm)
0
-10
-20
-30
-40
-50
-60
OAM value on SLM-3 ( )
Δpower=25dB
For Δ =3
Loop is blocked;
Only recirculation#0 exists.
SLM-1: =8
0
-10
-20
-30
-40
-50
-60
Detected power (dBm)
(a) (b)
-8 -6 -4 -2 0 2 4 6 8
Lorentzian
fitting γ= 0.46
Lorentzian
fitting γ= 1.12
-8 -6 -4 -2 0 2 4 6 8
57

5.6(b), show the 1-ns pulses without crosstalk for recirculation#0 and recirculation#1, and with
2.2 ns delay. Also, we observe that reciucration#2 suffers from crosstalk due to the higher
power recirculation#1. The constellations and error-vector magnitudes (EVMs) in Figure
5.6(c) shows the detection of 20 Gbaud QPSK signal up to recirculation#1, and undetectable
recirculation#2. The bit-error rate (BER) performance is shown in Figure 5.6(d).
Based on these observations, we decide to transmit an OAM beam with a larger mode
and down-shift the beam order (charge) inside the loop, to maximize the number of possible
generated delays with sufficient power. Thus, we feed the loop with an OAM beam of order
ℓ
𝑖𝑛
= 8 from SLM-1 and apply the charge of ℓ
𝑠 ℎ𝑖𝑓𝑡 = −5 on SLM-2. We show the
recorded OAM spectrum by scanning SLM-3 in Figure 5.6(e). We also show the recorded 1-
ns delayed pulses from recirculations#0 to #3 in Figure 5.6(f). Next, we transmitted a 20-
Gbaud QPSK signal into the loop and show the recorded constellations in Figure 5.6(e). We
measure the BER of the recorded delayed beams in Figure 5.6(f). The BER of recirculations#0
to #2 show negligible penalty compared to the back-to-back baseline. Recirculation#3 suffers
~2 dB additional penalty at the FEC level which we believe is due to the loss from passing the
coupler and SLMs multiple times, resulting in received power below -35 dBm.
58

Figure 5.6 (a) Power on the detected OAM delayed modes when the loop is enabled when transmitting
ℓ
𝑖𝑛
= 0 and shifting by ℓ
𝑠 ℎ𝑖𝑓𝑡 = −3 . (b) Detected 1-ns pulses to measure the delays. (c) The
corresponding constellations when transmitting 20 Gbaud QPSK. (d) The BER performance of detected
recirculations. (e-h) The results when sending ℓ
𝑖𝑛
= 8 and shifting by ℓ
𝑠 ℎ𝑖𝑓𝑡 = −5, showing the
performance of the delayed recirulations#0 to #3.
5.7 Discussion and Conclusion
In conclusion, we demonstrate an all-optical free-space recirculating delay loop
by shifting the spatial mode order using the orbital-angular momentum (OAM) basis.
The orthogonality of the OAM modes was used to easily select the desirable delay at
Power
(10dB/div)
Power
(10dB/div)
Power
(10dB/div)
Power
(10dB/div)
recirculation
#0
OAM+8
recirculation
#1
OAM+3
recirculation
#2
OAM-2
recirculation
#3
OAM-7
recirculation#0
OAM+8
EVM=7.3%
recirculation#1
OAM+3
EVM=7.7%
recirculation#2
OAM-2
EVM=9.1%
recirculation#3
OAM-7
EVM=23.3%
(g)
Time (10ns/div)
2.2 ns
delay
(b)
2.2 ns
delay
1-ns pulse, 62.5 MHz repetition rate
20 Gbaud QPSK
Detected power (dBm)
OAM value on SLM-3 ( )
Delay loop is active.
SLM-1: =8 , SLM-2 =-3
recirculation
#0
#1
#2
0
-10
-20
-30
-40
-50
-60
(a)
-8 -6 -4 -2 0 2 4 6 8
Detected power (dBm)
OAM value on SLM-3 ( )
Delay loop is active.
SLM-1: =8 , SLM-2 =-5
recirculation
#0
#1
#2
#3
0
-10
-20
-30
-40
-50
-60
(e)
-8 -6 -4 -2 0 2 4 6 8
recirculation#0
OAM 0
EVM=7.2%
recirculation#1
OAM-3
EVM=8.5%
recirculation#2
OAM-6
20 Gbaud QPSK
Crosstalk from
recirculation #1
Time (10ns/div)
Power
(10dB/div)
Power
(10dB/div)
Power
(10dB/div)
recirculation
#0
OAM 0
recirculation
#1
OAM -3
recirculation
#2
OAM -6
2.2 ns
delay
1-ns pulse, 62.5 MHz repetition rate
(c) (f)
FEC
2
3
4
5
6
2
4
10 11 12 13 14 15 16
-Log10(BER)
2
4
10 11 12 13 14 15 16
-Log10(BER)
B2B
recirculation#0
recirculation#1
recirculation#2
recirculation#3
FEC
2
3
4
5
6
OSNR (0.1nm) (dB) OSNR (0.1nm) (dB)
(d)
(h)
59

the loop output. In our experiment, the output delayed signal is at the same wavelength
of the incoming beam. Therefore, we believe this technique can be compatible with
the WDM systems. Also, multiple delays could by separated and accessed at the same
time by using techniques like multi-plane light conversion (MPLC) [58]. To increase
the number of recirculation, one can add an OAM amplifier to compensate for the loop
loss caused by the SLMs and the beam splitter [59]. Moreover, the loss that is caused
by misalignment and divergence could be avoided by guiding the OAM beams and
propagating them in vortex fibers [60].

60

Chapter 6 Homodyne Detection of WDM and Dual-
polarization PSK Channels by Automatically
Locking the Channels to a Local Pump Laser Using
Nonlinear Mixing
6.1 Introduction
Historically, there have been two major categories of coherent communication
systems: homodyne and heterodyne. Optical homodyne detection is known to provide
optimally 3 dB more sensitive than optical heterodyne detection [61]. Homodyne
detection requires accurate frequency and phase locking of the incoming signal to a
carrier, such that the offset frequency is zero. The carrier can be: (a) a local oscillator
(LO) laser which is generated at the receiver and typically requires an electronic-based
phase-locked loop to stabilize the locking of the LO to the incoming signal [62–65],
or (b) a simple frequency tone that may have been sent along with the signal and can
be located out of the original signal band or on the orthogonal polarization, thus
consuming some bandwidth [66–70].
In [71], a different approach was demonstrated that enabled automatically
locked frequency/phase homodyne detection for the incoming data signal without the
need for frequency/phase tracking. This scheme uses the optical nonlinearity of PPLN
waveguides to generate the signal conjugate, which is coherently added to the signal
and the local oscillator [72,73]. This chapter proposes applying this approach to detect
WDM DP-signals. We utilize PPLN waveguides inside polarization-diversity loops
(PDL) to achieve the homodyne detection on a DP-signal and then apply multiplexing
to enable detection of two single-polarization (SP) WDM channels
simultaneously [74,75]. The system exhibits a bit-error rate (BER) below 3.8×10
-3
for
baud rates of up to 32 Gbaud when detecting: (a) the dual-polarization quadrature
phase-shift keyed (QPSK) signal, and (b) two single-polarization binary phase-shift
61

keyed (BPSK) channels up to 20 Gbaud. A summary addresses the requirements and
limitations of implementing the system to detect WDM DP-signals based on this
homodyne receiver.
6.2 Concept
The concept of homodyne detection of WDM DP-signals is depicted in Figure
6.1. Input WDM DP-QPSK signals Si(t)=Si,x(t)x+ Si,y(t)y (i : is the channel number),
as shown in Figure 6.1(a) are sent along with a dual-polarization free-running local
oscillator laser LO(t)=LOx(t)x+LOy(t)y into the system such that LO(t) is at the quasi-
phase matching (QPM) frequency of the PPLN waveguide fLO=fQPM. The signals and
LO first propagate through a PDL containing a PPLN waveguide (Stage-1). In this
PDL, the two orthogonal polarizations are separated using a polarization beam splitter
(PBS) and propagate in opposite directions, in which cascaded second-harmonic
generation (SHG) of LO(t) and difference-frequency generation (DFG) with each Si(t)
generates the conjugates of each signal at each polarization independently. The output
of the loop is shown in Figure 6.1(b) with conjugates at fSi*=2fLO-fSi and expressed as
S
*
i(t)= LO
2
x(t).S
*
i,x(t)x+LO
2
y(t).S
*
i,y(t)y.

62

Figure 6.1 (a) Concept of homodyne detection of WDM DP-signals utilizing PPLN waveguides inside
polarization-diversity loops to coherently multiplex the signals, conjugates, and LO. The generated
multi-level eye diagrams at the photodiode outputs correspond to multiplexing the in-phase and
quadrature data on both polarization states, respectively, of the two channels. (b) Conjugates generation
in Stage-1 using a dual-polarization LO in a PDL. (c) Multiplexing of the DP-signals, conjugates and
LO using a DP-pump (P(t)), and PPLN waveguides inside two PDLs (for the in-phase and quadrature
paths) in Stage-2.
In the next step, a programmable amplitude/phase liquid crystal on silicon (LCoS)
filter is used to induce a one-symbol delay (T) between each signal and its conjugate
copy. The programmable filter is also used to fine tune phases and optimize the power
levels and add loss of (0.5)
i-1
on each individual WDM signal. This loss is needed to
obtain multi-level multiplexed eyes at the output. Then, inside Stage-2, two PDLs (for
the in-phase (I) and quadrature (Q) paths) perform simultaneous SHG of LO(t) and
sum-frequency generation (SFG) of each signal and its delayed conjugate, which are
multiplexed at 2fQPM and subsequently converted back to the C-band via DFG using
an additional DP-pump P(t). Therefore, the output Z(t) at fZ=2fQPM-fP as shown in
Figure 6.1(c) becomes:
S2*
y
(t)
S2*
x
(t)
S2
y
(t)
S2
x
(t)
BPF
λ
BPF
λ
Conjugates generation
of WDM DP-channels in
a PPLN waveguide
multiplexing the
in-phase components
with LO in a PPLN
waveguide
multiplexing the
Quadrature
components with LO
in a PPLN waveguide
polarization diversity-
loop (PDL)
P(t)
LO
y
(t)
λ
f
QPM
PBS
(b)
S1
y
(t)
S1
x
(t)
S1*
y
(t)
S1*
x
(t)
λ
Z(t)
P(t)
PBS
Photodiode
Photodiode
Pol-y
Pol-x
λ
S1
y
(t)
S1
x
(t)
Received WDM
DP-QPSK signals
DP-Local
Oscillator
(laser)
S2
y
(t)
S2
x
(t)
Pol-y
Pol-x
LO
x
(t)
Stage-1
Stage-2
In-phase S1(t)
In-phase 0.5×S2(t)
+
Pol-X
PBS
Photodiode
Photodiode
Quadrature S1(t)
Quadrature 0.5×S2(t)
+
Pol-Y
In-phase S1(t)
In-phase 0.5×S2(t)
+
Pol-Y
Quadrature S1(t)
Quadrature 0.5×S2(t)
+
Pol-X
Homodyne detected eyes for
the WDM DP-channels
LO
y
(t)
LO
x
(t)
(c)
S2*
y
(t-T)
S2*
x
(t-T)
S2
y
(t)
S2
x
(t)
S1
y
(t)
S1
x
(t)
S1*
y
(t-T)
S1*
x
(t-T)
λ
LO
y
(t)
LO
x
(t)
P
y
(t)
P
x
(t)
Programmable
Phase and
Amplitude Filter
+
Adding 1-bit
delay on
conjugates
3dB
Output
63

(6.1)
where Xi(t)=Si(t).S
*
i(t-T) is the multiplication between the signal and its delayed
conjugates; Xi(t) is basically the phase modulated differential data pattern of the
channel i and acts as a phase filter that significantly attenuates lower frequency phase
noise which is usually the transmitter’s laser phase noise. Because lasers phase noises
are reduced, the system’s output data can be considered phase and frequency locked
to LO
2
(t) [71]. Finally, the output Z(t) is selected via a band-pass filter (BPF) on the
I/Q paths and the polarization states are separated using PBSs and sent onto the
photodiodes (square-law detectors) to detect the signal components, in which the eye
diagrams will have 2
i
levels and output electrical power is proportional to equation
(6.2) for the in-phase component and equation (6.3) for the quadrature component,
respectively.

(6.2)

(6.3)
6.3 Experimental Setup of Dual-Polarization QPSK Detection
The experimental setup of single DP-signal detection is shown in Figure 6.2(a). Laser-
1 at λ 1=1535.6 nm is modulated in a single-polarization nested I/Q Mach-Zehnder modulator
(MZM) driven by a 2
15
-1 pseudo-random binary sequence (PRBS) to generate the QPSK
signal at 20 and 32 Gbaud. The signal is transformed into DP signal S(t) using the emulator
and amplified to 25 dBm using an EDFA2. LO(t), which originates from Laser-2 at
λ QPM=λ LO=1540.3 nm, is amplified to 26 dBm in EDFA3 and subsequently combined with
the signal. The BPFs in the experiment have 1-2 dB loss. The signal and LO are sent into
Stage-1 to generate the conjugate; the spectrum after the PDL is shown in Figure 6.2(b). The
64

signal, LO, and conjugate then go into the LCoS filter to add the one-symbol delay on the
conjugate and to adjust the phases before amplification in EDFA4, which is set to 26 dBm.
Afterwards, a pump P(t) from Laser-3 at λ P=1530.6 nm with 25 dBm power is added using a
50/50 coupler and the output at 1551.6 nm is generated in the second PDL, as shown in the
spectrum in Figure 6.2(c).
The output is filtered and the polarization states are separated in a PBS and detected.
The eyes are captured using a 32-GHz PIN photodiode which received +8 dBm optical power
and was connected to a 50-GHz sampling oscilloscope. The BER measurements are
performed by recording the stream using an 80-Gsample/s real-time oscilloscope, in which
threshold is fixed and errors are counted. Furthermore, the 0.1 nm OSNR is adjusted and
measured prior to EDFA2. This experiment demonstrates the concept of detecting I and Q
channels by building only one path with one PPLN waveguide in Stage-2, and we switch
between in-phase and quadrature data by adding 45° phase to LO(t) in the LCoS filter which
corresponds to a phase shift of 2×45°=90
°
on LO
2
(t). However, for full system deployment,
we believe that two paths with separate PPLNs are needed to independently multiplex the in-
phase and quadrate data with LO
2
(t). Furthermore, the PPLN waveguides should have similar
QPM frequencies. In this experiment, the PPLN waveguides are identical and the QPM
frequency was temperature-controlled to 90°C throughout the experiment for both
waveguides.

65

Figure 6.2 (a) Experimental setup for a homodyne receiver for a DP-QPSK signal using PPLNs inside
a PDL. (b) Experimental spectrum after the first stage (Stage-1). (c) Experimental multiplexing
spectrum after Stage-2.
6.4 Results for Dual-Polarization QPSK Homodyne Detection
Results of this experiment are depicted in Figure 6.3. In Figure 6.3(a,b), captured
eyes are shown for the I and Q data up to 32 Gbaud. This figure also shows the
detection of inverse data patterns by adding 90° to LO(t) (180° on LO
2
(t)). The BER
curves for the system are shown in Figure 6.3(c), indicating that the 20 Gbaud channel
performed only ~0.5 dB better than the 32 Gbaud case; this difference is observed
because the 20 Gbaud case requires a 50 ps delay in the LCoS, which is at the
performance edge of that device. Consequently, the signal incurred 1-2 dB of
additional loss and more noise is loaded in the subsequent EDFA.
Power 25
dB/div
Power 25
dB/div
1530 1535 1540 1545 1550
Wavelength [nm]
1530 1535 1540 1545 1550
Wavelength [nm]
(b) Stage-1 Output (c) Stage-2 Output
S(t)
LO(t)
S*(t) S(t)
LO(t)
S*(t-T)
P(t) Output
Z(t)
50/50
PC
λ
1
BPF
LCoS
Filter
50/50
PPLN
PBS
PBS
Dual-Pol
Emulator
Scope
Scope
90
o
20/32Gbaud QPSK
λ
Lo
λ
P
8dBm
10
dBm
2nm 2nm
1nm 26dBm
Pol-x
Pol-y
26dBm
25dBm
9nm
1nm
1nm
1nm
Laser-1
Photodiode
Laser-2
Laser-3
(a)
Photodiode
PDL
Stage-1
PDL
PBS
PPLN
Stage-2
EDFA1
EDFA2
EDFA3
EDFA4
EDFA5
EDFA6
25dBm
66

Figure 6.3 Experimentally recorded eyes the from homodyne detection of a DP-QPSK signal showing
the I/Q components under different conditions at (a) 32 Gbaud, and (b) 20 Gbaud. (c) BER performance
of the homodyne detection system and the BER measured using a coherent receiver.
6.5 Experimental Setup for WDM Homodyne Detection
The system was modified to detect two single-polarization channels using the
experimental setup shown in Figure 6.4(a). Two lasers (Laser-1 and Laser-2) are
modulated using the nested I/Q MZM driven by 10 and 20 Gbaud 2
15
-1 PRBS data to
generate the BPSK signals S1(t) and S2(t) at λ1=1535.7 nm and λ2=1537.3 nm,
respectively. The two data channels are de-correlated by separating them in a
wavelength-selective switch (WSS) and then combined using a 50/50 coupler with an
additional ~1 meter delay in one path. Signals are amplified to 20 dBm in EDFA2,
filtered in a BPF, and then combined with the LO(t), which originates from Laser-3 at
λQPM=λ LO=1540.4 nm with a power of 25 dBm. The combined signals and LO are sent
into Stage-1. The spectrum after the first nonlinear stage is shown in Figure 6.4(b), in
which the conjugates of the two signals are generated. Next, the PPLN output is sent
into the LCoS filter to adjust phases, add delays to the conjugates, and add a 3-dB loss
1
9 11 13 15 17 19 21
Homodyne 20-Gbaud
Pol-X
Homodyne 20-Gbaud
Pol-Y
Homodyne 32-Gbaud
Pol-X
Homodyne 32-Gbaud
Pol-Y
Coherent receiver 20-
Gbaud, Single Pol
Polarization X
In-phase
Quadrature
Y
Polarization
X

+

20 Gbaud QPSK (b)
32 Gbaud QPSK (a)
In-phase Quadrature Inverse In-phase Inverse Quadrature

+

−

+

−

+

2 2 2 2
OSNR (0.1nm) (dB)
2
3
5
-Log
10
(BER)
6
(c)
1
7
4
3.8x10
-3
FEC
67

on S2(t) compared to S1(t). Also, after the amplifier that boosts the LCoS output to 30
dBm in EDFA4, an additional delay between the signals and conjugates is introduced
using a short dispersion-compensating fiber (DCF). This delay is added because this
experiment uses a 10 Gb/s signal with a 100 ps pulse width, but the LCoS filter delay
is limited to ±25 ps. The DCF has a dispersion of 160 ps/nm.km and lengths of 100 m
and 25 m are used in the 10 Gbaud and 20 Gbaud experiments, respectively. A pump
P(t) from Laser-4 at λP= 1530.4 nm with 20 dBm power is combined with the DCF
output and sent into Stage-2 to generate the multiplexed output at 1550.8 nm. The
spectrum of the multiplexed output of both channels with the LO is shown in Figure
6.4(c). The spectra of the multiplexed outputs of Stage-2, when only one signal and its
corresponding conjugate pass the LCoS filter while the other signal/conjugate pair is
blocked, are shown in Figure 6.4(d,e).

68

Figure 6.4 (a) Experimental setup of homodyne detection for two SP-PSK signals using nonlinearity.
(b) Spectrum after conjugate generation in Stage-1. (c) Spectrum of the multiplexing of both signals
with LO after Stage-2. (d,e) Multiplexing spectra when only one signal/conjugate pair is transmitted at
the LCoS filter while the other pair is blocked.
6.6 Results for WDM Homodyne Detection
Results for the simultaneous homodyne detection of two signals are shown in
Figure 6.5. Figure 6.5(a) shows the output eyes when only the signal/conjugate pair of
signal 1 is passed in the LCoS filter corresponding to the output Z1(t) in Figure 6.4(d).
Figure 6.5(b) shows how the system detects the output Z2(t), corresponding to the
signal/conjugate pair of signal 2 as in the spectrum shown in Figure 6.4(e). The next
configuration passes all signals and conjugates to yield the four-level multiplexed
output at 20 Gbaud shown in Figure 6.5(c). The BER of the multiplexed output signals
is measured against the OSNR in Figure 6.5(d), which confirms that the system can
(e) Stage-2 Output for Signal2
P(t)
S2(t)
LO(t)
S2*(t-T)
Power 25
dB/div
Wavelength [nm] Wavelength [nm]
Wavelength [nm] Wavelength [nm]
(b) Stage-1 Output
S2(t)
S1(t)
LO(t) S1*(t)
S2*(t)
(d) Stage-2 Output for Signal1
P (t)
S1(t)
LO(t)
S1*(t-T)
(c) Stage-2 Output for (Signal1+Signal2)
S2(t)
S1(t)
LO(t)
S1*(t-T) S2*(t-T)
P(t) Output
Z(t)
Output
Z2(t)
Output
Z1(t)
Power 25
dB/div
Power 25
dB/div
Power 25
dB/div
1530 1535 1540 1545 1550 1530 1535 1540 1545 1550
1530 1535 1540 1545 1550 1530 1535 1540 1545 1550
λ
P
Laser-4
50/50
PC
BPF
LCoS
Filter
DCF
50/50
Scope
90
o
50/50
WSS
10/20 Gbaud
QPSK/BPSK
10dBm
λ
1
λ
2
λ
Lo
8dBm
20dBm
5nm
25dBm
1nm
30dBm
20dBm
1nm
11nm
1nm 1nm
Laser-1
Photodiode
Laser-2
Laser-3
(a)
50/50
PPLN
Stage-2
PPLN
Stage-1
EDFA1
EDFA2
EDFA3
EDFA4
EDFA5
EDFA6
69

perform below a threshold of 3.8×10
-3
. For comparison, the BER measured with a
coherent receiver for a single 10 Gbaud BPSK signal is also indicated on the plot

Figure 6.5 (a) Experimental homodyne detection eyes for the first BPSK signal. (b) Detected eyes for
the second BPSK signal. (c) The multiplexed four-level eyes composed of two BPSK signals at 20
Gbaud. (d) BER performance of the four-level multiplexed output.
Finally, the detection of two QPSK signals is evaluated. In Figure 6.6(a,b) the
detection of each 20 Gbaud QPSK signal when the other signal/conjugate pair is
blocked shows that eyes of both signals get noisier compared to the BPSK experiment;
when a multiplexed output of two signals is detected (Figure 6.6(c)) the BER exceeds
the 3.8×10
-3
threshold.

1
5 8 11 14 17 20 23 26 29 32
20-Gbaud
multiplex Z(t)
10-Gbaud
multiplex Z(t)
Coherent receiver
10-Gbaud BPSK
OSNR (0.1nm) (dB)
3
4
5
6
-Log
10
(BER)
1
2
7
3.8x10
-3
FEC
(d)
Z1(t) Z2(t)
20-Gbaud
(c)
Z(t)
2 2
2
(b) (a)
70

Figure 6.6 (a) Homodyne detection of the first QPSK signal in a system of two 20 Gbaud channels (in-
phase component). (b) In-phase component of the second QPSK signal. (c) Experimental homodyne
detection of the multiplexed two QPSK signals at 20 Gbaud showing noisy eyes with BER exceeding
3.8×10
-3
due to power handling and conversion efficiencies limitations.
6.7 Discussion and Conclusion
This homodyne detection scheme needs to be augmented to fully detect WDM
DP-signals. A diversity loop structure is required to process both polarizations
concurrently, and that loop is likely to exacerbate the performance degradation issues
seen in the detection of two QPSK channels, notably which drive the BER above the
FEC threshold. The challenge is the result of the limit of power sent into the PPLN
waveguides while avoiding photorefractive damage. The diversity loop’s
bidirectionality means that this power limit applies to the sum of the directional
components, thus each conversion stage needs to be reduced by 3dB. This can be
addressed using nonlinear devices with improved conversion efficiencies that support
higher total input power levels (as noted in [76,77]), especially in the first stage, which
is operated at 100 mW in this experiment. Raising the PPLN power limit would help
to overcome the noise arising from amplifying lower power conjugates in the next
stage. Furthermore, the maximum number of channels that can be detected
simultaneously here appears to be limited by the additional 3db loss needed for each
additional channel to achieve 2
i
multiplexed eyes. Further, balanced detection as
described in [71] might be needed to improve performance, providing an additional
gain of up to 3 dB.
In conclusion, this chapter demonstrates automatically-locked homodyne
detection of a DP-QPSK up to 32 Gbaud and two single-polarized BPSK signals up to
(c)
Z(t) In-phase
20-Gbaud
(a) (b)
Z2(t) In-phase Z1(t) In-phase
71

20 Gbaud using two stages of PPLN waveguides with a BER below the FEC threshold
and reports the corresponding eye diagrams.

72

Chapter 7 Phase-Sensitive Regeneration of a BPSK
Channel without Phase-Locked Loop Using
Brillouin Amplification
7.1 Introduction
All-optical regeneration of phase-shift-keyed (PSK) data channels is of high interest
since the reduction of phase noise can significantly increase the communication system
performance [78]. One promising regeneration technique is the use of phase-sensitive
amplification (PSA), where the phase noise is attenuated (i.e., squeezed) during the PSA
process [79]. ). A data pattern-free idler is generated in a HNLF, similar to [80–83], and the
narrow bandwidth (BW) nature of the Brillouin amplifier (~25 MHz 3-dB
bandwidth) [11,84–87] is used to amplify the idler “in-line” in a single-mode fiber (SMF).
Because amplification occurs without path separation, the pump, signal, and amplified idler
encounter the same environmental phase changes, allowing stable phase regeneration without
a PLL [88]
PSA-based regeneration for phase-encoded data occurs using nonlinear wave mixing.
For example, in a highly nonlinear fiber (HNLF), two pumps and a BPSK data channel can
mix with each to reduce the signal’s phase noise, but this mixing is efficient only when the
data channel is placed in the middle between the two pump lines, and the data channel as well
as pumps are coherent with each other. This will result in the signal getting added with its
conjugate. Therefore, the part of the signal that has a different phase from the pumps will be
“squeezed” which reduces the phase noise for the BPSK channel [79,81,89].
A key requirement of this approach is that the pumps and the data channel must be
phase-locked and coherent with each other. Various methods for meeting this requirement
include: (i) using a phase-locked loop (PLL) to adjust the relative phase alignment [80–83],
(ii) using multiplication between the data channel and its delayed conjugate which alters the
73

data coding format [72], and (iii) using a comb of three mutually coherent frequency lines as
well as cross-phase modulation between the middle line and the data channel [90].
In this chapter, we demonstrate a phase-sensitive regeneration of a BPSK channel up to
30 Gb/s without the need for a PLL using a Brillouin amplifier (BA). A data pattern-free idler
is generated in a HNLF, similar to [80–83], and the narrow bandwidth (BW) nature of the
Brillouin amplifier (~25 MHz 3-dB bandwidth) [11,84–87] is used to amplify the idler “in-
line” in a single-mode fiber (SMF). Because amplification occurs without path separation, the
pump, signal, and amplified idler encounter the same environmental phase changes, allowing
stable phase regeneration without a PLL [88]. This results in an observed phase reduction of
up to 56% and up to 11 dB gain at 10
-5
BER for a 10 Gb/s signal. This chapter also examines
the regeneration system performance using different types of HNLFs and signal under
different types of phase noise. System stability and sensitivity to tuning the BA pump power
and frequency are also added.
7.2 Concept
The concept of an all optical BPSK regenerator using Brillouin amplification is
shown in Figure 7.1. A BPSK signal (S), which is degraded with phase noise, such
that φsignal=φdata+φnoise and φdata is either 0 or π, is combined with a CW pump (P) and
both are sent into HNLF1 to generate a data pattern-free idler with the phase
φidler=2φsignal-φpump=2φnoise-φpump (i.e., BPSK signal’s second-harmonic). The HNLF1
output is split into two paths using a 90/10 coupler. On the 10% tap, the appropriate
frequency-locked Brillouin pump is generated by setting a slave laser to frequency-
lock to the tapped idler. The slave laser output is then frequency up-shifted by νB,
amplified, and sent into the SMF as a counter-propagating BA pump, where νB is the
Brillouin gain frequency shift of a SMF and ≃10.8 GHz. On the 90% path, the idler is
amplified in the SMF with gain (GB) using the counter-propagating Brillouin pump,
such that the idler acts as the Brillouin probe [11,84–87]. Because the idler is amplified
in the SMF without path separation from the signal and pump, its phase remains locked
to the signal and pump. The BA pump generation configuration using the slave laser
74

guarantees frequency-locked Brillouin interaction. Since BA is narrow bandwidth
(BW), it acts as a filter that amplifies only the central frequency components of the
idler. After propagating through the SMF, the pump, the signal and the amplified idler
are additionally amplified by an EDFA and sent into HNLF2 for phase regeneration.
In the phase regeneration stage, the signal phase is squeezed when the signal conjugate
(S*) is created through FWM as φS*=φpump+φidler-φsignal and constructively added to the
signal. The output is thus proportional to S+S* and phase noise effect on the modulated
BPSK data channel would be reduced.

Figure 7.1 Concept of BPSK regeneration without a phase-locked loop using narrow bandwidth
Brillouin amplification (BA) to amplify the idler “in-line”. The idler is generated in HNLF1 and
exclusively amplified in an SMF using a counter propagating Brillouin pump. Because the idler is
amplified in the same path in which the signal and the pump propagate, their phase relationships remain
fixed; avoiding the need for phase stabilization.
7.3 Experimental Setup
The experimental setup is depicted in Figure 7.2(a). A 1-kHz line-width laser at
1550.7 nm is modulated with BPSK-NRZ data at 10-30 Gb/s using a 2
31
-1 PRBS
pattern in a Mach-Zehnder modulator (MZM). The phase noise is loaded using a phase
modulator driven with a 1 GHz tone or white noise for various experiments. The signal
and a CW pump at 1552.4 nm are amplified, combined in a 50/50 coupler, and both
sent into a 357 m HNLF1 (ZDW=1545 nm), in which the signal and pump power
levels are set at 18.6 dBm and 17.1 dBm at the HNLF1 input, respectively. The signal
and pump lasers are independent and each laser has a wavelength stability of ± 50MHz
over one hour. The HNLF1 output is split into two paths using a 90/10 coupler. On the
P
BPSK
signal
with
high
phase
noise
BPSK with
Lower phase
noise
S+S*
f
f
Pump
S
f
BA Gain Medium
HNLF2 HNLF1
Isolator
BPF
90%
10% tap
BA
Pump
`
Generate Idler
Amplify Idler using Narrow BW
Brillouin Amplification
Phase Regeneration
BA Pump
Generation
S P
Idler
f
SMF
f
idler
+10.8GHz
f
Slave
Laser
ν
B
shifter
10.8 GHz
S P
Idler G
B
f
S+S*
P
Idler G
B
f
Pass
Idler
75

90% arm, a Liquid Crystal on Silicon (LCoS) filter is used to adjust the power levels
and align relative phases, and its output is sent into the 500 m SMF BA gain medium.
On the 10% arm, the slave laser output is frequency up-shifted in a MZM biased at
null and fed with a νB=10.821 GHz tone (which yields the best gain for a BA). A sharp
filter is then used to pass only the upper tone needed for Brillouin amplification, which
is boosted in an EDFA5 and filtered before reaching the 500m SMF. The path loss
between the EDFA5 and the 500 m SMF is ~6 dB and the EDFA5 output is set at 26.1
dBm. The BA pump power is operated at nearly the stimulated Brillouin scattering
(SBS) threshold of the 500 SMF, as demonstrated in the stimulated Brillouin scatting
(SBS) plot of the 500m SMF as EDFA5 power varies, as shown in Figure 7.2(b). The
spectra before the BA (see Figure 7.2(c)) and after the idler amplification (see Figure
7.2(d)) show an idler gain of GB≃22 dB. The idler’s spectrum at EDFA6 input is
captured using a 10 MHz resolution optical spectrum analyzer (OSA), as shown in
Figure 7.2(e), when the signal is not loaded with phase noise. The spectrum shows that
only the idler’s central frequency is subject to gain. Yet the 20 GHz tones (originating
from the periodicity of the data pattern) remain without gain. Circulator crosstalk was
observed between port 1 and 3, as well as possible pump reflection on the optical
connector between port 2 the SMF, which together induce a tone with ~30 dB less
power than the idler at port 3. The pump, signal, and amplified idler are amplified in
EDFA6, set to 29 dBm, and sent into the regeneration stage of a 450 m HNLF2
(ZDW=1556 nm). Finally, the regenerated output signal is filtered and sent to an 80
Gsample/s coherent receiver for analysis. At the receiver, the circulator crosstalk was
too small on the RF spectrum. Additional crosstalk reduction could also be achieved
by adding a filter or using a better circulator.
76

Figure 7.2 (a) Experimental setup of BPSK regeneration using a BA. (b) SMF SBS performance as a
function of EDFA5 output power (BA pump power) to illustrate the operating point. (c) Spectrum at
the 500m SMF input. (d) Spectrum at the 500m SMF output with idler amplification. (e) Spectrum of
the idler of a 20 Gb/s signal recorded at EDFA6 input using a 10 MHz resolution OSA without loading
the phase noise. (f) Spectrum after regeneration at HNLF2 output.

Idler
f
Idler
f
Idler
+10.8 GHz
10.821GHz
~
Laser 1
1550.7nm
357 m
HNLF1
10-30 Gb/s
PRBS 2
31
-1
BPF BPF
Laser2
1552.4nm
BPF
50/50
90/10
10%
Pass
upper
tone
BPF
EDFA5
LCoS
Filter
Isolator
500m SMF
BA gain medium
BPF
450 m
HNLF2
BPF
EDFA6
MZM
EDFA1 EDFA2
EDFA3
MZM
EDFA4
BPF
90%
BA pump
BPSK
f
Idler
Slave
Laser
Phase noise
Coherent
Receiver
1nm
1 GHz tone /
white noise
Phase
Modulator
a
Circulator
1
3 2
Circulator
Crosstalk
Wavelength (nm)
Power (20 dB/div)
P
Idler
S
Wavelength (nm)
Power (20 dB/div)
P
Idler
G
B S
Wavelength (nm)
Power (20 dB/div)
P
S+S*
c
f
d
22 dB
1548 1550 1552 1554
1548 1550 1552 1554
Relative frequency(GHz)
Power (20 dB/div)
-20 -10 0 10 20
SBS Power (dBm)
EDFA5 Power (dBm)
BA OFF
BA ON
-65
-50
-35
-20
-5
15 20 25 30
e
b
Operating
point
Idler
G
B
22 dB
20 GHz
Tones
RBW
10MHz
1548 1550 1552 1554
77

7.3 Experimental Results

Performance is characterized by varying the phase noise level and recording the
constellations and error-vector-magnitude (EVM) values for 10 Gb/s and 20 Gb/s signals, as
shown in Figure 7.3(a) and (b) at the system input and output. HNLF2 was replaced with a
500 m Furukawa dispersion-stable HNLF (ZDW=1556 nm) to increase the SBS threshold of
HNLF2 [91]. This would allow higher pumping power from EDFA6 to HNLF2 which
improves the conversion and regeneration performance, as observed in Figure 7.3(c-e), by
enabling creating S* with relatively close power to S. EDFA6 was set at 32.2 dBm, and the
constellations were recorded for a 20 Gb/s signal, as shown in Figure 7.3(c). The φ noise was
changed from a tone to white noise; the latter was generated using amplified spontaneous
emission (ASE) and a photodiode, to roughly emulate the phase noise that could be
accumulated in optical fiber links, and the performance was recorded for 20-30 Gb/s signals,
as shown in Figure 7.3(d) and (e). The improvements in EVM and in φ noise are shown in Figure
7.3(f) and (g), respectively, in which the φ noise measurement is calculated by defining the phase
noise deviation (δ(θ)) between the two ends of a constellation (as shown in Figure 7.3 (a) input
with level-4 phase noise) and calculating the percentage of its reduction after regeneration. For
case (a) with 10 Gb/s and 1 GHz tone φ noise, the EVM improvement reaches 60.7 % when the
input EVM is 57.1%, but the EVM improvement for case (b) at 20 Gb/s does not exceed 48 %.
This degradation can be overcome with a better HNLF2 as shown in case (c). Also, loading
broadband phase noise as in cases (d-e) would reduce the improvement gained from the
regeneration system. We believe this happens because that the white phase noise had power
within the slave laser tracking range (±300MHz, Eblana photonics 1550-NLW), unlike the
previously examined 1-GHz noise tones, which consequently degraded the slave laser
performance and BA gain.
78

Figure 7.3 Constellations before and after the phase-sensitive regeneration system at different bitrates
ranging between 10-30 Gb/s with different phase noise levels, different types of HNLF2, and different
types of phase noise (1 GHz tone or white noise) (a-e). (f) EVM percentage of improvement for the
various scenarios in (a-e). (g) Percentage of improvement in the φ noise for the different scenarios.
BER improvement was evaluated for phase noises of level-1 and level-2 at 10Gb/s, as
shown in Figure 7.4(a), and at 20Gb/s, as shown in Figure 7.4(b), corresponding to the cases
(a) and (b) in Figure 7.3. For the 10 Gb/s signal, prior to regeneration and at a BER of 10
-5
,
level-1 phase noise caused the eye to degrade with at least a 12 dB penalty compared to the
clean back-to-back (B2B) signal, and level-2 noise caused a 2 dB degradation. After
regeneration, improvement at level-1 reached 11 dB and level-2 improvement was 1.5 dB.
For the 20 Gb/s channel, level-1 φ noise introduced penalty of 14 dB and the regeneration
10 Gb/s
φnoise: 1GHz tone
a
20 Gb/s
φnoise: 1GHz tone
20 Gb/s
φnoise: 1GHz tone
HNLF2: Dispersion-stable
20 Gb/s
φnoise: white noise
HNLF2: Dispersion-stable
30 Gb/s
φnoise: white noise
HNLF2: Dispersion-stable
0
25
50
75
20 30 40 50 60 70
a b c d e
EVM
improvement(%)
Input EVM (%)
0
25
50
75
20 30 40 50 60 70
a b c d e
Φnoise
improvement(%)
Input EVM (%)
f g
EVM=57.1% EVM=41.3% EVM=27.9%
Level-1 Level-2 Level-3 Level-4
EVM=26.2% EVM=21.5% EVM=18.3% EVM=16.1%
δ(θ))
Input Output
EVM=65.0%
b
Output Input
EVM=36.7%
EVM=67.9%
EVM=27.3%
EVM=48.4%
Level-2 Level-1
Input Output
EVM=22.4% EVM=19.4%
EVM=49.3% EVM=38.1%
Level-1 Level-2 c
Input Output
EVM=28.8% EVM=24.7%
EVM=50.8% EVM=43.6%
Level-1 Level-2 d
Input Output
EVM=36.0% EVM=29.4%
EVM=56.2% EVM=43.6%
Level-1 Level-2 e
79

reduced that by 9.1 dB, and for level-2 the penalty was 2.8 dB and the regeneration system
improved this by 1.5 dB at the BER of 10
-5
.

Figure 7.4 BER Performance and corresponding eyes before and after the regeneration system when
φ noise is 1 GHz tone for signals at: (a) 10 Gb/s, and (b) 20 Gb/s (same cases (a) and (b) in Figure 7.3 for
level-1 and level-2).
Figure 7.5 indicates the impact of tuning different parameters on the regenerator stability
and performance for the 10 Gb/s signal at phase noise of level-2 degraded with the φ noise of 1
GHz tone. In Figure 7.5(a), the BA frequency shifter is manually varied from the optimal ν B
by tuning the synthesizer feeding the MZM shifter, and the EVM of the output signal is
recorded. When the BA frequency drifts, gain on the idler decreases and its phase might
change, both of which degrade regeneration performance. Although the regeneration setup
lowers the EVM from 51.7% to 20.3%, the EVM after regeneration might exceed the EVM
of a noisy input signal if the idler and the Brillouin amplifier pump frequencies drift by 10
MHz. The BA pump power was adjusted by tuning the power of EDFA5 and the EVM and
constellations were recorded, as shown in Figure 7.5(b). The output EVM indicates that the
optimal performance was achieved when the BA pump power was set to 26.2 dBm; the idler
had almost the same power as the signal and pump for the best conversion at HNLF2. Further
-Log10(BER)
1
5 8 11 14 17 20 23 26 29
B2B
Level1-Input
Level2-Input
Level1-Output
Level2-Output
2
3
4
5
6
OSNR (0.1 nm) (dB)
11 dB
a
1
1
5 8 11 14 17 20 23 26 29
B2B
Level1-Input
Level2-Input
Level1-Output
Level2-Output
-Log10(BER)
OSNR (0.1 nm) (dB)
9.1 dB
b
2
3
4
5
6
1
Input Output
Level-1 Level-2
Input Output
Level-1 Level-2
80

increase of the pump power would introduce power mismatch and drive the BA to operate
above the SBS threshold with higher added spontaneous noise and worse output EVM. The
phase of the idler was tuned on the LCoS filter and the phase sensitive dynamic range (PSDR)
was measured at 7.4 dB for the 10 Gb/s signal with the Level-2 of φ noise. Stability was
examined, as shown in Figure 7.5(c), by setting the system to its optimal configuration and
letting the system run without feedback for an hour, after which the EVM varied by 3
percentage points

Figure 7.5 Experimental Study of tuning various parameters on system performance and its stability
when regenerating a 10 Gb/s signal with φ noise of level-2: (a) Effect of tuning the BA pump frequency
from the optimal ν B and recording the EVM and constellations of different frequency tunings cases. (b)
Effect of tuning the BA gain through tuning BA’s pump power (EDFA5 power) on the EVM, showing
the regeneration output constellations at different EDFA5 power levels. (c) Measurement of phase
sensitive dynamic range (PSDR). (d) System EVM performance over an hour while running the system
without PLL feedback.
Relative Frequency Tuning of BA
pump from the optimal ν
B
(MHz)
EVM (%)
a
0
20
40
60
0 5 10 15
Input
Output
EDFA5 Power (dBm)
EVM (%)
b
0
20
40
60
22 24 26 28
Input
Output
Relative Phase Tuning (deg) Time (minutes)
4
6
8
10
12
14
16
-240 -120 0 120 240
7.4 dB
0
20
40
60
0 20 40 60
Input Output
EVM (%)
3%
c
d
2 MHz 4 MHz 6 MHz 8 MHz 10 MHz 12 MHz
23.2 dBm 24.7 dBm 25.5 dBm 26.1 dBm 26.7 dBm 26.9 dBm
Output Signal
Power (2dB/div)
81

7.4 Discussion and conclusion
In conclusion, this chapter describes the experimental demonstration of a PSA-based
BPSK channel phase regeneration system without a PLL by applying in-line idler
amplification using a Brillouin amplifier. We found that using nonlinear elements with higher
conversion efficiency and higher SBS threshold can help achieving better results and that the
regeneration system could be more useful in environments with higher phase noise.
We believe that BA amplification of the idler in-line should be insensitive to the bitrate.
However, this approach could be limited by other different parameters. For example, Brillouin
interaction is a polarization sensitive process, which should be considered for practical
deployment. In addition, ν B is temperature dependent [87], and may need to be optimized and
carefully managed. Additionally, Brillouin interaction spontaneous noise depends on the input
signal and pump power levels [87]. In this experiment, we optimized these parameters to
maximize the amplified idler central frequency power compared to the phase noise spectral
components while minimizing BA noise. For practical implementations, input power levels
may be so low that the added BA noise may overwhelm the phase noise reduction. We
anticipate that this approach is thus useful where input power is sufficiently high

82

Chapter 8 QPSK Regeneration by Amplifying the
Fourth-harmonic Idler Using Counter-
Propagating Brillouin Amplification
8.1 Introduction
Phase-modulated data channels may benefit from all-optical regeneration to avoid the
optical-electrical-optical conversions [92]. A potentially promising technique to all-optically
regenerate a QPSK signal (S) and reduce its phase noise is to combine the signal with its
conjugate third-harmonic (S
3*
) using phase-sensitive (PS) processes [27,93]. For example,
PS-based QPSK regeneration takes place in a highly nonlinear fiber (HNLF) with four-wave
mixing (FWM), when two pumps are used to mix and add the S
3*
to S. This “squeezes” the
part of the signal that has a different phase from the ideal QPSK phase states, thereby
regenerating the signal.
Previously reported approaches for optical phase regeneration of QPSK signals include:
(i) the amplification of the fourth-harmonic idler using injection-locked laser and phase-locked
loop (PLL) for stabilization [27,76,94], (ii) wave mixing of a signal with its delayed conjugate,
which alters the original data pattern mapping [95], and (iii) the use of cross-phase modulation
and frequency comb lines [96].
PS-regeneration for binary phase-shift keying (BPSK) signals has been realized without
a PLL by amplifying the idler with the signal’s second harmonic using Brillouin amplification
(BA) [88]. In this chapter, we use that principle to regenerate a QPSK signal without a PLL
by applying the following changes [97]: (i) create the signal’s third- and fourth-harmonic
idlers in the first FWM stage by sending the signal and pump with higher power levels, (ii)
compensate for the delay between the signal and higher-order harmonics that is induced by
dispersion walk-off in the BA gain medium, (iii) amplify the weak signal’s fourth-harmonic
idler with ∼ 40 dB BA gain [11,87,98], and (iv) mix the pump and amplified fourth-harmonic
idler to add the signal to its S
3*
in a second FWM stage. We send a 10-20 Gbaud QPSK signal
83

loaded with phase noise to the system and observe up to a 65% reduction in the phase noise
variance and 4.6 dB OSNR improvement at a BER of 10
−4
. In addition, the system shows
operation without a PLL for 36 minutes.
Section 8.2 explains the theory of all-optically regenerating the QPSK signal’s phase.
Section 8.3 explains the concept of regenerating the QPSK signal without a PLL using
Brillouin amplification. Section 8.4 describes the experimental setup. Section 8.5 presents the
experimental results of regenerating a 10-20 Gbaud QPSK channel along with the effect of
tuning the BA’s frequency shifter. Section 8.6 presents the conclusions.
8.2 Theory
Regenerating a phase modulated channel can be achieved by adding the signal to its (M-
1)
th
harmonic coherently (i.e., with stable phase-locking), where M is the number of the
constellation points [93]. This generates a staircase phase quantization function. For a QPSK
channel, M=4 and the phase regeneration equation is given by:
𝑆 𝑜𝑢𝑡 ∝ 𝑒 𝑗 𝜑 𝑖𝑛

+
1
3
𝑒 −𝑗 3𝜑 𝑖𝑛

(8.1)
Where Sout is the regenerated signal and φ in is the input signal’s phase. A simulation of
regenerating a QPSK signal loaded with phase noise is shown in Figure 8.1.

Figure 8.1 Constellations of an input QPSK signal with phase noise, and the regeneration output
(simulation).

Constellation of a QPSK
signal loaded with
phase noise
Constellation of the
regenerated QPSK signal
84

8.3 Concept
The concept of an all-optical QPSK regenerator without a PLL using Brillouin
amplification is shown in Figure 8.2. A QPSK signal (𝑆 ∝ 𝑒 𝑗 𝜑 𝑆
), degraded with φ noise is
combined with a CW pump (𝑃 ∝ 𝑒 (𝑗 𝜑 𝑝𝑢𝑚𝑝 )
) and sent into HNLF 1 to generate the second-,
third-, and fourth-harmonic idlers, where φ S is the input signal’s phase and φ pump is the pump
laser’s phase noise. The idlers will be created in HNLF 1 through FWM as:
𝑖𝑑𝑙𝑒 𝑟 2𝜑 𝑆 ∝ 𝑃
𝑆 2
∝ 𝑒 (−𝑗 𝜑 𝑝𝑢𝑚𝑝 )
𝑒 𝑗 2𝜑 𝑆
(8.2)
𝑖𝑑𝑙𝑒 𝑟 3𝜑 𝑆 ∝ 𝑃

2
𝑆 3
∝ 𝑒 (−𝑗 2𝜑 𝑝𝑢𝑚𝑝 )
𝑒 𝑗 3𝜑 𝑆

(8.3)
𝑖𝑑𝑙𝑒 𝑟 4𝜑 𝑆 ∝ 𝑃

2
𝑆 3
∝ 𝑒 (−𝑗 3𝜑 𝑝𝑢𝑚𝑝 )
𝑒 𝑗 4𝜑 𝑆

(8.4)
Idler 4φS is a continuous wave (CW) because 4φ S=4φ data+4φ noise and φ data ∈ [π/4, 3π/4, 5π/4,
7π/4]. So, 4φ data∈ [π,π,π,π] and 4φ S ∝ 4φ data+4φ noise π + 4φ noise which can be interpreted as a
CW wave with four times the phase noise. Next, in a Liquid Crystal on Silicon (LCoS)
programmable filter, idler 2φS is blocked and S is slightly attenuated to adjust the amplitude
levels and apply the relative 1/3 scaling factor (see eqn. 1) that will be needed in the following
mixing stage. Also, the delay between S and idlers due to dispersion walk-off in the
forthcoming BA gain medium is compensated.
Then, idler 4φS gets amplified in the single-mode fiber (SMF-28) with Brillouin gain (G B)
using a counter-propagating BA pump. BA depends on the frequency-locking between the
pump and probe (the probe is idler 4φS in our case) [11,87,98]. To ensure frequency-locking
between idler 4φS and the BA pump, the BA pump is generated by tapping idler 4φS after HNLF 1
and sending it to a slave laser (the blue area in Figure 8.2). The slave laser gives a frequency-
locked CW output, which is then frequency up-shifted by ν B (ν B:Brillouin gain frequency shift
of the medium), amplified, and sent into the SMF-28 as a counter-propagating BA pump. For
SMF-28, ν B≈10.8 GHz.
At the SMF-28 output, the P, S, idler 3φS, and idler 4φS×G B are boosted using an erbium-
doped fiber amplifier (EDFA) and sent into HNLF 2. In HNLF 2, non-degenerate FWM mixing
between the pump, idler 4φS × G B, and idler 3φS, creates e
(-j3φS)
at the same frequency as of the
signal (ω S), and Sout is then realized. Also, because idler 4φS propagates in the forward direction
85

in the same path as the other harmonics, its phase will relatively remain locked (i.e.,
synchronized) to P, S, and idler 3φS without requiring a PLL [11].

Figure 8.2 The concept of QPSK channel phase regeneration without a phase-locked loop using
Brillouin amplification.
8.4 Experimental Setup
The experimental setup is depicted in Figure 8.3(a). A QPSK signal is generated
by modulating a laser at wavelength λS=1553.9 nm in an I/Q MachZehnder modulator
(MZM) with 2
31
-1 pseudorandom binary sequence (PRBS) non-return-to-zero (NRZ)
pulses at 10-20 Gbaud. φnoise is loaded using a phase modulator driven by a 5.5-GHz
clock source. The signal and a CW pump at λP=1553.1 nm are combined in a 50/50
coupler, and sent together into a 450 m HNLF1. HNLF1 has zero-dispersion
wavelength (ZDW) at 1556 nm. Linewidths of Laser-1 and Laser-2 are less than 10
kHz, and each of the signal and pump has ∼ 20 dBm at HNLF1 input. The measured
reflected power from HNLF1 at the power meter (PM1) due to the stimulated Brillouin
scattering (SBS) is ∼ +2 dBm.
The output spectrum of HNLF1 is shown in Figure 8.3(b). HNLF1 output is sent
to the LCoS programmable filter to attenuate S, block idler2φS, adjust relative phases,
and compensate for the delay that will be induced by dispersion walk-off in the
upcoming 500 m SMF-28. The added delay values are shown in Figure 8.3(c).
Afterwards, the LCoS filter output is sent to the BA gain medium (500 m SMF-28) to
amplify the central carrier of idler4φS using the counter-propagating BA pump.
λ
S
QPSK
with
high
phase
noise
QPSK with
lower phase
noise
λ
BA Gain
Medium
HNLF2 HNLF1
Isolator
BPF
tap
BA
Pump
ν
B
Shifter
10.8GHz
Slave
Laser
f
idler,4φs
+10.8GHz
Pass idler
4φs
BA Pump
Generation
SMF-28
λ
P
Pump
idler
4φs
Generate higher-
harmonic idlers
Idler
4φs
Idler
3φs
P S Idler
2φs
Attenuate S
& Block idler
2φs
P
Brillouin amplification
for idler
4φs
idler
4φs
G
B
idler
3φs
P S
Phase regeneration
S
λs

LCoS
filter
Idler
4φs
Idler
3φs
86

The BA pump is generated in the “BA pump generation” path by selecting
idler4φS using a band-pass filter (BPF) after the 50/50 coupler and sending it to a slave
laser. The slave laser (Eblana photonics 1550-NLW) is temperature-controlled so that
it locks to idler4φS within ± 200 MHz range. The slave laser output is then frequency
up-shifted in a MZM biased at null and driven by a νB=10.805 GHz tone. The
modulator is followed by a sharp filter to passes only the upper tone. The upper tone
is boosted in an EDFA and sent to the 500 m SMF-28 from its opposite end as the
counter-propagating BA pump.
The BA pump EDFA is operated at ∼27 dB, and the pump power level
corresponds to the operating point shown in Figure 8.3(d). The SMF-28 output is
shown in Figure 8.3(e) before (in red) and after (in blue) amplifying idler4φS. Figure
8.3(f) shows the spectrum of idler4φS after the SMF-28, which is captured using a high-
resolution (10-MHz) optical spectrum analyzer (OSA). The central carrier of idler4φS
has gained GB∼40 dB while the 5.5-GHz φnoise spectral components are not amplified.
The spectrum is captured for a 10 Gbaud NRZ signal with bandwidth extending ±10
GHz around the optical carrier, and the 5.5-GHz φnoise tones thus reside within the
signal’s band. Also, in Figure 8.3(f), a crosstalk tone appears at 10.8 GHz due to the
BA pump leakage between port 1 and port 3 in circulator2. This power leakage could
fall within the signal’s band if the signal’s baud rate becomes greater than 10.8 GHz.
Next, P, S, idler3φS, and idler4φS×GB are amplified in EDFA6, which is set to
deliver 26 dBm at HNLF2 input. HNLF2 has ZDW=1545 nm and the measured
reflected power due to the SBS is -10 dBm at PM2. The regeneration stage output is
shown in Figure 8.3(g) along with the case of blocking S, to illustrate that the created
e
(−j3φS)
at λS, is optimized to be 10 dB lower than the signal (~ 1/3 difference in
magnitude). The OSNR of Sout is 22.3 dB (20.6 measured dB at 0.1 nm resolution).
The low OSNR is caused by noise-loading in EDFA6 when amplifying the relatively
low power signal and idler3φS. At the output, the regenerated QPSK signal is filtered
and sent to an 80 Gsample/s coherent receiver.
87

Figure 8.3 (a) Experimental setup. (b) The spectrum of generated idlers after HNLF 1. (c) Applied delay
in the LCoS filter to compensate for the dispersion-induced walk-off in the 500 m SMF-28 between P,
S, idler 3φS, and idler 4φS. (d) BA operating point as a function of EDFA 5 output power. (e) Spectrum at
the SMF-28 output to show the amplification on idler 4φS. (f) Spectrum of the amplified idler 4φS captured
using a 10-MHz resolution optical spectrum analyzer, showing that idler 4φS’s central component gains
40 dB, while the 5.5-GHz φ noise components are not amplified. (g) HNLF 2 output when the system is
regenerating the phase, and when S is blocked to observe the ∼10 dB power difference between e
(jφS)
and e
(−j3φS)
.

Optical Power
(20dB/Div)
F
idler,4φs
f
idler,4φs
+ν
B
ν
B
=10.805GHz
~
Laser 1
λ
S
=1553.9nm
450m
HNLF1
PRBS 2
31
-1
BPF BPF
Laser2
λ
P
=1553.1nm
BPF
50/50
Pass
upper
tone
BPF
EDFA5
420mW
LCoS
Filter
Isolator
500m SMF-28
Brillouin gain
medium
BPF
357 m
HNLF2
BPF
1nm
EDFA6
800mW
EDFA1
10mW
EDFA2
510mW
EDFA3
550mW
EDFA4
10mW
BPF
BA pump
QPSK
10-20
Gbaud
f
idler,4φs
Phase noise
5.5GHz
tone
idler
4φs
50/50
2 3
1
I/Q
MZM
Phase
Modulator
Slave
Laser
BA pump generation
Circulator2
Circulator3
b
-20
-10
0
10
20
1550 1551 1552 1553 1554 1555
Delay (ps)
Wavelength (nm)
c
idler
4φs
idler
3φs
P
S
1550 1552 1554
Wavelength (nm)
Wavelength (nm)
1550 1552 1554
3Φs
4Φs
e
idler
4φs
G
B
idler
3φs
P
S
f
-20 0 20
Relative Frequency (GHz)
-40
Φnoise
5.5GHz
Tones
40dB
idler
4φs
G
B
Circulator
crosstalk at
10.8GHz
40
RBW
10MHz
RBW0.05nm
1548 1552 1556
Wavelength (nm)
1550 1554
g
10 dB
Optical Power
(20dB/Div)
RBW
0.05nm
-60
-50
-40
-30
-20
16 18 20 22 24 26 28 30 32
SBS Power
(10dB/Div)
Operating point
BA: OFF
BA: ON
d
35dB
Regeneration
Blocked S
OSNR
22.3dB
Sout
EDFA5 output power (dBm)
Idler
4φs
idler
3φs
P S
idler
2φs
Optical Power
(20dB/Div)
RBW:0.05nm
Optical Power
(20dB/Div)
MZM
Coherent
Receiver
PM2
PM1
BA: OFF
BA: ON
a
88

8.5 Experimental Results
Figure 8.4(a) depicts the constellations resulted from regenerating the degraded
signal with φnoise. The phase noise levels are varied and following parameters are
recorded: (i) constellation, (ii) error-vector-magnitude (EVM) (iii) phase noise
variance (∆φ), (iv) magnitude error (MagErr), and (v) the Q-factor (Q). From the
noise-free (Level-5) scenarios, the system adds 1.3-dB Q-factor penalty to the 10-
Gbaud signal and 2-dB penalty to the 20-Gbaud case. Figure 8.4(b) shows the
percentages of improvement for the figures-of-merit with respect to the input ∆φ.
When the 10-Gbaud QPSK signal is transmitted, reductions of up to 65% in ∆φ and
48% in the EVM are observed for the high phase noise scenario (corresponding to
Level-1). At 20 Gbaud, the highest recorded improvements in ∆φ and EVM are 43.9%
and 30.3%, respectively. Figure 8.4(c) shows the BER of the output and indicates up
to a 3.4-dB improvement at a BER of 10
-4
for the 10-Gbaud case. The BER is
calculated by counting the errors of ∼500,000 bits for every point. The 20-Gbaud
signal exhibits receiver sensitivity improvement of 1.8 dB at Level-3 and the
improvement is 2.6 dB at Level-2. We also observe a BER floor for the 20 Gbaud
Level-2 input signal, and the output follows the same error floor at a BER of 5.6×10
-
5
.
89

Figure 8.4 (a) Constellations before and after the regeneration system at various φ noise levels, (b)
Percentages of improvement in the figures-of-merit corresponding to input phase noise variance (∆Φ)
levels. (c) BER performance of the regeneration system.
Next, we tune the system and examine the regeneration performance for a 10-
Gbaud QPSK with Level-2. In Figure 8.5(a), the phase of the amplified idler4φS is tuned
using the LCoS filter, and the output EVM exceeds the input EVM (23.3%) after 60
◦
of phase tuning. The BA pump is then frequency-shifted from the optimal νB and the
regeneration performance is recorded in Figure 8.5(b). Results in Figure 8.5(b) show
that EVM exceeds the input EVM level of 23.3% after ∼3 MHz of BA-pump
frequency tuning.
EVM=27.9%
ΔΦ=15.5
o
MagErr=7.1%
Q=5.5dB
EVM=19.2%
ΔΦ=10.5
o
MagErr=6.0%
Q=7.1dB
EVM=14.7%
ΔΦ=7.8
o
MagErr=5.5%
Q=8.3dB
EVM=7.0%
ΔΦ=2.8
o
MagErr=4.9%
Q=11.5dB
EVM=14.4%
ΔΦ=6.1
o
MagErr=9.9%
Q=8.4dB
EVM=13.9%
ΔΦ=5.7
o
MagErr=9.7%
Q=8.6dB
EVM=12.3%
ΔΦ=5.1
o
MagErr=8.5%
Q=8.8dB
EVM=11.1%
ΔΦ=4.6
o
MagErr=7.8%
Q=9.5dB
EVM=9.5%
ΔΦ=3.8
o
MagErr=6.8%
Q=10.2dB
INPUT OUTPUT
a Level-1 Level-2 Level-3 Level-4 Level-5
EVM=23.2%
ΔΦ=12.7
o
MagErr=6.7%
Q=6.3dB
10 Gbaud
INPUT OUTPUT
Level-1 Level-2 Level-3 Level-4 Level-5
EVM=26.7%
ΔΦ=14.8
o
MagErr=7.0%
Q=5.7dB
EVM=19%
ΔΦ=10.1
o
MagErr=7.1%
Q=7.1dB
EVM=14.8%
ΔΦ=7.6
o
MagErr=6.7%
Q=8.2dB
EVM=8.9%
ΔΦ=3.5
o
MagErr=3.5%
Q=10.5dB
EVM=22.7%
ΔΦ=12.4
o
MagErr=7.1%
Q=6.4dB
EVM=18.6%
ΔΦ=8.3
o
MagErr=11.4%
Q=7.2dB
EVM=16.5%
ΔΦ=7.5
o
MagErr=10.5%
Q=7.8dB
EVM=15.1%
ΔΦ=6.6
o
MagErr=9.9%
Q=8.1dB
EVM=14.7%
ΔΦ=6.4
o
MagErr=9.6%
Q=8.3dB
EVM=14%
ΔΦ=5.9
o
MagErr=9.5%
Q=8.5dB
20 Gbaud
Input ΔΦ
Percentage of
improvement (%)
-90
-60
-30
0
30
60
90
0 3 6 9 12 15 18
EVM MagErr
ΔΦ Q
b
Input ΔΦ
Percentage of
improvement (%)
-90
-60
-30
0
30
60
90
0 3 6 9 12 15 18
EVM MagErr
ΔΦ Q
1
8 10 12 14 16 18 20
B2B
Level-2 in
Level-2 out
Level-1 in
Level-1 out
OSNR (0.1 nm) (dB)
-Log10(BER)
3.4 dB
B2B
Level-2 Input
Level-2 Output
Level-3 Input
Level-3 Output
c
1
10 12 14 16 18 20 22 24
B2B
Level-2 in
Level-2 out
Level-1 in
Level1-out
-Log10(BER)
OSNR (0.1 nm) (dB)
1
2
3
4
5
6
2.6dB
1.8dB
B2B
Level-2 Input
Level-2 Output
Level-3 Input
Level-3 Output
error floor
1
2
3
4
5
6
90

Figure 8.5 (a) Impact of tuning the phase of idler 4φS on the regeneration system, (b) Effect of tuning the
frequency shifter of the BA on regeneration the output.
Moreover, we measure the noise-loading on the amplified idler4φS. The
measurement is conducted by shifting the BA pump from the optimal frequency as
well as measuring the ON/OFF ratio; defined as the power ratio of the amplified signal
to the amplified spontaneous emission [99]. In Fig. 8.6(a), we characterize the gain
when tuning the BA pump frequency shifter away from νB ≃ 10.8 GHz. We observe
that the 35-dB gain (measured using 0.05 nm OSA) decreases by 7.7 dB and then
saturates after ±4 MHz of tuning the BA pump frequency. The output power saturation
after ±4 MHz could indicate amplified-spontaneous emission (ASE) noise
loading [11]. We support our result by characterizing the BA’s ON/OFF ratio in Fig.
8.6(b), and we find that the ratio to be 9.8 dB.

Figure 8.6 (a) BA Gain with respect to tuning the BA pump frequency. (b) ON/OFF ratio of the BA
process for the idler 4φS.
0
10
20
30
0 30 60 90 120
EVM ΔΦ
MagErr Q
Pump phase shift (
o
)
Pump phase shift
Input
EVM
a
BA Pump frequency tuning(MHz)
0
10
20
30
0 1 2 3 4 5
BA Pump frequency tuning
Input
EVM
b
Phase 0
o
Phase 30
o
Phase 60
o
Phase 120
o
3MHz 5MHz 2MHz 0 MHz
EVM(%) ΔΦ(
o
)
MagErr(%) Q (dB)
1550 1550.5 1551
RBW
0.01nm
Circulator
crosstalk
BA
ON/OFF
ratio
9.8 dB
b
Idler4:OFF,BA:ON
Idler4:ON, BA:ON
Optical Power
(20dB/Div)
-90
-70
-50
-30
-20 -15 -10 -5 0 5 10 15 20
Gain d[dB]
Series1
Series2
Optical Power
(20dB/Div)
idler3xG
B
Idler3 input
BA Pump frequency tuning(MHz)
Gain:35dB
RBW0.05nm
a
7.7dB
Wavelength (nm)
91

Finally, the phase-locking behavior of the regeneration system is examined over
time. Figure 8.7(a) shows the histogram of input and the regenerated output at 10
Gbaud with φnoise of Level-3. Figure 8.7(b,c) characterizes the performance over an
hour without phase adjustments or a PLL, using the EVM and ∆φas figures-of-merit.
Results indicate that the output started operating around EVM of 15%, but abrupt
degradation happened after 36 minutes. This degradation is caused by bias drifting of
the MZM frequency shifter and the changes in the room temperature. The MZM
should operate at the null but instead varied, because it was manually adjusted at the
start and then left to run freely. Also, slight room-temperature variations cause
degradation, because νB varies with 1 MHz per degree centigrade in the SMF-28 [11].
Once the MZM bias and νB are re-optimized, the system could return to operate as
normal.

Figure 8.7 (a) Histograms of input and regenerated 10-Gbaud output signal. (b,c) Free-running stability
test over an hour without a PLL. The performance is characterized by (b) EVM and (c) ∆φ.
8.6 Discussion and Conclusion
In conclusion, we experimentally demonstrated a phase-sensitive QPSK signal
regeneration system without an active phase-locked loop by amplifying the fourth-
harmonic idler “in-line” using narrow bandwidth Brillouin amplification. The system
performance under different baud rates and phase noise levels was investigated. We
also evaluated the system sensitivity to various changing scenarios and showed stable
regeneration performance over 36 minutes without a PLL compared to a few
seconds [27].
EVM=19.1%
ΔΦ=10.5
o
INPUT
OUTPUT
EVM=12.3%
ΔΦ=5.1
o
Time (mins)
EVM(%)
0
10
20
30
0 20 40 60
EVM2
EVM
Linear (mean)
Input EVM
Output EVM
Mean output EVM
b
Time (mins)
0
10
20
30
0 20 40 60
phase error2
phase error
Linear (mean)
Input Δ Φ
Output Δ Φ
Mean output Δ Φ
ΔΦ(
o
)
c
a
36 mins
92

We believe our regeneration system performance is limited by the final OSNR,
and this can be improved by achieving better conversion efficiency in the HNLFs. For
example, the improvement of conversion efficiency in HNLF1 can result in creating
idler3φS with a higher power which can help to reduce the amount of loss applied to S
for realizing the 10-dB power difference. Therefore, the overall OSNR after EDFA 6
can be increased.
The elimination of active PLL comes at the expense of adding Brillouin
amplifier components. Although our system could operate without a PLL over 36
minutes, actual system operation requires other means of feedback. For example, the
system is polarization sensitive, and a polarization tracking system should be added.
Long-timescale feedback circuits to sense the temperature and tune the frequency shift
accordingly might also be needed. Finally, a conventional bias control circuit should
be added to maintain the bias of the shifting MZM at the null.

93

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Abstract (if available)

Abstract Optical communication systems have benefited from the tremendous bandwidth of optical signals (beyond tera‐hertz) to transmit information for a long time. Through using the optical nonlinear wave mixing, this Ph.D. dissertation explores the potential of developing tunable delay lines and processing high‐speed signals in the optical domain. ❧ The first part of this dissertation studies tunable multiple‐access optical delay lines. Traditionally, optical delays have been created by sending a signal through a fixed optical path which provides a fixed delay. On the other hand, having tunable optical delays can create possibilities of more optical signal processing functions capable of accommodating the heterogeneous data traffic of future networks, as well as baud‐rate‐adjustable, reconfigurable and tunable signal processing and arbitrary filter designs. In the past, tunable optical delays have been achieved using wavelength conversion and group‐velocity dispersion (GVD). However, for many signal‐processing functions, accessing multiple delays at the same time is needed. In this dissertation, we first explore using nonlinear multicasting with a frequency comb to create multiple delays. We next investigate reducing the latency excess lengths of fibers in the delay system by replacing kilometers of dispersive fibers with the time‐of‐flight in fiber Bragg gratings shorter than 100 meters. We also present a new concept to access different delays at the same time by using orthogonal spatial modes in a recirculating loop. ❧ The second part of this dissertation is about using the wave mixing to enable signal processing functions. We demonstrate all‐optical signal processing functions that bring together various nonlinear devices and processes, and different data modulation formats. Our goal is to achieve high‐speed signal processing functions that can potentially operate at the line rate of fiber optic communications. Therefore, we employ the recent advances in the enabling technologies to demonstrate various techniques that can process phase‐ and amplitude‐encoded optical signals. We use nonlinear media, such as highly nonlinear fiber, and periodically poled lithium niobate for nonlinear mixing of optical signals. We propose and experimentally demonstrate all‐optical homodyne detection of dual‐polarization and WDM phase modulated channels. We also describe BPSK signal regeneration in the optical domain with assistance from Brillouin amplification to reduce the requirements on the phase‐locked loop tracking. Finally, we extend our approach to regenerate a QPSK channel by generating the signal’s higher harmonics and mixing them.

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Asset Metadata

Creator Almaiman, Ahmed Sami (author)

Core Title Optical wave mixing for tunable delays and high‐speed signal processing

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 04/07/2020

Defense Date 03/20/2018

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

Tag Ahmed,Almaiman: fiber,Brillouin,delay,HNLF,OAI-PMH Harvest,optical,PPLN

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Willner, Alan Eli (committee chair), Haas, Stephan (committee member), Sawchuk, Alexander (committee member)

Creator Email ahmedalmaiman@gmail.com,almaiman@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-2650

Unique identifier UC11671543

Identifier etd-AlmaimanAh-6166.pdf (filename),usctheses-c89-2650 (legacy record id)

Legacy Identifier etd-AlmaimanAh-6166.pdf

Dmrecord 2650

Document Type Dissertation

Rights Almaiman, Ahmed Sami

Type texts

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

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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