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Optical communications, optical ranging, and optical signal processing using tunable and reconfigurable technologies

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Optical communications, optical ranging, and optical signal processing using tunable and reconfigurable technologies

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Content Optical Communications, Optical Ranging, and Optical Signal Processing using Tunable
and Reconfigurable Technologies
by
Hao Song
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
May 2023
Copyright 2023 Hao Song
Thisdissertationisdedicatedtomylovinggirlfriend,XiaofanZhu,mysupportivefamily,XiaoliChi,Xianhua
Song, Xiangxiang Song, and my lifelong respectful advisor, Prof. Alan E. Willner.
ii
Acknowledgements
Firstly, I would like to express my deepest gratitude to my Ph.D. advisor, Alan E. Willner. He is a great
mentor in shaping and sculpting me into the scholar I am now. He is the role model that I aspire to follow
beyond my Ph.D. journey. His wisdom, smile, and trust is the best gift I have ever received. I would also
like to thank Prof. Moshe Tur at Tel Aviv University for his invaluable discussions during my Ph.D. study.
His patient mentoring extensively supports my research. Moreover, I would like to thank Prof. Todd A.
Brun and Prof. Aiichiro Nakano for serving on my dissertation and qualification exams. I would also like to
thank Prof. Andreas F. Molisch and Prof. Wei Wu for serving on my qualification exam.
Secondly, I want to thank my colleagues in OCLab, including Dr. Jing Du, Dr. Guodong Xie, Dr.
Changjing Bao, Dr. Ahmed Almaiman, Dr. Long Li, Dr. Yinwen Bao, Dr. Peicheng Liao, Dr. Zhe Zhao,
Dr. Cong Liu, Dr. Ahmad Fallhpour, Dr. Kai Pang, Dr. Runzhou Zhang, Dr. Haoqian Song, Mr. Kaiheng
Zou, Mr. Huibin Zhou, Mr. Xinzhou Su, Mr. Amir Minoofar, Mr. Narek Karapetyan, Mr. Yuxiang Duan,
Mr. Zile Jiang, Mr. Murale Ramakrishnan, Mr. Stanley Ko, Mr. Abdulrahman Alhaddad, Ms. Yingning
Wang, and Mr. Ruoyu Zeng. Working together with them is one of the best jobs in the world.
Thirdly, I would also like to acknowledge my collaborators, including Dr. SungWon Chung, Mr. Samer
Idres, Prof. Hossein Hashemi, Prof. Janathan Habif at USC, Dr. Kiyoul Yang and Prof. Jelena Vuˇ ckovi´ c at
Stanfard University, Prof. Robert W. Boyd at University of Rochester, Mr. Asher S. Novick, Dr. Madeleine
Glick and Prof. Keren Bergman at Columbia University, Prof. Eric Johnson at Clemson University, Dr.
Zi Wang and Prof. Tingyi Gu at University of Delaware, Dr. Zhifeng Zhang and Prof. Liang Feng at
University of Pennsylvania, Dr. Haoran Ren at Monash University, Dr. Brittany Lynn at Naval Information
Warfare Center Pacific, Dr. Ricard Menchon-Enrich, Dr. Anthony Kelly, and Dr. Conor O’Keeffe at Intel,
iii
Dr. Giovanni Milione at NEC Laboratory, Dr. Robert Bock at R-DEX Systems inc., and Dr. Doohwan Lee
at NTT.
Moreover, I would like to thank the professional support and warm help from the staff team of the ECE
department at USC, including Ms. Diane Demetras, Ms. Corine Wong, Ms. Gerrielyn Ramos, Ms. Susan
Wiedem, Mr. Ted Low, Mr. Seth Scafani, and Mr. John Diaz.
Lastly, I would thank my lover and my family for always being there to listen to the dreams and as-
piration of mine, for giving me the strength to overcome the challenges of mine, and for celebrating the
accomplishments of mine. They are the prolonged source of comfort and courage in my short life.
iv
Table of Contents
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List Of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Orbital Angular Momentum of Structured Light . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Free-space Optical Beams through Turbulent Medium . . . . . . . . . . . . . . . . . . . . . . 5
1.3 OAM-based Communication Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Underwater Optical Ranging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Optical Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Digital Modulation Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.7 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Chapter 2: Tunable Photonic Integrated Circuits for OAM-based Optical Communication Links . . . 11
2.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 SimulationofPixel-array-basedModeConvertorforGeneratinganOAMBeamwithaTunable
OAM Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Concept of Tunable Pixel-array-based OAM Emitters/Receivers . . . . . . . . . . . . . . . . . 20
2.4 Experimental Characterization of the Tunable Pixel-array-based OAM PIC . . . . . . . . . . 22
2.5 100-Gbit/s OAM-based Link with a Tunable OAM order . . . . . . . . . . . . . . . . . . . . . 30
2.6 200-Gbit/s OAM-multiplexed Link using the Pixel-array-based PIC. . . . . . . . . . . . . . . 31
2.7 400-Gbit/s WDM and OAM-multiplexed Link using the Pixel-array-based PIC . . . . . . . . 32
2.8 GenerationofanLGbeamwith2-DTunableSpatialIndicesusingIntegratedCircularAntenna
Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.9 Experimental Characterization of the LG Beam Generation using the Integrated Circular
Antenna Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.10 Communication Link using a Single LG Beam with 2-D Tunable Spatial Indices . . . . . . . . 39
Chapter 3: Free-space Optical Communication under Atmospheric Turbulence Effects . . . . . . . . . 41
3.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Turbulence-resilient Free-space Optical Communication using a Photodetector Array . . . . . 44
3.3 Simultaneous Turbulence Mitigation and Channel Demux. using a Single Multi-Plane Light
Convertor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Chapter 4: Underwater Optical Ranging through Underwater Scattering . . . . . . . . . . . . . . . . 63
4.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Concept of z-dependent Angular Rotation of a Structured Beam . . . . . . . . . . . . . . . . 64
4.3 Optical Ranging using a Single Structured Beam in Clean Water . . . . . . . . . . . . . . . . 66
4.4 Optical Ranging using a Single Structured Beam in Turbid Water . . . . . . . . . . . . . . . 67
v
Chapter 5: Optical Half-adder of Phase Encoded Channels . . . . . . . . . . . . . . . . . . . . . . . . 72
5.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2 Nonlinear Wave Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.3 Concept of Phase-encoded Optical Half Adder . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.4 Experimental Demonstration of Optical Half Adder for 5/10-Gbaud 4-PSK Inputs . . . . . . 76
Chapter 6: Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
vi
List Of Figures
1.1 The wavefronts, intensity profiles, and phase profiles of OAM beams with different ℓ values. . 1
1.2 OAM generation and detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Laguerre-Gaussian (LG) beams. (a) Intensity and phase profiles of LG beams with different
pairs of indices (ℓ, p). (b) A structured beam can be decomposed into a set of LG modes with
different ℓ and p values. The coefficients of LG components can be represented by a complex
modal spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Generation of a pure LG beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Intensity and phase profiles of Bessel modes with different orders. OAM order ℓ determines
both the order of the Bessel beam and the azimuthal phase change. The radial wavenumber
k
r
determines the radial ring spacings in the intensity profile. The longitudinal wavenumber
k
z
can be used to determine the phase velocity of the Bessel beam along the longitudinal
direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.6 Atmospheric turbulence effects on a free-space beam. . . . . . . . . . . . . . . . . . . . . . . . 6
1.7 Concept of OAM-multiplexed link. Multiple independent data-carrying OAM beams can
be multiplexed, spatially copropagate, and be demultiplexed with little crosstalk, thereby
multiplying the system’s data capacity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.8 Potential advantages of optical signal processing. . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.9 (a)Thedatasignalcanbemodulatedontheamplitudeand/orphaseofanopticalwave. (e.g.,
on-off keying (OOK), quadrature phase shift keying (QPSK), and 16-quadrature amplitude
modulation (16-QAM)). (b) The constellation and the error vector of a QPSK signal. . . . . 8
1.10 Overview of the tunable and reconfigurable technologies for different applications, including
optical communications, optical ranging, and optical signal processing, in the scope of this
dissertation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1 Overview of the tunable photonic integrated circuits for OAM-based optical communications
discussed in this dissertation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Concept of (a) the phase-dependent OAM beam generation using the pixel-array structure.
The OAM order of the output beam is dependent on the phase delay of four inputs. (b) Top
view of the pixel-array structure of the silicon-on-insulator (SOI) OAM emitter supporting
the OAM tunable range ℓ={− 2,− 1,+1,+2} (c) 3D view of the light emission in the vertical
direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
vii
2.3 Simulated intensity and phase profiles of the individual fields generated by the (a) k-th input.
and (b) the combined fields with different phase delays. Pairwise overlap integral of (c1) the
individual fields and (c2) the combined fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 (a) Designed structures for OAM emission. (b) Mode purity of the generated OAM beams for
structures 1–4 with different OAM tunable ranges. (c) Mode purity of the generated OAM
beam ℓ= -1 as a function of phase delay ∆ φ for structures 1–4. . . . . . . . . . . . . . . . . . 16
2.5 Simulated emission efficiency of structure 4 over the wavelengths ranging from 1.45 to 1.65 µm. 17
2.6 (a)ConceptofgeneratingmultiplecoaxialOAMbeams. Theinsettableshowsthefixedphase
delays induced by different ports of the 4 × 4 coupler. (b) Intermodal crosstalk of 2–4 coaxial
OAM beams when tuning the phase delay ∆ φ
2
for structure 4 at the wavelength of 1550 nm.
(c) Maximum intermodal crosstalk within the C-band (from 1530 to 1565 nm) for structures
2–4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.7 (a) Concept of the pixel-array-based OAM emitter. The emitter is composed of a 3-to-4 cou-
pler, four tunable phase controllers, and a mode convertor. The OAM order of the output
beam is dependent on the phase delay of waveguides. This phase delay is related to both
the phase delay and induced by the 3-to-4 coupler and the tunable phase controllers, respec-
tively. (b) SEM image of the pixel-array-based 3-to-4 coupler. (c) Integrated thermal phase
controllers. (d) SEM image of the pixel-array-based mode convertor. . . . . . . . . . . . . . . 20
2.8 (a) Concept of the pixel-array-based tunable OAM receiver. The receiver is composed of a
mode converter, tunable phase controllers, and a 4-to-3 coupler. (b1) The OAM receiver
can receive a single OAM beam (OAM -1 or OAM +1) and convert it into a fundamental
waveguide mode at one output port. The target OAM mode to be received could be tuned
from OAM -1 to OAM +1. (b2) The OAM receiver can also demultiplex two coaxial OAM
beams (OAM -1 and OAM +1) and convert them to fundamental waveguide modes at two
output ports. The target OAM mode to be received at the corresponding output port could
be changed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.9 Experimental setup of free-space beam characterization generated by the pixel-array-based
OAM emitter. EDFA: Erbium-doped fiber amplifier. Col: Collimator. BS: beam splitter.
HWP: half-wave plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.10 Measured (a1-b1) beam profiles, (a2-b2) interferogram, and (a3-b3) modal power distribution
of a single beam when port 2 is fed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.11 Measured modal power distribution at different wavelengths of a single beam with a tunable
OAM order of (a) OAM -1 or (b) OAM +1. As proof of concept, port 2 is selected as the
input port. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.12 Measured modal power distribution of a single beam when port 1 or port 3 is fed. . . . . . . 25
2.13 Measured optical power at different output ports under different bias voltages when a single
OAM beam is transmitted. (a1) Layout of the applied bias voltages on the heaters. (a2-a4)
Layout of receiving power at different output ports. (b) The received optical power at port
1/2/3 when no bias voltages are applied. (c-f) The received optical power at port 1/2/3. The
input optical power is 0 dBm. The red bars show the received power of the target OAM mode
at the specific output port. (g) The applied bias voltages for different scenarios. . . . . . . . . 25
viii
2.14 (a) Concept of the polarization-induced power loss and inter-modal crosstalk for pixel-array-
based OAM receiver. (b1-b2) Normalized received power of a single OAM beam at a different
polarization mismatch angle when the target mode of the OAM receiver is tuned from (b)
OAM -1 and (c) OAM +1.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.15 (a) Misalignment between transmitter and receiver in an OAM-based link. (b) Measured
received power when a single OAM beam with a lateral displacement. The power spectrum
is measured by changing transmitted OAM order. (c1) Measured received power and (c2)
intermodal crosstalk with a different lateral displacement. . . . . . . . . . . . . . . . . . . . . 28
2.16 Experimental setup of free-space communication link using the (a) pixel-array-based OAM
emitter and (b) pixel-array-based OAM receiver. HWP: half-wave plate. . . . . . . . . . . . . 29
2.17 Single-channel communication link with a tunable OAM order using the OAM emitter. Mea-
sured(a)constellationdiagramsand(b)BERperformanceofasingle50-GbaudQPSKchannel
on a tunable OAM beam at 1550.9 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.18 (a) Measured power spectrum of the received signal of a single 50-Gbaud QPSK channel
carried by the corresponding OAM beam generated by the pixel-array-based OAM emitter.
Different colors indicate different carrier wavelengths. Measured (b) OSNR, (c) BER per-
formance at different carrier wavelengths. Measured BER at different wavelengths. A single
channel carried by a tunable OAM beam is transmitted at one wavelength at one time with
the same transmitted power. Port 2 is the input port. Voltages for bias 1 and bias 2 are
(0.4V,3.3V,2.5V,0.8V) and (0.2V,0.1V,1.8V,2.3V), respectively. . . . . . . . . . . . . . . . . . 31
2.19 Experimental demonstration of a 200-Gbit/s OAM-multiplexed link using pixel-array-based
receiver. (a)Measured crosstalk matrix of the received OAM channels under different bias
voltages. (b1-b2) Constellation diagrams of the recovered signal for receiving different OAM
channels with the corresponding bias voltages. (c) Measured BER performance for the data
channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.20 WDM and OAM-multiplexed link using the tunable OAM emitter. Measured inter-channel
crosstalk and BER performance for the OAM-multiplexed and WDM link under (a, b) two
different bias voltages. λ 1
: 1550.9 nm, λ 2
: 1551.7 nm. . . . . . . . . . . . . . . . . . . . . . 33
2.21 WDM and OAM-multiplexed link using the tunable OAM receiver. Measured (a1-a2) inter-
channel crosstalk and (b1-b2) BER performance for the OAM-multiplexed and wavelength-
division-multiplexed(WDM)linkunderdifferentbiasvoltages. Carrierwavelength λ 1
: 1550.9
nm, λ 2
: 1551.7 nm. A single OAM beam with the carrier wavelength of λ 1
is transmitted as
a comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.22 MeasuredBERperformancewithoutinter-channelcrosstalk,withinter-modalcrosstalkinthe
OAM-multiplexed link, and with inter-channel crosstalk in the OAM-multiplexed and WDM
link. The channel is carried by the OAM beam (OAM -1) with the carrier wavelength of
1550.9 nm (λ 1
). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.23 Concept of the tunable Laguerre Gaussian beam (LG
ℓp
) generation using integrated uniform
circular arrays (UCAs) of optical antennas. By tuning the amplitude and phase distribution
between the two concentric UCAs, the p value of the generated beam can be changed. By
tuning the circular phase inside the UCAs, the ℓ value of the generated beam can be changed. 36
ix
2.24 The simulated intensity and phase profiles of the generated beam. By tuning the azimuthal
phase delay of each UCA, the ℓ order of the generated beam can be tuned. By tuning the
amplitude distribution and phase delay among different concentric UCA, the p order of the
generated beam can be tuned. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.25 Experimental setup of the tunable LG beam generation. . . . . . . . . . . . . . . . . . . . . . 38
2.26 Measuredintensityprofiles,phaseprofilesandtheLGmodalpowerspectrumofthegenerated
(a1-b1) LG
ℓ=0,p=0
(a2-b2) LG
ℓ=0,p=1
(a3-b3) LG
ℓ=+1,p=0
(a4-b4) LG
ℓ=+1,p=1
. . . . . . . . . 38
2.27 Measured (a) data constellation diagram and (b) BER performance of the 5-Gbaud QPSK
data channel carried by a signal LG beam with tunable modal indices. A single beam is
transmitted and received one at a time. The constellation diagram is measured with the
OSNR of 18 dB. EVM: error vector magnitude. FEC: forward error correction. . . . . . . . . 39
3.1 Atmospheric turbulence effects on free-space optical communication links. . . . . . . . . . . . 42
3.2 Atmospheric turbulence effect on OAM-multiplexed links. . . . . . . . . . . . . . . . . . . . . 43
3.3 OverviewofthemitigationapproachesforFSOlinksunderturbulenceeffects(discussedinthis
dissertation). LO: local oscillator. PD: photodetector. MPLC: multi-plane light convertor. . 44
3.4 (a) Concept of turbulence-resilient self-coherent FSO communications using a pilot tone and
an array of smaller photodiodes. SSBI: signal–signal beating interference; SPB: signal–pilot
beating. (b) Concept of utilizing an array of smaller PDs to enhance the system bandwidth.
In general, a larger free-space PD tends to have a relatively narrower frequency response,
while a single smaller PD might have a relatively higher electrical mixing power loss under
turbulence distortion. Utilizing an array of smaller PDs could potentially enhance the system
bandwidth while maintaining a relatively large PD area. . . . . . . . . . . . . . . . . . . . . 44
3.5 Experimental setup of the PD-array-based turbulence-resilient FSO link. AWG: Arbitrary
Waveform Generator; EDFA: Erbium-doped Fiber Amplifier; PC: Polarization Controller;
FM: flip mirror; SMF: single-mode fiber; DSP: Digital Signal Processing; LO: local oscillator.
Pilot λ 2
is switched off for the LO-based SMF-coupled receiver. The inset shows the sizes of
the free-space PDs used in our experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.6 MeasuredelectricalmixingpowerlossofthetwobeatingtermsbetweentwoCWlasers(∆ f=1
GHz) in an FSO link under 1000 turbulence realizations (D/r
0
=8.4). (a) LO-based coherent
detectionutilizinganSMFPD.(b-d)pilot-assistedself-coherentdetectionutilizing(b)asingle
smaller PD, (c) a single larger PD, and (d) an array of smaller PDs. The electrical mixing
power loss is normalized by the corresponding electrical mixing power without turbulence. . . 48
3.7 Measured(a1-a2)amplitudeandphaseprofiles,(b1-b2)LGspectrumwith/withoutturbulence
(oneturbulencerealization). Measuredelectricalspectraandrecovered1-Gbaud16-QAMdata
constellation for (c1-c2) the LO-based heterodyne coherent detector and (d1-d2) the pilot-
assistedself-coherentPD-arrayreceiverwith/withoutturbulence(oneturbulencerealization).
(e) Measured BER of the 1-Gbaud 16-QAM signal under 100 turbulence realizations (D/r
0
=∼ 8.4). FEC: forward error correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.8 Measured electrical spectrum and constellation diagram of the 0.5-Gbaud and 1-Gbaud pilot-
assisted FSO link utilizing (a1-a2) array of smaller PDs, (b1-b2) single larger PD, (c1-c2)
single smaller PD without and with the turbulence effects. . . . . . . . . . . . . . . . . . . . . 50
x
3.9 Concept of utilizing one MPLC to simultaneously mitigate turbulence-induced crosstalk and
demultiplex OAM channels. The turbulence distorts the coaxial OAM beams and introduces
powercouplingamongmultipleneighboringmodesbeforecouplingintotheMPLC.Thephase
patterns of MPLC are initialized for channel demultiplexing without considering turbulence
distortion. Withthefeedbackofthemonitoredinter-channelcrosstalk,thegeneticalgorithmis
appliedtoadaptivelyupdatethephasepatternsofMPLC.Subsequently, eachdistortedbeam
propagates through the cascaded phase patterns and gets converted to the corresponding
Gaussian beam with relatively low inter-channel crosstalk. . . . . . . . . . . . . . . . . . . . . 52
3.10 Examples of the (a) phase patterns for channel demultiplexing and (b) superimposed mitiga-
tion and demultiplexing patterns for a turbulence realization. . . . . . . . . . . . . . . . . . . 52
3.11 Experimental setup of using MPLC for turbulence-induced crosstalk mitigation and channel
demultiplexing in an OAM-multiplexed link. QPSK: quadrature phase-shift keying. EDFA:
erbium-doped fiber amplifier. PC: polarization controller. Mux: multiplexer. SLM: spatial
light modulator. PM: power meter. FM: flip mirror. . . . . . . . . . . . . . . . . . . . . . . . 54
3.12 Measured crosstalk matrix. The MPLC can be reconfigured to demultiplex different OAM
beams, e.g., ℓ = {− 1,+1} or ℓ = {− 1,+2}. Before applying the mitigation patterns, the
turbulence introduced extra crosstalk. After applying the mitigation patterns, the intermodal
crosstalk can be mitigated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.13 (a) Measured Beam profiles of and without turbulence and with turbulence under different
realizations. (b) Measured crosstalk without (dashed line) and with (solid line) mitigation for
the channels carried by ℓ=− 1 (black line) and ℓ=+2 (red line) under 10 turbulence . . . . 57
3.14 Measured transmission matrix of OAM-multiplexed channels. (a1-a3) ℓ= -1 and +1, (b1-b3)
ℓ = -1 and l=+2 for channel demultiplexing without turbulence, without and with crosstalk
mitigation (miti.) under the turbulence (turb.). (c) Beam profiles of ℓ =-1 and +2 without
turbulence and with turbulence under different realizations. (d) Measured crosstalk without
(dashed line) and with (solid line) mitigation for the channels carried by ℓ = -1(black line)
and ℓ = +2( (red line) under 10 turbulence realizations. . . . . . . . . . . . . . . . . . . . . . 58
3.15 Measured crosstalk with a different number of mitigation patterns applied under one turbu-
lence realization in the experiment for OAM-multiplexed channels ℓ={− 1,+2}. . . . . . . . 59
3.16 Simulated (a) crosstalk and (b) number of iterations under 200 turbulence realizations for
OAM-multiplexedchannelℓ={− 1,+2}. Eachred/blackdotrepresentsthesimulatedcrosstalk
and the simulated number of iterations under one turbulence realization emulated by a single
turbulence plate/two turbulence plates. The circles/squares represent the simulated average
crosstalk and the simulated average number of iterations under 200 turbulence realizations
emulated by a single turbulence plate/two turbulence plates. The bars show the correspond-
ing standard deviation values. (c) Simulated average insertion loss of the MPLC without
turbulence, without and with mitigation under 100 turbulence realizations. . . . . . . . . . . 61
4.1 Concept of the z-dependent angular rotation of the spatially structured beam. The generated
spatially structured beam carries two Bessel modes with different OAM orders and different
longitudinal wavenumbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2 Concept of utilizing angular rotation of spatially structured beam for underwater optical
ranging. The reflector distance is retrieved by measuring the rotating angle of the petal-like
intensity profile of the reflected beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
xi
4.3 Experimental setup of the underwater ranging utilizing z-dependent angular rotation of the
spatially structured beam. PC: polarization controller. Col: collimator. BS: beam splitter.
SLM: spatial light modulator. PM: optical power meter. . . . . . . . . . . . . . . . . . . . . . 66
4.4 Measured (a) intensity profiles and (b) rotating angle of the generated spatially structured
beam (∆ k
z
= 6.2m
− 1
) propagated through the air or clean water at different reflector dis-
tances. The solid black lines indicate the linear relationship between the angular rotation (θ )
and reflector distance (z) in the air and clean water. . . . . . . . . . . . . . . . . . . . . . . . 66
4.5 Experimental setup of the underwater ranging utilizing z-dependent angular rotation of the
spatiallystructuredbeam. Thescatteringmediumisemulatedbyadilutedcommercialantacid
solution. The value of extinction ratio γ is characterized by measuring the optical power loss
of a collimated Gaussian beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.6 (a) Measured intensity profiles of the reflected spatially structured beam through scattering
with different extinction coefficients ( γ ) at different reflector distances (z). (b) Measured
distance with different extinction coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.7 (a)Measurementerrorasafunctionofreflectordistance. (b)Measuredbeamcenterwhenthe
reflector is moving. Such beam wandering is measured and compensated after beam detection. 70
4.8 Measured intensity profiles of the reflected spatially structured beam with and without ad-
justing exposure time. The inset number shows the exposure time for capturing the intensity
profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.9 (a) Exposure time (adjustable) of the camera for different extinction coefficients at different
reflector distances. (b) Comparison of the distance measurement with and without adjusting
exposure time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.1 Concept of second-order χ (2)
nonlinear process of cascaded sum frequency generation and
difference frequency generation (cSFG-DFG). PPLN: period-poled lithium niobate. . . . . . 73
5.2 Concept of optical half-adder. (a1) Schematic diagram of the 4-ary half-adder applying
symbol-to-symbol addition operation to the inputs. (a2) Relationship between the inputs
and outputs of the 4-ary half-adder. (b) Concept of a 4-ary phase-encoded optical half-adder.
TogenerateSum,Twoinputs(A
2
,B
2
)areencodedwithfourphaselevelsπ /4,3π /4,5π /4,7π /4
and the corresponding output (A
2
B
2
) is generated by accumulating the phase of A
2
and B
2
with nonlinear wave mixing. The resultant output (i.e., Sum) is represented by four phase
levels π /2,π ,3π /2,2π .To generate Carry, two inputs (A, B) are encoded with four phase lev-
els ((-3π )/16, π /16,5π /16,9π /16), two inputs (A
∗ , B
∗ ) are simultaneously encoded with four
conjugate phase levels (3π /16, (-π )/16,(-5π )/16,(-9π )/16) and are fed together with A and B
for nonlinear wave mixing. The output (AB +A
∗ B
∗ ) is generated by combining the corre-
sponding mixing terms AB and A
∗ B
∗ . The resultant output (i.e., Carry) is represented by
two phase levels (0,π ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.3 (a)ConceptofutilizingnonlinearwavemixingtogenerateSumandCarrysimultaneouslywith
(b) the input subcarriers of S
A
and S
B
and (c) the output mixing terms AB,A
∗ B
∗ ,A
2
B
2
. φ
N
P
indicates the phase noise of the pump. QPM: quasi-phase-matching. . . . . . . . . . . . . . . 75
5.4 Experimental setup of the optical half adder. AWG: arbitrary waveform generator. EDFA:
Erbium-doped fiber amplifier. PC: polarization controller. PPLN: periodically poled lithium
niobate. OSA: optical spectrum analyzer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
xii
5.5 (a) Measured optical spectrum at the output of PPLN with 5-Gbaud 4-PSK channels. The
wavelength resolution is 0.1 nm. (b) Recovered constellation diagrams of the 5-Gbaud phase-
encoded inputs and outputs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.6 Receovered phase levels and the date sequence of 5-Gbaud inputs ( and ) and outputs (Sum
and Carry). The corresponding target phase levels are calculated based on the input data
sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.7 (a) Measured optical spectrum at the output of PPLN with 10-Gbaud 4-PSK channels. (b)
Measured BER performance of the 5-Gbaud/10-Gbaud channels. . . . . . . . . . . . . . . . . 79
xiii
Abstract
There is a growing interest in structured light, especially beams carring orbital angular momentum (OAM),
for its unique spatial structure. OAM beams are characterized by a twisting phase front having an angular-
dependent term exp(jℓθ ), where θ is the azimuthal angle and ℓ is the OAM order and counts the number of
2π phase shifts in the azimuthal directions. There are differnet types of OAM beams including (a) Laguerre-
Gaussian(LG
ℓ,p
)beamswhichtypicallycarrytwodiscreteazimuthalandradialindices(ℓ,p),and(b)Bessel
beams which have one discrete azimuthal index ℓ and a continuous radial wavenumber k
r
.
On the one hand, OAM-carrying structured light provides a new degree of freedom and toolkit for
the potential optical systems (e.g., high-capacity coherent communication, free-space optical link through
a turbulent medium, or optical ranging). On the other hand, the manipulation of the structured light
necessities the development of tunable and reconfigurable techniques ( e.g., photonic integrated circuits or
mitigation of free-space beam distortions).
This thesis will discuss (i) OAM-multiplexing links with tunable ℓ indices using an integrated pixel-
array-baseddevice,(ii)LGbeamgenerationwithbothtunableℓandpinducesusinganintegratedconcentric
circularantennaarray,(iii)turbulencemitigationapproachesforsingle-channelandmulti-channelFSOlinks,
(iv) optical underwater ranging through turbid water using a structured beam with OAM-carrying Bessel
modes, and (v) optical half adder of 4-ary phase-encoded channels.
xiv
Chapter 1
Introduction
1.1 Orbital Angular Momentum of Structured Light
Structured light, specifically beams carrying orbital angular momentum (OAM), has gained much interest
due to their unique amplitude and phase structures [1, 2, 3]. An OAM beam usually has a helical phase
structure described by exp(iℓθ ) (ℓ refers to the OAM order). The OAM beam has a wavefront that twists
along the propagation axis, which produces a central intensity null (i.e., phase singularity) and annular ring.
One of the properties of OAM is that discrete series of values for the rate of the phase front twisting can
be created, such that each OAM beam with one value is orthogonal to all other OAM beams with different
values [1, 2, 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
= =+
-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
=+ =+
Intensity Phase Intensity Phase Intensity Phase Intensity Phase
Figure 1.1: The wavefronts, intensity profiles, and phase profiles of OAM beams with different ℓ values.
A Gaussian beam can be converted to an OAM beam by propagating through a spiral phase pattern as
shown in Fig. 1.2. The OAM beam could also be converted back to a Gaussian-like beam by propagating
1
Incoming
Gaussian beam
Incoming OAM
beam
Spatially de-multiplexed
Converted into an
OAM beam
Re-converted into
Gaussian beam
OAM generation
OAM detection
Different approaches including:
q Spatial light modulator (SLM)
q Integrated devices
Holographic
phase filter
Figure 1.2: OAM generation and detection.
through a conjugate spiral phase pattern. There are various approaches for OAM generation/detection
including spiral phase plate [5, 6], spatial light modulator (SLM) [7], and metasurfaces [8, 9, 10, 11, 12].
OAM generation/detection can also be achieved by tunable photonic integrated circuits (PICs) which will
be shown in Chapter 2.
In general, an OAM beam could refer to any helically phased light beam, irrespective of its radial
distribution. However, a complete two-dimensional (2-D) modal basis can generally be characterized by
two modal indices. For example, Laguerre-Gaussian (LG
ℓp
) modes have ℓ and p indices, which corresponds
to azimuthal and radial distribution, respectively as shown in Fig.1.3(a). The electric field of LG modes
[1, 2, 13] can be represented as follows,
LG
ℓp
(r,θ,z )=E
0

√
2r
w(z)
!
|ℓ|
L
|ℓ|
p

2r
2
w
2
(z)

w
0
w(z)
exp[− iψ
ℓp
(z)]exp

ik
0
r
2
2q(z)

exp[iℓθ ] (1.1)
2
-π +π 0 1
LG
5,0
LG
5,3
p
ℓ
Intensity Phase
LG
5,1
Complex LG spectrum of structured light
LG mode
number
LG spectrum
(Imag. part)
LG spectrum
(Real part)
θ
ℓ2, p2
A
ℓ2, p2
θ
ℓ3, p3
A
ℓ3 , p3
ℓ
1
, p
1
θ
ℓ1, p1
ℓ
2
, p
2
ℓ
3
, p
3
A
ℓ1, p1
! ",$ =&'
(,)
*+
(,)
(",$-
(,)
Laguerre-Gaussian modes
(b)
(a)
Figure 1.3: Laguerre-Gaussian (LG) beams. (a) Intensity and phase profiles of LG beams with different
pairs of indices (ℓ, p). (b) A structured beam can be decomposed into a set of LG modes with different ℓ
and p values. The coefficients of LG components can be represented by a complex modal spectrum.
where w(z)=w
0
[(z
2
+z
2
R
)/z
2
R
]
1/2
(beam size at the beam waist w
0
, Rayleigh range z
R
=πw
2
0
/λ ) is the 1/e
radius of the Gaussian term, L
|ℓ|
p
are the generalized Laguerre polynomials, q(z) = z− iz
R
is the complex
beam parameter, ψ ℓp
(z)=(2p+|ℓ|+1)tan
− 1
(z/z
R
) is the Gouy phase, (r,θ ,z) is the cylindrical coordinate
[2]. For the LG beam with a non-zero ℓ value, p+1 indicates the number of rings in its intensity profile, and
ℓ represents the number of 2π phase shift along the azimuthal direction in its phase profile. Importantly, LG
beams with different ℓ and/or p values are orthogonal to each other [1, 2]. Since LG modes are a complete
2-D modal basis set, the structured light can be decomposed into LG modes of which the modal coefficient
can be represented by the complex LG modal spectrum [2, 3, 4] as shown in Fig. 1.3(b). Each modal
coefficient contains the information of both amplitude and phase, such that a specific structured beam can
be tailored by the coherent combination of these LG components for desired functions [14, 15].
InordertogeneratedapureLG
ℓp
beamwithahighbeamquality,bothphaseandamplitudeoftheinput
beam should be joint controlled as shown in Fig. 1.4. Specifically, this could be achieved by a phase-only
SLM. The phase of the beam is spatially modulated by loading the corresponding spiral phase pattern on
the SLM, and the amplitude of the beam can be spatially controlled by adding a grating pattern whose
3
Impure LG beam generation
q Phase structure only in the azimuthal direction
Pure LG beam generation
Impure LG
ℓ,0
Beam
Gaussian
beam
Azimuthal
q Phase and intensity structure in both
the azimuthal and radial directions
Pure LG
ℓ,0
beam
Azimuthal
Radial
Gaussian
beam
Figure 1.4: Generation of a pure LG beam.
diffraction efficiency is carefully designed at radial directions [16, 17, 18, 19]. A similar concept could be
migrated into the PIC design for generating tunable LG beams with both tunable ℓ and p indices which will
be shown in Chapter 2.
Bessel modes
ℓ =0;
A smaller

ℓ =0;
A larger

ℓ =+2;
A larger

Intensity Phase
-π +π
0 1
Wavenumber
!
=
"#
$

!

"

§ ℓ: the number of 2 phase shifts in the
azimuthal direction (OAM value)
§
"
: transverse wavenumber determines the
radial ring spacings in the intensity profile.
§
#
: longitudinal wavenumber which
determines the phase velocity of the Bessel
beam along the longitudinal direction
Figure 1.5: Intensity and phase profiles of Bessel modes with different orders. OAM order ℓ determines both
the order of the Bessel beam and the azimuthal phase change. The radial wavenumber k
r
determines the
radial ring spacings in the intensity profile. The longitudinal wavenumber k
z
can be used to determine the
phase velocity of the Bessel beam along the longitudinal direction.
4
In addition, Bessel beams, as another type of solution to the Helmholtz equation [20, 21, 22], can also
carry OAM as shown in Fig. 1.5. The electrical field of an ideal Bessel mode follows a Bessel function in the
radial direction and can have a phase change in the azimuthal direction [13, 21, 22],
E(r,θ,z )=E
0
J
ℓ
(k
r
r)exp[ik
z
z]exp[iℓθ ] (1.2)
where J
ℓ
is the ℓ-th order Bessel function of the first kind, k
z
and k
r
are the longitudinal and transverse
wave number, respectively. Higher-order (|ℓ| > 0) Bessel beams have helical phase fronts that carry OAM.
The transverse wavenumber k
r
determines the radial ring spacings in the intensity profile. Importantly, the
longitudinalwavenumberk
z
, whichisrelatedtok
r
, canbeusedtodeterminethephasevelocityoftheBessel
beamalongthelongitudinaldirection(i.e., beampropagationdirection). Suchpropertycouldbepotentially
utilized for optical ranging, shown in Chapter 4.
1.2 Free-space Optical Beams through Turbulent Medium
In a free-space environment, temperature fluctuation and air current in a turbulent atmosphere can induce
a dynamic change of the refractive index distribution [23, 24, 25, 26]. When an optical beam propagates
through such turbulent medium, the refractive index changes could result in random phase distortion on
the unique spatial structure of the beam (either carrying OAM or not). After beam propagation, both the
intensity and phase profiles of the received beam can be distorted. Such distortion could induce random
power coupling from the transmitted mode to other modes (both ℓ and p mode) as shown in Fig.1.6. This
could potentially cause signal degradation in free-space optical (FSO) communication links. The turbulence
mitigation approaches for FSO links will be shown in Chapter 3.
1.3 OAM-based Communication Links
Data communication capacity needs have been increasing dramatically, presenting new challenges to optical
communicationsystemsnowadays. Importantly,differentapproacheshavebeenusedtoincreasethecapacity
for optical communications. One of the techniques, known as space division multiplexing (SDM), is based
5
Intensity
1
0
-π
+π
Phase
-π
+π
1
0
Intensity Phase

!

!

%

%

,

!

!

%

%

,

Single mode
Modal power coupling
Transmitted beam
Received beam
Atmospheric
turbulence
beam cross section
beam cross section
Figure 1.6: Atmospheric turbulence effects on a free-space beam.
on the simultaneous transmission of multiple independent data-carrying beams [27, 28, 29]. As a subset of
SDM, mode division multiplexing (MDM) utilizes unique spatial modes from an orthogonal modal basis set.
Suchspatialorthogonality(OAM-multiplexedlinkasanexample)minimizescrosstalkamongthemodesand
enables efficient multiplexing at the transmitter, co-propagation of coaxial optical beams, and low-crosstalk
demultiplexing at the receiver [29] as shown in Fig. 1.7.
Muxed OAM beams
OAM mode
generation 1
Mode Mux
OAM mode
generation n
...
Transmitter
OAM mode
detection 1
Data 1
OAM mode
generation n
...
Mode DeMux
Data n
...
Data 1
Data n
...
-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
[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
Intensity
Gaussian
Intensity Phase
OAM 1
OAM n
Data 1
Data n
...
OAM 1
OAM n
...
[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
Receiver
Intensity
Gaussian
...
Figure1.7: ConceptofOAM-multiplexedlink. Multipleindependentdata-carryingOAMbeamscanbemul-
tiplexed, spatially copropagate, and be demultiplexed with little crosstalk, thereby multiplying the system’s
data capacity.
6
1.4 Underwater Optical Ranging
In unmanned underwater vehicles and underwater sensor networks, underwater ranging (i.e., z distance
measurement of underwater objects) is of increasing importance [30]. Laser-based ranging techniques offer
the potential of high resolution, and high speed [31, 32, 33, 34]. However, the challenging underwater
environments could limit the performance of the optical ranging system [35, 36, 37]. Specifically, (a) the
dynamic scattering particles could distort the optical beam in both time and space, which limits ranging
resolutionandthemaximumrangingdistance[35],and(b)theturbulencecouldfurtherdistortthewavefront
of the optical beam and thus affect the ranging resolution [35].
1.5 Optical Signal Processing
Optical signal processing (OSP) refers to various techniques that operate on optical data signals [38, 39, 40].
OSP techniques could operate on high-speed optical data at the line rate and avoid optical-to-electrical-to-
optical (OEO) conversion, as shown in Fig. 1.8. There is a broad range of OSP functions which include
but are not limited to wavelength conversion, multicasting, equalization, optical regeneration, correlation,
and optical logic gates (e.g., NOT, AND, OR and XOR) [40, 41, 42]. One potential building block among
thoseOSPfunctionsistheopticalhalfadderwhichtakestwodigitalopticalinputsandgeneratestwodigital
optical outputs (i.e., Sum and Carry). Such work will be shown in Chapter 5.
Optical signal processing
Input
Output
t t
O/E E/O
Electrical signal
processing
Potential advantages of optical
signal processing:
q Avoid O-E-O conversion
q Multiple dimensions (amplitude, phase,
time, wavelength, polarization)
q Processing at line rate
Figure 1.8: Potential advantages of optical signal processing.
1.6 Digital Modulation Formats
In general, digital data signals can be modulated on the amplitude and phase of the optical wave in time
domainasshowninFig. 1.9. Foramplitudemodulation,thebitsinthedatastreamsaremappedtomultiple
7
0 1
Amplitude and Phase Modulation
Amplitude Modulation
Phase Modulation
00 01
10 11
1111 1110 1101 1100
OOK
0 1 1 0 1 0
01 10 00 11
QPSK
011
0
001
1
16-QAM
A
ref
A
error
In-phase (I)
Quadrature (Q)
φ
E = A cos (2 πft + φ)
(a)
(b)
Constellation and error vector
1011 1010 1001 1000
0111 0110 0101 0100
0011 0010 0001 0000
Figure 1.9: (a) The data signal can be modulated on the amplitude and/or phase of an optical wave. (e.g.,
on-off keying (OOK), quadrature phase shift keying (QPSK), and 16-quadrature amplitude modulation (16-
QAM)). (b) The constellation and the error vector of a QPSK signal.
amplitudelevelsoftheopticalwave. Forexample, anon-offkeying(OOK)signalhastwopossibleamplitude
levels representing the bit ”0” and ”1”. Since only a single photodiode is required at the receiver to recover
the amplitude information (intensity modulated/direct detection (IM/DD)), such modulation is usually
considered to have a low cost and simple implementation [43, 44]. For the phase modulation, the bits are
mapped to the temporal phase, and the amplitude remains constant. As an example, the quadrature phase
shift keying (QPSK) has four possible phase levels, and one QPSK symbol can carry two bits. In addition,
theamplitudeandphasemodulationcanbeutilizedsimultaneouslytoincreasethenumberofbitscarriedby
onesymbol. Asanexample,the16-quadrature-amplitude-modulation(16-QAM)has16possibilitiesmapped
on the in-phase and quadrature amplitude axes encoding four bits of information. Unlike the amplitude-
modulated signals, coherent detection is often used at the receiver to extract the phase information when
the temporal phase is also encoded with data [45]. In a coherent receiver, the received signal is sent to a 90
◦ hybrid along with a continuous-wave (CW) local oscillator (LO) laser and detected by balanced photodiodes
[45].
8
The quality of the received signal can be characterized by the bit error rate (BER), which is defined as
theratiobetweenthenumberofbiterrorsandthetotalnumberofthereceivedbits[46]. Alternatively, error
vector magnitude (EVM) can be used to determine the quality of the received signal [46]. As shown in Fig.
1.9(b), the received symbols are represented by the points on the constellation according to their amplitudes
and temporal phases. Due to the noise and distortions during the transmission, the received symbol may
deviate from the transmitted symbol, resulting in an error vector A
error
. The EVM is calculated by the ratio
between the mean root square of the error vectors A
error
and the reference vector A
ref
as follows [46],
EVM (%)=
q
1
N
P
N
i=0
|A
error,i
|
2
|A
ref
|
× 100% (1.3)
1.7 Thesis Outline
This thesis will mainly discuss different tunable and reconfigurable techniques for high-capacity optical com-
munication, high-resolution optical ranging, and high-speed optical signal processing, as shown in Fig. 1.10.
Specifically, Chapter 2 shows designs, numerical simulation, and experimental characterization of tunable
photonics integrated circuits for tunable OAM-carrying beam generation in optical communication systems.
Chapter 3 discusses turbulence-resilient free-space optical communication links utilizing a photodetector ar-
ray as well as free-space OAM-multiplexed links with turbulence mitigation using a single multi-plane light
convertor device. Chapter 4 shows the experimental demonstration of high-resolution optical underwater
ranging using a single structured beam. Chapter 5 shows the experimental implementation of a phase-
encoded optical half adder.
9
Optical Communications,
Optical Ranging and Optical
Signal Processing using
Tunable and Reconfigurable
Technologies
Rx Tx
Free-space optical communications
(Chapter 3)
Optical half adder
(Chapter 5)
Photonic integrated circuits
(Chapter 2)
Optical
half
adder
Outputs Inputs
q LG beams
generation with
both tunable ℓ
and orders
Tunable PICs for
OAM-based
communication
Underwater optical ranging
(Chapter 4)
q Optical ranging through underwater
scattering using structured beam
with OAM-carrying Bessel modes
Tx/Rx
z
012320...
012310...
001100...
020230...
Carry
Sum
A
B
q Optical half adder for 4-ary
phase-encoded channels
q OAM beams
generation and
detection with a
tunable ℓ order
q Single channel: turbulence-resilient
FSO link using PD array for
bandwidth enhancement
q Multiple channels: simultaneous
turbulence mitigation and OAM
channel demultiplexing
Turbulence
Figure 1.10: Overview of the tunable and reconfigurable technologies for different applications, including
optical communications, optical ranging, and optical signal processing, in the scope of this dissertation.
10
Chapter 2
Tunable Photonic Integrated Circuits for OAM-based Optical
Communication Links
2.1 Background and Motivation
OverthedecadesoftheWDMcommunicationsystemdeployment, thedevelopedWDMintegrationtechnol-
ogy with lower cost played an essential role. However, the devices utilized in MDM optical communication
experiments were bulky, expensive, and not originally designed for MDM communication. To enable the
future deployment of MDM communication, cost-efficient integration technology would be likely important.
In an OAM-based communication system, there are some desirable features of the integrated OAM devices
including a large number of modes, high mode purity, large bandwidth, fast tunability, and high conversion
efficiency [4].
For OAM-based communication systems, there are some key desirable features for the integrated OAM
devices, including low insertion loss, fast tunability, a large number of modes, efficient mode conversion,
and wide wavelength range. There have been various efforts on the integrated devices for OAM generation,
(de)multiplexing, and detection [10, 11, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57]. Different designs of
photonic integrated circuits have been employed in OAM-based communication links, including (a) ring-
resonator-based OAM emitters/receivers embedding angular grating structures with a periodic modulation
of the refractive index in the azimuthal direction, which supports OAM beams with tunable OAM orders
[47, 48, 49]; (b) circular-phase-array OAM emitters/receivers with multiple circularly distributed optical
11
antennas to generate/receive multiple OAM beams [50, 51, 52]; and (c) subwavelength pixel-array-based
OAM antenna with a relatively compact and specifically designed metasurface to achieve broadband OAM
generation/detection [53, 54, 58].
Tunable photonic integrated
circuits for OAM-based
optical communications
Pixel-array-based OAM
emitter/receiver
Concentric
uniform circular array (UCA)
OAM beams generation/detection
with a tunable ℓ order
LG beams generation with
both tunable ℓ and orders
Figure 2.1: Overview of the tunable photonic integrated circuits for OAM-based optical communications
discussed in this dissertation.
In this section, two types of integrated structures will be discussed as shown in Fig. 2.1 including: (a) a
pixel-array-basedOAMemitter/receiver, whichmainlyutilizesspecificallydesignedpixelarraystructures, is
usedforOAMbeamsgeneration/detectionwithatunable ℓorder(Sec. 2.2-Sec. 2.7)[58,59,60,61,62,63];
(b) a concentric uniform circular array, which consists of multiple surface grating couplers, is utilized to
generate LG beams with tunable ℓ and p orders (Sec. 2.8 - Sec. 2.10) [64].
12
+
0×∆
1×∆
2×∆
3×∆
Free-space
OAM output
Fundamental
TE mode input
1×∆
2×∆
3×∆
x
y
(b)
Input
0×∆
(a)
4µm
Si SiO
2
0.1µm
Input Input
Input
Output
x
y
z
OAM mode convertor
Shape,
combine
and emit
(c)
Phase tuning
Figure 2.2: Concept of (a) the phase-dependent OAM beam generation using the pixel-array structure.
The OAM order of the output beam is dependent on the phase delay of four inputs. (b) Top view of the
pixel-array structure of the silicon-on-insulator (SOI) OAM emitter supporting the OAM tunable range
ℓ={− 2,− 1,+1,+2} (c) 3D view of the light emission in the vertical direction.
2.2 SimulationofPixel-array-basedModeConvertorforGenerating
an OAM Beam with a Tunable OAM Order
Figure 2.2 shows the concept of generating OAM beams using a pixel-array structure. As shown in Fig.
2.2(a), four inputs carrying fundamental waveguide TE modes (TE00) with tunable phase delays are fed
to the OAM mode convertor with the designed pixel-array structure for phase-dependent OAM generation.
Figure2.2(b)showsanexampleofthedesignedstructure, whichshapesandcombinesthefourinputs, where
the k-th input carries a tunable phase delay (k− 1)∆ φ. As shown in Fig. 2.2(c), the combined field with a
helical phasefront is vertically emitted. The phase-dependent generation of OAM beams using a pixel-array
structure can be divided into 3 steps: (i) For the k-th input (k={1,2,3,4}), the in-plane propagating TE00
mode is scattered by the pixel array and vertically emitted into free space; meanwhile, the spatial phase of
the emitted field is modulated due to the spatial-variant refractive index of the pixel array [65]; therefore, it
13
(b1) (b5)
1×Δ
(b2) (b6)
2×Δ
(b3) (b7)
3×Δ
(b4)
(b8)
Δ=0
Δ=
Δ=

2
(c1)
(c3)
(c4)
(c5)
(c7)
(c8)
(c2) (c6)
Δ=−

2
+

∡

"

#

$

%
0×Δ
(b) Combined fields

with a phase delay
Combine
(a) Individual fields

from k-th input

)

*+/#

+/#

+

∡
0
-20.3
-20.7
-17.4
-20.3
0
-22.3
-26.5
-20.7
-22.3
0
-21.2
-17.4
-26.5
-21.2
0
-35
-30
-25
-20
-15
-10
-5
0

"

#

$

%

"

#

$

%
(c1)
0
-22.4
-23.1
-20.3
-22.4
0
-37.3
-24.3
-23.1
-37.3
0
-24.9
-20.3
-24.3
-24.9
0
-35
-30
-25
-20
-15
-10
-5
0
0
-20.3
-20.7
-17.4
-20.3
0
-22.3
-26.5
-20.7
-22.3
0
-21.2
-17.4
-26.5
-21.2
0
-25
-20
-15
-10
-5
0

)

*+/#

+/#

+

)

*+/#

+/#

+
0dB
-40dB
(c2)
0
-20.3
-20.7
-17.4
-20.3
0
-22.3
-26.5
-20.7
-22.3
0
-21.2
-17.4
-26.5
-21.2
0
-25
-20
-15
-10
-5
0
1
0

−
Figure 2.3: Simulated intensity and phase profiles of the individual fields generated by the (a) k-th input.
and(b)thecombinedfieldswithdifferentphasedelays. Pairwiseoverlapintegralof(c1)theindividualfields
and (c2) the combined fields.
evolves into an individual electric field E
k
(k=1,2,3,4) after free-space propagation. The simulated intensity
and phase profiles of E
k
are shown in Fig. 2.3. Moreover, the simulation results show that each electric
field E
k
is spatially orthogonal to the other electric fields. (ii) When feeding four inputs, where each k-th
input has a phase delay (k− 1)∆ φ, the output is a coherent combination of four electric fields E
k
, which is
denoted as follows,
E
∆ φ
=E
1
+E
2
e
j∆ φ
+E
3
e
j2∆ φ
+E
4
e
j4∆ φ
(2.1)
Eq. 2.1 indicates that the electric field depends on the value of ∆ φ. (iii) By judiciously selecting the values
of ∆ φ, it is possible to transform a set of orthogonal electric fields of E
k
(k ={1,2,3,4}), into another set of
orthogonal ones. Specifically, by designing the pixel-array structure, one transformation function could be
tailoredtoshapetheelectricfieldsintoasetoforthogonalOAMbeamswithdifferentorders. Intheexample
shown in Fig. xx, the combined field is shaped to be an OAM beam of OAM order ℓ=− 2,− 1,+1,+2, when
we select the value of ∆ φ as 0,− π/ 2,π/ 2,π , respectively. In general, the output fields could remain their
mutual orthogonality if the inputs are orthogonal to each other and all the inputs transmit through a linear
14
structure/system. Inoursimulations,thefourinputsfromthefourwaveguidesarespatiallyseparatedsothat
they are orthogonal, and the pixel-array structure has a linear transformation function. Such orthogonality
might be maintained if we (i) change the number of inputs while keeping them to be orthogonal to each
other; and (ii) vary the pixel array structure while keeping it as a linear system.
In order to tailor the transformation function between the phase delay ∆ φ and the OAM order ℓ, the
pixel-arraystructureisdesignedusingfinite-differencetime-domain(FDTD)simulationandthedirectbinary
search (DBS) algorithm [29]. In the FDTD simulation, the pixel-array structure is composed of 1600 sili-
con/silica pixels, each with a size of 100× 100 nm. The thickness of the silicon waveguides and silicon/silica
pixels are all 220 nm on top of the 2-µ m buried oxide layer. A 3-µ m SiO
2
layer is added on top of the
structure. The electric field monitor is placed at 2.5 µ m above the top of the silicon layer. The electric field
with polarization along 45
◦ of the x-axis and the center wavelength of 1550 nm is calculated numerically.
Associated with the FDTD simulation, the DBS algorithm [65] is iteratively applied to design the structure.
During each iteration, the performance is evaluated by the power difference between the designed mode and
theothermodesinthedesignedtunablerange, whichisdenotedas[66],
P
ℓ,k
(− 1
δ ℓk
|
RR
E
out
ℓ
E
OAM
∗ k
dxdy|
2
),
where E
out
ℓ
is the normalized output simulated field corresponding to the designed OAM order of ℓ, E
OAM
∗ k
is the normalized conjugated ideal field with OAM order of k, and δ ℓk
is the Kronecker delta function. It
should be noted that all the simulation results are obtained with the commercial software of Lumerical
FDTD solutions. In our simulation, it takes ∼ 107, ∼ 214, ∼ 320, ∼ 427 hours for designing structures 1-4,
respectively, on the workstation with dual Intel Xeon E5-2667 CPU. Using the same initial pattern and
iteration number, four different transformation functions between the phase delays and the OAM tunable
rangearetailoredasfollows: ∆ φ={− π/ 2}forℓ={-1},∆ φ={− π/ 2,π/ 2}forℓ={-1,+1},∆ φ={− π/ 2,0,π/ 2}for
ℓ={-1,0,+1}, and ∆ φ={− π/ 2,0,π/ 2,π } for ℓ={-1,-2,+1,+2}. The tunable range of our structures might be
increased by increasing the number of inputs in order to still maintain the orthogonality of the output fields
[60]. However, this could produce additional challenges since more inputs might induce more accumulated
phase error between the inputs.
The performance of the pixel-array structures for generating an OAM beam within different tunable
rangesisshowninFig. 2.4. Figure2.4(a)showsfourdesignedOAMmodeconvertorswithdifferentstructures
15
(a)
{-1,+1} {-1,0,+1} {-2,-1,+1,+2} {-1}
-
1
+
1
+
1
+
1
-
1
-
1
-
1
0
+
2
-
2
(b)
1
0.8
0.6
0.4
0.2
0
Mode purity
Tunable range
Structure 3 Structure 2 Structure 1 Structure 4
(c)
ℓ=−1
Tunable range
increases

0 −/8 −/4 −3/8 −/2
Structure 1
Structure 4
Structure 2
Structure 3
1
0.8
0.6
0.4
0.2
0
Mode purity
Figure 2.4: (a) Designed structures for OAM emission. (b) Mode purity of the generated OAM beams for
structures 1–4 with different OAM tunable ranges. (c) Mode purity of the generated OAM beam ℓ= -1 as a
function of phase delay ∆ φ for structures 1–4.
to support the transformation functions with different tunable ranges. Figure 2.4(b) shows the mode purity
of the generated OAM beams for structures 1–4. The mode purity of the designed OAM mode is calculated
by the overlap integral of the generated field with the ideal OAM field. For different structures with tunable
ranges increasing from 1 to 4, the mode purity of the designed OAM modes tends to decrease. For instance,
the mode purity of OAM mode ℓ=-1 is 91%, 89%, 82%, and 75% for structures 1–4, respectively. By tuning
the phase delay from –π /2 to 0, the mode purity of OAM mode ℓ=-1 decreases for all four structures, as
shown in Fig. 2.4(c). To investigate the phase dependence of the OAM beam generation, the phase delay
is tuned from –π /2 to 0. As shown in Fig. 2.4(c), the mode purity of OAM mode ℓ=-1 decreases for all
16
four structures. We note that for the structure which is not tunable (i.e., structure 1 only supports ℓ=-
1), changing the phase delay will still affect the mode purity of the generated OAM beam. Furthermore,
the phase-dependent mode purity tends to become lower when the tunable range increases. The trade-off
between the tunable range and the mode purity might be explained as follows: when the tunable range
increases, thepixel-arraystructureneedstosupportmoreOAMbeams; andwhengeneratinganOAMbeam
withaspecificorder,theremightbemorepowerleakagefromthedesignedOAMbeamtootherOAMbeams
with other OAM orders, and thus the mode purity of the designed OAM order decreases.
Emission efficiency for structure 4
Emission efficiency (dB)
Wavelength (µm)
1.4 1.45 1.5 1.55 1.60 1.65 1.7
-30
-25
-20
-15
-10
-5
ℓ=−
ℓ=+
ℓ=−
ℓ=+
1.4 1.45 1.5 1.55 1.60 1.65 1.7
-30
-25
-20
-15
-10
-5
3-dB bandwidth of emission efficiency for structure 1-4
Bandwidth (nm)
-5
-10
-15
-20
1.45 1.55 1.60 1.50 1.65
Structure
1
(a)
(b)
Structure
3
Structure
2
Structure
4
3-dB bandwidth: ~122 nm
Figure 2.5: Simulated emission efficiency of structure 4 over the wavelengths ranging from 1.45 to 1.65 µm.
To investigate the bandwidth performance of the pixel-array structure, emission efficiency at different
wavelengths is calculated. The emission efficiency is defined as the power ratio between the power of the
output mode and the total input. Figure 2.5(a) shows the emission efficiency for the OAM mode convertor
(structure 4) when generating different OAM beams at the wavelengths ranging from 1.45 µ m to 1.65 µ m.
The 3-dB bandwidth for structure 4 is∼ 122 nm, which is mainly limited by the bandwidth when generating
OAM ℓ=± 2 . Furthermore, the 3-dB bandwidths for different structures are compared as shown in Fig.
17
2.5(b). When comparing structure 3 (ℓ=± 1) to structure 4 (ℓ =± 2), the bandwidth decreases from 273 nm
to122nm. Thisdecreaseislikelyduetostructure4havinganadditional2π phaseshiftwhichwouldrequire
a longer light propagation inside the pixel array. This longer path tends to introduce a higher wavelength-
dependent phase error and decreased bandwidth. Generally, the phase delay induced by the phase shifter
might depend on wavelength [67]. Such wavelength-dependent phase delay at the input is not considered
in the simulation. The wavelength dependence of the phase delay might limit the operating bandwidth [51]
which could possibly be mitigated by using the broadband phase shifter [67]. Furthermore, the emission
efficiency might be improved by adding a substrate reflector which might require extra fabrication efforts.
Utilizing the phase-dependent OAM transformation function of the designed OAM mode convertor,
multiple independent coaxial OAM beams can be generated by simultaneously feeding multiple independent
beams, suchthateachbeamhasitsown∆ φvalueforthefourinputs. Onepotentialapproachisusinga4× 4
coupler as shown in Fig. 2.6(a). Each input at each port of the coupler can be split into four outputs with
equal amplitudes and different fixed phase delays, denoted as ∆ φ
1
. The simulated phase delay ∆ φ
1
when
feeding each input port is shown in the inset table of Fig. 2.6(a). Then, a tunable phase delay (k− 1)∆ φ
2
is added to k-th connecting waveguide between the coupler and the mode convertor. Both the fixed phase
delay ∆ φ
1
and the tunable phase delay ∆ φ
2
contribute to the resulting phase delay ∆ φ = ∆ φ
1
+∆ φ
2
.
Different phase-dependent OAM beams can be generated by feeding light into different input ports. When
multiple ports are fed simultaneously, multiple coaxial OAM beams can be generated. Moreover, the OAM
orders of the multiple coaxial OAM beams can be tuned by tuning the phase delay ∆ φ
2
. The performance
of the pixel-array structures for generating multiple OAM beams is explored. The crosstalk of port j is
defined as XT
j
=
P
k=K,k̸=j
|
RR
E
out
k
E
OAM
∗ j
dxdy|
2
/|
RR
E
out
j
E
OAM
∗ j
dxdy|
2
where E
out
k
is the output field
byfeedingportk. Figure2.6(b)showsthatthecalculatedcrosstalkperformanceofstructure4forgenerating
multipleOAMbeamswhentuningthephasedelay∆ φ
2
from–3π /4to5π /4atthecenterwavelengthof1550
nm. Furthermore, Figure 2.6(c) shows that the calculated maximum crosstalk of multiple generated beams
when selecting the phase delay ∆ φ
2
from a set of{-π /2,0,π /2,π } within the C-band for structures 2–4. For
structure4, themaximumintermodalcrosstalkincreasesfrom–16.8to–13.2dBwhenthenumberofcoaxial
OAM beams increases from 2 to 4. When generating two coaxial OAM beams, the maximum intermodal
18
(a)
OAM
mode
convertor
Port 1
Port 2
Port 3
Port 4
Port# ∆

1 −/2
2 /2
3 0
4
4×4
coupler
0×∆
"
1×∆
"
2×∆
"
3×∆
"
0×∆
#
1×∆
#
2×∆
#
3×∆
#
Phase tuning
(b)
Intermodal crosstalk of 2-4 beams for structure 4
2 coaxial beams
(port 1,2)
4 coaxial beams
(port 1,2,3,4)
3 coaxial beams
(port 1,2,3)
Port #
Number of coaxial beams
2 2 3 2 2 3 4 2
1,2 1,3 1,2 1,2,3 1,3 1,2 1,2,3 1,2,3,4
Maximum crosstalk within the C-band for structures 2-4
Structure
2
Structure
3
Structure
4
-10
-15
-30
-20
-25
Maximum crosstalk (dB)
(c)
Δ
#
−/2
0 /2
Δ
#
−/2 0 /2
Δ
#
−/2 0 /2
-50
-10
-20
-30
-40
Crosstalk (dB)
ℓ=+ ℓ=− ℓ=+ ℓ=−
...
Figure 2.6: (a) Concept of generating multiple coaxial OAM beams. The inset table shows the fixed phase
delays induced by different ports of the 4 × 4 coupler. (b) Intermodal crosstalk of 2–4 coaxial OAM beams
when tuning the phase delay ∆ φ
2
for structure 4 at the wavelength of 1550 nm. (c) Maximum intermodal
crosstalk within the C-band (from 1530 to 1565 nm) for structures 2–4.
crosstalkwithintheC-bandincreasesfrom–23.7to–16.1dBasthetunablerangeincreasesfrom2to4. The
results show that the structure with the same area but a larger tunable range for generating multiple OAM
beams tends to have higher intermodal crosstalk. The trade-off between tunable range and crosstalk might
be due to the issue that when the tunable range increases, the power leakage from other OAM beams to the
designedOAMtendstoincreasewhen(i)beamswithhigherorders(i.e.,ℓ=± 2)havelowermodepurity, and
(ii) the number of generated OAM beams increases. In order to increase the mode purity, reduce crosstalk,
19
and achieve a higher mode order, three approaches can be considered: (i) increase the emission area [53], (ii)
decrease the pixel size [53], and (iii) utilize more efficient optimization algorithms [53, 65]; we note that all
three of these approaches would likely require more simulation time and/or increased fabrication resolution.
2.3 ConceptofTunablePixel-array-basedOAMEmitters/Receivers
Output
x
y
z
x
y
Port 3
Port 2
Port 1
x
y
Input 200µm
Heaters
x
y
3-to-4 coupler
0×(∆
!
)
1×(∆
!
)
2×(∆
!
)
3×(∆
!
)
Mode convertor
Phase
controllers

OAM
/2 +1
−/2 -1
Port
#

1 −/2
2 0
3 /2
0×(∆
!
+ ∆
"
)
1×(∆
!
+ ∆
"
)
2×(∆
!
+ ∆
"
)
3×(∆
!
+ ∆
"
)
Fundamental
waveguide
mode input
Free-space
OAM output
(a)
(b) (c) (d)
Figure 2.7: (a) Concept of the pixel-array-based OAM emitter. The emitter is composed of a 3-to-4 coupler,
four tunable phase controllers, and a mode convertor. The OAM order of the output beam is dependent
on the phase delay of waveguides. This phase delay is related to both the phase delay and induced by the
3-to-4couplerandthetunablephasecontrollers, respectively. (b)SEMimageofthepixel-array-based3-to-4
coupler. (c) Integrated thermal phase controllers. (d) SEM image of the pixel-array-based mode convertor.
TheconceptoftunableOAMgenerationbyapixel-array-basedOAMemitterisshowninFig. 2.7(a). The
3-to-4couplerisdesignedtointroduceaspecificphasedelay( k− 1)∆ φ
1
tothefundamentalwaveguidemode
inthek-thwaveguideasshowninFig. 2.7(b). Additionally,theintegratedthermalphasecontrollersareused
to introduce additional phase delay (k− 1)∆ φ
2
in the k-th waveguide. Subsequently, the phase-dependent
OAMgenerationusingthepixel-array-basedmodeconvertorworksasfollows[58,60],(i)in-planepropagating
waveguide modes from the four different waveguides are vertically coupled into free space and coherently
combined, (ii) the spatial phase of each emitted field is individually modulated by the pixel-array structure;
(iii) as the input fields from the four waveguides are spatially separated, the corresponding output fields are
mutually orthogonal; (iv) by judiciously selecting the values of relative phase delay ∆ φ = ∆ φ
1
+∆ φ
2
, the
spatial profile of the combined field can be tailored [60, 58]; (v) specifically, by designing the pixel-array
20
0×∆
!
1×∆
!
2×∆
!
3×∆
!
4-to-3 coupler
0×(∆
!
+ ∆
"
)
1×(∆
!
+ ∆
"
)
2×(∆
!
+ ∆
"
)
3×(∆
!
+ ∆
"
)
Mode convertor
Phase
controllers
OAM

-1 /2
+1 −/2

+

Port #
/2 1
0 2
−/2 3
Fundamental
waveguide
mode output
Free-space
OAM input
(a)
Single input
(single OAM beam of
ℓ=−1 or ℓ=+1)
Single output
(fundamental
waveguide mode)
Two inputs
(coaxial OAM beams of
ℓ=−1 and ℓ=+1)
(b1)
From ℓ=−1
From ℓ=+1
(b2)
Tunable
OAM
receiver
Two outputs
(fundamental
waveguide mode)
From ℓ=−1
From ℓ=+1
Bias 1
Tunable
OAM
receiver
OAM
order
OAM
order
Bias 2
Bias 3 Bias 4
OAM
order
Figure 2.8: (a) Concept of the pixel-array-based tunable OAM receiver. The receiver is composed of a mode
converter, tunable phase controllers, and a 4-to-3 coupler. (b1) The OAM receiver can receive a single OAM
beam (OAM -1 or OAM +1) and convert it into a fundamental waveguide mode at one output port. The
targetOAMmodetobereceivedcouldbetunedfromOAM-1toOAM+1. (b2)TheOAMreceivercanalso
demultiplex two coaxial OAM beams (OAM -1 and OAM +1) and convert them to fundamental waveguide
modes at two output ports. The target OAM mode to be received at the corresponding output port could
be changed.
structure, the mode conversion function could be tailored to shape the phase-dependent combined fields into
a set of orthogonal OAM beams with different mode orders as shown in Fig. 2.7(d); and (vi) by further
tuningthe∆ φ
2
withthephasecontrollersshowninFig. 2.7, theOAMorderofthegeneratedbeamcouldbe
tuned. For example, by feeding port 2 (∆ φ
1
= 0) and tuning the phase delay from ∆ φ
2
=-π /2 to ∆ φ
2
=π /2 ,
the OAM order of a single beam could be tuned between ℓ=-1 and ℓ=+1, respectively. Moreover, by feeding
port 1 (∆ φ
1
= -π /2) and port 3 (∆ φ
1
= π /2) of the coupler simultaneously, two multiplexed OAM beams
(ℓ=-1 and +1) could be generated.
Such pixel-array-based OAM emitter can also be used reversely as the OAM receiver (Fig. 2.8(a)). For
convenience, the phase delays induced by the mode convertor and the phase controller are denoted as ∆ φ
1
and ∆ φ
2
, respectively. Utilizing the tunable OAM receiver, different scenarios of OAM receiving could be
achieved as shown in Figure 2.8(b1-b2). When a single OAM beam (ℓ = + 1 or ℓ = -1) is transmitted,
the power of the OAM beams can be received at one of the output ports as shown in Figure 2.8(b1). For
example,toreceivethepowerofOAMbeamℓ=+1atport2,anOAM-dependentphasedelay∆ φ
1
=− π/ 2
is induced by the mode converter and a conjugate phase ∆ φ
2
= π/ 2 is added by the phase controller to
21
match the input phase (∆ φ
1
+∆ φ
2
=0) of the coupler. In addition, Figure 2.8(b2) shows that the tunable
OAM receiver can also demultiplex two coaxial OAM beams (ℓ = -1 and ℓ = + 1), and the power of each
OAM beam can be received at a different output port.
Both pixel-array structures (i.e., coupler and mode convertor) are composed of 1600 silicon/silica pixels,
each with a size of 100× 100 nm. The thickness of the silicon waveguides and silicon/silica pixels are all
220 nm. The width of the waveguides is chosen as 500 nm to support a fundamental waveguide mode.
Silicon-on-insulator wafers of 220-nm device thickness and 2-µ m buffer oxide thickness are used as the base
material for the fabrication. After an initial wafer clean, patterning of the photonic devices is performed
usingtheresistexposedinanelectronbeamlithography(EBL)systemusing100keVbeamenergy. Afterthe
resist development, the pattern is then transferred into the silicon device layer using an inductively coupled
plasma-reactive ion etching (ICP-RIE) process. Subsequently, the remaining resists are then stripped and a
2.2-µ m oxide cladding is deposited using a plasma-enhanced chemical vapor deposition (PECVD) process.
Toimplementthethermo-opticphaseshifters,aresistivemetalheaterisplacedabovethesilicondevicelayer.
It consists of two layers of metal, titanium-tungsten (Ti/W) and Aluminum (Al), and an oxide protection
layer. Thehigh-resistanceTi/Wlayerisusedtoimplementheaterdeviceswhereasthelow-resistanceTiW/Al
bilayerefficientlydeliverstheelectricalpowerfromtheoff-chipprobestotheheaterdevices. Thesetwolayers
arethenpassivatedwithathinoxidelayertoprotecttheheatersfromoxidationdamage. Windowsareetched
through the oxide to access the aluminum probing pads.
2.4 Experimental Characterization of the Tunable Pixel-array-
based OAM PIC
To characterize the OAM beams generated by the PICs, an experimental setup is built as shown in Figure
2.9. A CW laser is amplified and then split into two arms. One is sent to the chip, and the other is sent
to generate a reference Gaussian beam. A fiber array or a lensed fiber is used to couple the light into the
chip. Limited by the fiber-to-fiber spacing of the fiber array, port 2 is fed using lensed fiber, and ports
1/3 are fed using fiber array separately. At the output, the generated beam is coupled by an objective lens
22
and propagates through ∼ 0.5 m of free space. At the receiver, a free-space half-wave plate is used to align
the polarization of the emitted OAM beams with that of the SLM. To measure the OAM modal power
distribution of the generated beam, the optical power is collected and measured in the fiber by loading the
spiral phase patterns on the SLM.
Objective
lens
chip
Lensed
fiber
Camera
Flip
mirror SLM
Mirror
Power
measurement
Collimator
Tunable CW
laser
EDFA
PC
HWP
Reference
beam
Col.
PC
90/10
coupler
10%
90%
BS
Bias control
...
Figure2.9: Experimentalsetupoffree-spacebeamcharacterizationgeneratedbythepixel-array-basedOAM
emitter. EDFA: Erbium-doped fiber amplifier. Col: Collimator. BS: beam splitter. HWP: half-wave plate.
Bias voltages=
(0.2V, 0.1V, 1.8V, 2.3V)
Bias voltages=
(0.4V, 3.3V, 2.5V, 0.8V)
OAM order OAM order
Normalized
power (dB)
~12
dB ~17 dB
From
port 2
From
port 2
(a1) (b1) (a2) (b2) ℓ=−1 ℓ=−1 ℓ=+1 ℓ=+1
Beam profile Interferogram Beam profile Interferogram
(a3) (b3)
From port 2
Normalized
power (dB)
Figure 2.10: Measured (a1-b1) beam profiles, (a2-b2) interferogram, and (a3-b3) modal power distribution
of a single beam when port 2 is fed.
The tunability of the pixel-array-based OAM emitter is experimentally characterized. Applying different
bias voltages and selecting port 2 as an input port, the beam profiles and interferogram are shown in Figure
2.10 (a1-a2) and (b1-b2), respectively. The interferogram of the output beam with a coherent Gaussian
23
reference beam, displaying the “twisting” phase front of the output beam which indicates the generation of
the OAM beam. The opposite “twisting” directions indicate that the OAM order is changed by tuning the
phase controllers. In addition, the modal power distribution of the output beam is measured as shown in
Figure 2.10 (a3, b3). Under the two different tuning conditions, the highest power coupled from the desired
modetotheneighboringmodesis <-17dBand<-12dBforOAMbeamsof ℓ=-1andℓ=+1, respectively.
The difference in the power coupling might be due to (i) imperfect phase tuning of the OAM emitter, and
(ii) the misalignment between the transmitter and the receiver.
ℓ=−2
ℓ=−1
ℓ=0
ℓ=+1
ℓ=+2
9.6 nm 9.7 nm
Normalized
received power (dB)
Modal power distribution vs wavelength
Wavelength (nm)
ℓ=−1
ℓ=+1
Wavelength (nm)
(a) (b)
Figure 2.11: Measured modal power distribution at different wavelengths of a single beam with a tunable
OAM order of (a) OAM -1 or (b) OAM +1. As proof of concept, port 2 is selected as the input port.
By varying the input wavelength from 1540 to 1565 nm, the bandwidth performance of the OAM gener-
ation is measured. The measured 3-dB bandwidth of the desired mode is 9 nm ( 1 THz) as shown in Figure
2.11. There could be several factors limiting the bandwidth of the PIC, including the wavelength-dependent
amplitude and phase error induced by the fabrication error as well as the length mismatch of the connecting
waveguides between the coupler and the emitter.
The mode multiplexing function of the pixel-array-based OAM emitter is further tested by selecting port
1 and port 3 as input ports. Figure 2.12(a) shows the measured modal power distribution of the beams
generated by the pixel-array-based OAM emitter. The intermodal crosstalk between the two beams is <-15
dB.Bytuningtheappliedvoltages,thecorrespondingOAMorderwhenfeedingport1/3couldalsobetuned
as shown in Figure 2.12(b). Based on the transformation function of the coupler, different OAM orders can
be generated by feeding different ports ( i.e., ports 1 and 3) under the same bias voltage.
24
OAM order OAM order
Normalized
power
Port 1
Port 3
Bias voltages=
(0.1V, 0.3V, 0.4V, 0.8V)
Bias voltages=
(0.2V, 2.5V, 0.5V, 3.1V)
(a) (b)
Figure 2.12: Measured modal power distribution of a single beam when port 1 or port 3 is fed.
Figure 2.13: Measured optical power at different output ports under different bias voltages when a single
OAM beam is transmitted. (a1) Layout of the applied bias voltages on the heaters. (a2-a4) Layout of
receiving power at different output ports. (b) The received optical power at port 1/2/3 when no bias
voltages are applied. (c-f) The received optical power at port 1/2/3. The input optical power is 0 dBm. The
red bars show the received power of the target OAM mode at the specific output port. (g) The applied bias
voltages for different scenarios.
Thepixel-array-basedOAMreceivercanbereverselyutilizedasanOAMreceiverwhichroutesthepower
of the transmitted OAM beam into different output waveguides. Figure 2.13 shows the received power at
different output ports by applying different bias voltages. A single OAM beam with ℓ = -1 or ℓ = + 1 is
25
transmitted and the bias voltages applied to the heaters are varied as shown in Figure 2.13(a1). Figure
2.13(b1-b3) shows the received power at port 1, port 2, and port 3, respectively, when no bias voltages are
applied. The received power of different transmitted OAM modes at each port is relatively low. This could
be due to that the fabrication-induced length mismatch between different waveguides, and thus the resulting
phase errors could degrade the receiving performance. To compensate such phase errors and achieve the
desired phase delay, the bias voltages are optimized as follows: (i) a single OAM beam with the target OAM
modeistransmitted, (ii)theopticalpowerismonitoredatthetargetoutputport, and(iii)fourbiasvoltages
are varied to maximize the received power.
By applying the optimized bias voltages, the received power of a single OAM beam (ℓ = -1 or ℓ = + 1)
at the single output port (i.e., port 2) is maximized. When bias 1 is applied, the OAM order with the peak
received power at port 2 is ℓ = -1 as shown in Figure 2.13(c). When the bias voltages are changed from bias
1 to bias 2, the OAM order with the peak received power at port 2 can be tuned from ℓ = -1 to ℓ = + 1
as shown in Figure 2.13(d). The inter-modal power coupling between ℓ = -1 and ℓ = + 1 is < -14 dB. This
could be potentially due to the field mismatch between the received OAM beam and the target OAM beam.
Moreover, the received power of target OAM mode at port 1 and 3 under the corresponding bias voltages is
relatively low as shown in Figure 2.13(c1, d1, c3, d3). This could be due to that the transformation function
of the 4-to-3 coupler is phase-dependent, and thus the power coupled to port 1 and port 3 is relatively low.
To enable the OAM mode demultiplexing, optimized bias voltages are applied and port 1/3 are selected
as the output port. Figure 2.13(e) shows that the OAM order with the peak received power at the output
port 1 and the output port 3 is ℓ = -1 and ℓ = + 1 , respectively, by applying bias 3. This indicates that
(i) by applying the given bias voltages, the phase delay ∆ φ
1
+∆ φ
2
= π/ 2 and − π/ 2 is induced when the
OAM beam of ℓ = -1 and ℓ = + 1 are transmitted, respectively, and thus (ii) based on the phase-dependent
transformation function of the coupler, the power of OAM ℓ = -1 and ℓ = + 1 is coupled to the output
port 1 and output port 3, respectively. When the bias voltages are changed to bias 4, the power of the
corresponding OAM beam is coupled at the other port as shown in Figure 2.13(f). Specifically, the OAM
order with the peak received power at port 1 and port 3 are tuned to ℓ = +1 and ℓ = -1, respectively. This
is due to that an additional phase delay (k− 1)π is induced on the k-th waveguide and thus, the resulting
26
phase delay between the neighboring waveguides is tuned to be − π/ 2 and π/ 2 when the OAM ℓ = -1 and ℓ
= +1 are transmitted, respectively. The applied bias voltages for the above-mentioned scenarios are shown
in Figure 2.13(g).

Target pol.
Input pol.
0 50 100 150
-20
-15
-10
-5
0
0 50 100 150
-20
-15
-10
-5
0
Normalized received
power (dB)
Normalized received
power (dB)
Port 2
Port 2
0 50 100 150
-20
-15
-10
-5
0
0
0.5
1
data1
data2
OAM -1 transmitted
OAM +1 transmitted
0 50 100 150
-20
-15
-10
-5
0
0
0.5
1
data1
data2
OAM -1 transmitted
OAM +1 transmitted
Bias voltages = 0.2V, 3.2V, 2.5V, 1.2V Bias voltages = 0.2V, 0.8V, 1.8V, 2.7V
Polarization mismatch angle (degree)
(a)
(b1) (b2)
Polarization mismatch angle (degree)
increases
Phase delay error at the
four output ports increases
Power coupled to the four
ports decreases
Power loss of the
received target
mode increases
Crosstalk from the
neighboring mode
increases
Figure 2.14: (a) Concept of the polarization-induced power loss and inter-modal crosstalk for pixel-array-
based OAM receiver. (b1-b2) Normalized received power of a single OAM beam at a different polarization
mismatch angle when the target mode of the OAM receiver is tuned from (b) OAM -1 and (c) OAM +1.
Furthermore, the polarization sensitivity of the pixel-array-based OAM receiver is measured as shown
in Figure 2.14(a). The results show that the increasing difference between the input polarization and the
target polarization could contribute to both the power loss and intermodal crosstalk. As proof of concept,
the OAM receiver is tuned to receive the power from a single OAM beam (ℓ = -1 or ℓ = + 1), and the
received power is collected at port 2. The received power is normalized by the input power of the target
mode when the polarization is aligned with the target polarization. Figure 2.14(b1) shows that the input
polarization changes from the target polarization to the orthogonal polarization (i.e., polarization mismatch
angle θ changes from 0 to 90 degrees), the normalized received power of the target mode (ℓ = -1) tends to
decrease by ¡ 12 dB. Similar trends could be observed when the target OAM mode is tuned from ℓ = -1 to ℓ
= + 1 as shown in Figure 2.14(b2). As the OAM receiver is designed to receive the OAM beam at a specific
polarization, the polarization mismatch could lead to the decreased power coupled to the four waveguide
ports and thus the increased power loss of the received target mode. In addition, when the polarization
mismatch increases (i.e., θ changes to ∼ 90 degrees), the received power of the undesired mode increases.
27
Thiscouldbeduetothattheincreasedcomponentsoftheundesiredpolarizationcouldinducerandomphase
error to the four output ports and thus the intermodal crosstalk tends to increase.
Tx: ℓ=−1, Rx: ℓ=+1
Δ(µm)
Tx: ℓ=+1,Rx: ℓ=−1
Δ(µm)
Δ (µm)
Δ(µm)
Phase
Intensity
Aligned
receiver
Off-axis receiver
No displacement
Large aperture
Displacement
Limited-size
aperture
Off-axis
reciever
Power

OAM order
Power

" # $ %
OAM order
Aligned
receiver
(a) (b)
Objective lens
Chip (OAM receiver)
Misaligned
incident beam
Tx: ℓ=−1, Rx: ℓ=−1 Tx: ℓ=+1,Rx: ℓ=+1
Normalized received power Intermodal crosstalk
-5 dB
-20 dB
0 dB
-7 dB
Δ (µm)
Δ(µm)
Δ(µm)
Δ(µm)
-4 -3 -2 -1 0 +1 +2 +3 +4
-30
-25
-20
-15
-10
-5
0
Incident
beam
Δ,Δ =0,0
A single OAM beam with a lateral displacement is sent
and the TRIP-based OAM receiver is tuned to receive
ℓ=−1
Normalized
received power
<-12 dB
170 -170
-170
170
170 -170
-170
170
170 -170
-170
170
170 -170
-170
170
(c1) (c2)
-4 -3 -2 -1 0 +1 +2 +3 +4
-30
-25
-20
-15
-10
-5
0
Incident
beam
Δ,Δ =−102µm,102µm
-4 -3 -2 -1 0 +1 +2 +3 +4
-30
-25
-20
-15
-10
-5
0
Incident
beam
Δ,Δ =−170µm,170µm
Normalized
received power
~-7 dB
>-5 dB
Transmitted OAM order
~-3 dB
<7 dB
Normalized
received power
Aligned
incident beam
Figure 2.15: (a) Misalignment between transmitter and receiver in an OAM-based link. (b) Measured
received power when a single OAM beam with a lateral displacement. The power spectrum is measured
by changing transmitted OAM order. (c1) Measured received power and (c2) intermodal crosstalk with a
different lateral displacement.
Furthermore, the misalignment effects on the received power and inter-channel crosstalk for the pixel-
array-based OAM receiver is experimentally explored. In general, one needs to know which modes are
being transmitted in an OAM-based link. However, an off-axis receiver aperture might not recover the full
azimuthal phase change and inadvertently “think” there is some power residing in the other modes as shown
inFigure2.15(a). Figure2.15(b)showsthenormalizedreceivedpowerwhenasingleOAMbeamhasalateral
displacement. When a lateral displacement increases from ∆ x, ∆ y = 0, 0 to ∆ x, ∆ y = -170µ m, 170µ m, the
received power of the desired mode (i.e., ℓ = -1) decreases by ∼ 7 dB and the largest power coupling from
the other modes increases from ∼ -12 dB to∼ 5 dB. In addition, the 2-dimensional misalignment effects on
the power loss and intermodal power coupling are shown in shown in Figure 2.15 (c1-c2). In general, the
28
power loss and intermodal crosstalk tend to increase when the lateral displacement increases in both the x
and y direction. It should be noted that the optimum positions for receiving two OAM beams are slightly
different. This could potentially be due to some mode-dependent coupling loss under different displacement
effects.
Col.
BS
Objective
lens
Bias control
HWP
PC
PC
Col.
EDFA
50/50
coupler
SLM
Coherent
receiver
2×50 Gbit/s
IQ-Mod
IQ-Mod
Delay fiber
(250 symbol)
Delay fiber
(500 symbol)
PC
PC
(b)
Local oscillator
Bias control
PC
PC
EDFA
50/50
coupler
Coherent
receiver
2×50 Gbit/s
IQ-Mod
IQ-Mod
Delay fiber
(250 symbol)
Delay fiber
(500 symbol)
PC
PC
(a)
Local
oscillator
Fiber
array
SLM
BS
Communication link using TRIP-based OAM emitter
Communication link using TRIP-based OAM receiver
Objective
lens
Figure 2.16: Experimental setup of free-space communication link using the (a) pixel-array-based OAM
emitter and (b) pixel-array-based OAM receiver. HWP: half-wave plate.
The experimental setup of the communication link using the pixel-array-based OAM emitter is shown
in Figure 2.16(a). Each WDM channel is firstly generated from a separate IQ modulator and combined.
The polarization controllers are used for keeping the same polarization of the two 50-Gbaud WDM QPSK
channels. Subsequently,thetwoWDMchannelsareamplifiedandsplitintotwocopies. Theyaredecorrelated
by passing through fibers with different lengths. Then, the two copies are respectively fed to port 1 and port
3 of the OAM emitter for generating multiplexed OAM beams (ℓ = -1 and ℓ = + 1). As the edge coupling
of the chip is polarization-sensitive, polarization controllers are used to align the polarization of the input
beams. By tuning the applied bias voltages, the OAM orders of the generated beams could be changed, and
thus the corresponding data channels carried by the OAM modes can be changed. At the receiver side, the
generated data-carrying OAM beams are demultiplexed by an SLM, and subsequently the collected optical
signal carried by the corresponding generated OAM beam is recovered by the coherent receiver.
29
Reversely, the pixel-array-based device can also be used as an OAM receiver in a communication system
as shown in Figure 2.16(b). The Gaussian beams are sent to the SLM loaded with different phase holograms
on each half of the SLM to generate OAM beams with mode order of ℓ = -1 or ℓ = + 1. The two beams are
multiplexed and coaxially propagate in free space for∼ 0.5 m. Then they are collected by the objective lens
and coupled vertically into the chip. A half-wave plate is used before the objective lens to align the input
polarization to the target polarization. By adjusting the bias voltages to the four independently controlled
heaters, the data channel carried by one of the multiplexed OAM modes is sorted to the designated port,
received by the lensed fiber, and sent to a coherent receiver.
2.5 100-Gbit/s OAM-based Link with a Tunable OAM order
Gaussian
(reference)
Bias 1
(OAM -1)
Bias 2
(OAM +1)
Bias 1 (OAM -1)
OSNR: 22.7 dB
EVM: 27.6%
Bias 2 (OAM +1)
OSNR: 22.7 dB
EVM: 27.8%
3.8e-3
FEC limit
16 18 24 20 22
10
!"
10
!#
10
!$
BER
(a)
(b)
OSNR (dB)
Figure 2.17: Single-channel communication link with a tunable OAM order using the OAM emitter. Mea-
sured(a)constellationdiagramsand(b)BERperformanceofasingle50-GbaudQPSKchannelonatunable
OAM beam at 1550.9 nm.
Utilizing the tunability of the pixel-array-based OAM emitter (see in Figure 2.7), a 100-Gbit/s data
channel through the pixel-array-based device is transmitted as shown in Figure 2.17. As proof of concept,
port 2 is fed as an input port. The carrier wavelength is chosen as 1550.9 nm. Figure 2.17(a) shows the
recovered constellation diagrams for the QPSK channels carried by the OAM beam ℓ = -1 and ℓ = + 1
30
, respectively. Each channel is transmitted at a different time. The two channels have a similar EVM
with the same OSNR. As a comparison, a 50-Gbaud QPSK data channel carried by the Gaussian beam is
characterized. Figure2.17(b)showsthatthedatachannelscarriedbythetunableOAMbeamhaveasimilar
BER performance as the one carried by the reference Gaussian beam.
Power
(5dB/div.)
Power
(5dB/div.)
Bias 1 (OAM -1)
Bias 2 (OAM +1)
OSNR (dB)
25
20
15
10
!"
10
!#
10
!$
BER
Wavelength (nm)
FEC limit
Bias 1
(OAM -1)
Bias 2
(OAM +1)
Bias 1
(OAM -1)
Bias 2
(OAM +1)
1545 1550 1555
1540 1545 1550 1555 1560
Wavelength (nm)
(a) (b)
(c)
Figure2.18: (a)Measuredpowerspectrumofthereceivedsignalofasingle50-GbaudQPSKchannelcarried
by thecorrespondingOAMbeamgeneratedby thepixel-array-based OAM emitter. Differentcolors indicate
different carrier wavelengths. Measured (b) OSNR, (c) BER performance at different carrier wavelengths.
Measured BER at different wavelengths. A single channel carried by a tunable OAM beam is transmitted
at one wavelength at one time with the same transmitted power. Port 2 is the input port. Voltages for bias
1 and bias 2 are (0.4V,3.3V,2.5V,0.8V) and (0.2V,0.1V,1.8V,2.3V), respectively.
To further characterize the bandwidth of the communication link with the pixel-array–based OAM emit-
ter, the carrier wavelengths are swept from 1544.6 nm to 1554.2 nm in steps of 0.8 nm, and the transmitted
power is kept the same as shown in Figure 2.18(a). Beyond the center wavelength of 1551 nm, the OSNR
tends to degrade as shown in Figure 2.18(b). In a wavelength range of 6.4 nm, the BER of the data channel
carried by either OAM ℓ = +1 or ℓ = -1 is lower than the 7% FEC limit as shown in Figure 2.18(c). The
bandwidth of the chip may be limited by the bandwidth of the coupler and the length mismatch of the four
connecting waveguides.
2.6 200-Gbit/sOAM-multiplexedLinkusingthePixel-array-based
PIC
In addition, an OAM-multiplexed link using the pixel-array-based OAM receiver is experimentally demon-
strated. Figure 2.19(a) shows the measured crosstalk matrix of the received OAM channels under different
31
(a)
OSNR (dB)
BER
50-Gbaud QPSK
Ch 1
(OAM +1)
Ch 2
(OAM-1)
Bias 1
Bias 2
0 dB -24 dB
EVM: 25.0%
OSNR: 23.9 dB
EVM: 30.6%
OSNR:23.4 dB
Bias 1
Bias 2
(b2)
(c)
(b1)
7% FEC limit
Figure 2.19: Experimental demonstration of a 200-Gbit/s OAM-multiplexed link using pixel-array-based
receiver. (a)Measured crosstalk matrix of the received OAM channels under different bias voltages. (b1-b2)
Constellation diagrams of the recovered signal for receiving different OAM channels with the corresponding
bias voltages. (c) Measured BER performance for the data channels.
bias voltages. The maximum crosstalk of the two received OAM channels in our system is up to -15 dB.
Figure 2.19(b1-b2, c) shows the constellation diagrams and BER performance respectively. For the data
channel carried by ℓ = +1 or ℓ = -1, there is around 0.2-dB and 2-dB OSNR penalty to achieve the BER of
3.8× 10
− 3
compared with that of back-to-back link.
2.7 400-Gbit/sWDMandOAM-multiplexedLinkusingthePixel-
array-based PIC
In addition, a WDM and OAM-multiplexed link using the pixel-array-based OAM emitter is experimentally
demonstrated. Giventhetransformationfunctionofthedesignedcoupler,port1and3canbesimultaneously
fed to generate two multiplexed OAM beams. By tuning the applied bias voltages, the OAM order of the
generated beams can be switched, and thus the corresponding data channels carried by the OAM modes can
beswitched. Figure2.20showsthemeasuredinter-channelcrosstalkandBERperformanceofdifferentWDM
channels and different data channels carried by the OAM beams under different bias voltages. Compared
withthesinglechannelinthereferencearm, thereisa 1-dBOSNRpenaltytoachievetheBERof3.8× 10
− 3
for the two WDM channels carried by either OAM ℓ = -1 or ℓ = + 1.
32
Ch.1
ℓ=−1,
!
Received channel
Transmitted channel
Ch.2
ℓ=+1,
!
Ch.3
ℓ=−1,
"
Ch.4
ℓ=+1,
"
Port 1

!
Port 3

!
Port 1

"
Port 3

"
Transmitted channel
Port 1

!
Port 3

!
Port 1

"
Port 3

"
(a1)
(a2)
Bias voltages=
(0.1V, 0.3V, 0.4V, 0.8V)
Bias voltages=
(0.2V, 2.5V, 0.5V, 3.1V)
(b1) (b2)
3.8×10
!"
FEC limit
3.8×10
!"
FEC limit
Ch.1
Ch.2
Ch.3
Ch.4
Gaussian
Ch.1
Ch.2
Ch.3
Ch.4
Gaussian
BER
10
!"
10
!#
10
!$
OSNR (dB)
OSNR (dB)
0 dB
-45 dB
Figure 2.20: WDM and OAM-multiplexed link using the tunable OAM emitter. Measured inter-channel
crosstalk and BER performance for the OAM-multiplexed and WDM link under (a, b) two different bias
voltages. λ 1
: 1550.9 nm, λ 2
: 1551.7 nm.
Furthermore, a WDM and OAM-multiplexed link using the pixel-array-based OAM receiver is experi-
mentally demonstrated. Figure 2.21(a1-a2) shows the measured inter-channel crosstalk between the OAM-
multiplexed and WDM channels. The measured crosstalk between different WDM channels carried by the
OAM beams with the same OAM order is <-20 dB. In addition, the crosstalk matrix also shows that the
OAM-carried data channels could be routed to different ports by tuning the OAM receiver. Figure 2.21(b1-
b2) shows the measured BER performance of the OAM-multiplexed and WDM channels. For comparison, a
single 50-Gbaud data channel carried by a single OAM beam (ℓ = -1 or ℓ = +1) at the carrier wavelength of
33
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
Single channel
transmitted Rx: Ch.1
(Port 1,
!
ℓ = +1)
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
data8
Rx: Ch.1
(Port 1,
!
ℓ = −1)
Rx: Ch.2
(Port 3,
!
,
ℓ = +1)
Rx: Ch.3
(Port 1,
"
,
ℓ = −1)
Rx: Ch.4
(Port 3,
"
,
ℓ = +1)
0
-18.4
-26.4
-43.5
-18.1
-0.5
-42.3
-23.6
-24.5
-45.1
-0.9
-20.2
-44.1
-26.4
-19.1
-0.1
15 20 25
-4
-3.5
-3
-2.5
-2
Ch.1
Port 1,
!
Received channel
Transmitted channel
OAM -1

!
OAM +1

!
OAM -1

"
(a1)
(a2)
Ch.2
Port 3,
!
Ch.3
Port 1,
"
Ch.4
Port 3,
"
3.8×10
!"
FEC limit
BER
10
!"
10
!#
OSNR (dB)
15 20 25
OAM +1

"
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
Four channels transmitted Single channel
transmitted
Tx: ℓ = −1,

Rx: ℓ = −1, Port 1
Rx: Ch.2
(Port 3,
!
,
ℓ = −1)
Rx: Ch.3
(Port 1,
"
,
ℓ = +1)
Rx: Ch.4
(Port 3,
"
,
ℓ = −1)
Four channels transmitted
Received channel
Ch.1
Port 1,
!
Ch.2
Port 3,
!
Ch.3
Port 1,
"
Ch.4
Port 3,
"
Transmitted channel
OAM -1

!
OAM +1

!
OAM -1

"
OAM +1

"
Rx: ℓ=−1 at port 1, ℓ=+1 at port 3
Rx: ℓ=+1 at port 1, ℓ=−1 at port 3
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
data8
Tx: ℓ = +1,

Rx: ℓ = +1, Port 3
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
data8
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
Tx: ℓ = +1,

Rx: ℓ = +1, Port 1
15 20 25
-4
-3.5
-3
-2.5
-2
data1
data2
data3
data4
data5
data6
data7
data8
Tx: ℓ = −1,

Rx: ℓ = −1, Port 3
15 20 25
-4
-3.5
-3
-2.5
-2
3.8×10
!"
FEC limit
BER
10
!"
10
!#
OSNR (dB)
15 20 25
-19.3
-0.5
-42.8
-26
0
-20.2
-23.9
-43.2
-41.6
-26.3
-19.2
-1.1
-24.9
-42
-0.2
-19.4
(b1)
(b2)
Figure 2.21: WDM and OAM-multiplexed link using the tunable OAM receiver. Measured (a1-a2) inter-
channel crosstalk and (b1-b2) BER performance for the OAM-multiplexed and wavelength-division- multi-
plexed (WDM) link under different bias voltages. Carrier wavelength λ 1
: 1550.9 nm, λ 2
: 1551.7 nm. A
single OAM beam with the carrier wavelength of λ 1
is transmitted as a comparison.
1550.9 nm is transmitted and received by the OAM receiver. Compared to the single OAM channels, there
is a∼ 2-dB OSNR penalty for all the OAM- multiplexed and WDM channels.
Furthermore, the BER performance under different scenarios is experimentally characterized when (i)
a single OAM beam (ℓ = -1) is transmitted, (ii) two coaxial OAM beams are multiplexed, and (iii) two
coaxial OAM beams are multiplexed combined with WDM as shown in Figure 2.22. Both scenarios ii and
34
15 20 25
-4
-3
-2
OSNR (dB)
BER
10
!"
10
!#
3.8×10
!"
FEC limit
10
!$
15 20 25
-4
-3
-2
data1
data2
data3
data4
Single channel
transmitted
(Tx: ℓ=−1,
!
)
15 20 25
-4
-3
-2
data1
data2
data3
data4
OAM-multiplexed
channels transmitted
(Tx: ℓ=−1, +1,
!
)
15 20 25
-4
-3
-2
data1
data2
data3
data4
OAM-multiplexed+WDM
channels transmitted
(Tx: ℓ=−1, +1,
!
,
"
)
Rx: ℓ=−1, port 1,
%
Figure 2.22: Measured BER performance without inter-channel crosstalk, with inter-modal crosstalk in the
OAM-multiplexed link, and with inter-channel crosstalk in the OAM-multiplexed and WDM link. The
channel is carried by the OAM beam (OAM -1) with the carrier wavelength of 1550.9 nm (λ 1
).
iii show∼ 2-dB OSNR penalty as compared to that of scenario i. This indicates that such OSNR penalty in
the aforementioned WDM and OAM-multiplexed link could be mainly related to the inter-modal crosstalk.
Suchintermodalcrosstalkcouldbeinducedby(a)nonidealphasedelaysinducedbythefabricationerror,(b)
misalignment between the incident beam and the OAM receiver, and (c) undesired polarization components
of the incident beam.
2.8 Generation of an LG beam with 2-D Tunable Spatial Indices
using Integrated Circular Antenna Arrays
TherehavebeenvariousreportsofPICs[47,58,68,69]whichexperimentallygenerateLGbeamswithvarying
1D modal indices, such as varying ℓ values for different OAM modes including the above-mentioned pixel-
array-based structures. It would be valuable to design the PIC and experimentally generate an LG beam to
tune both ℓ and p values [70]. To generate the LG beam with tunable 2-D mode indices, a concentric UCA
structure is designed as shown in Fig. 2.23. The in-plane waveguide mode in each waveguide is coupled
into a free-space Gaussian-like mode by the corresponding optical antenna. The generated Gaussian-like
modes are coherently combined by the concentric UCA structure. Subsequently, the combined beam evolves
35
UCA1
UCA2
Amplitude
distribution
control
between
UCA 1&2
Phase
distribution
control
between
UCA 1&2
Phase
control of
UCA1
Phase
control of
UCA2
MZI
Phase
shifter
Phase
shifters
Concentric UCAs
Input
port
Output port
(free-space)
Figure 2.23: Concept of the tunable Laguerre Gaussian beam (LG
ℓp
) generation using integrated uniform
circular arrays (UCAs) of optical antennas. By tuning the amplitude and phase distribution between the
twoconcentricUCAs, thepvalueofthegeneratedbeamcanbechanged. Bytuningthecircularphaseinside
the UCAs, the ℓ value of the generated beam can be changed.
into an LG beam after propagation. By tuning the azimuthal phase delay of each UCA, the ℓ value of
the generated beam can be tuned. By tuning the amplitude distribution and phase delay among different
concentric UCA, the p value of the generated beam can be tuned. To achieve both amplitude and phase
control of the concentric phase array structure, we added an MZI and multiple phase controllers to the
concentric UCA structure. An MZI structure is utilized to control the amplitude and phase between the
two UCAs. The output of MZI with controlled amplitude and phase is split into multiple copies. For each
copy, a thermo-optic phase controller is added to tune the phase delay inside each UCA. At the output port,
the generated LG beam of the concentric UCA structure is vertically coupled into free space. To reduce the
propagation phase error, the length of each waveguide is designed to be identical. To monitor the power
splitting of MZI, one port of the MZI structure is coupled into the fiber.
Based on the design of the concentric UCA , the simulated beam profiles of the tunable LG beams are
shown in Figure 2.24. The generated beam at the top of the device is composed of multiple Gaussian-like
modesintwocirculararrays. Inthesamecirculararray,theintensityisuniformlydistributed,andthephase
is circularly tuned to generate the corresponding OAM order. Between the two circular arrays, the intensity
distribution is carefully designed, and a specific phase delay is introduced. After propagation, generated
beam evolves into a beam carrying both ℓ and p values. The simulation results show that the OAM order
(ℓ value) of the generated LG beam can be tuned from -1 to +1 and the corresponding p value can be
independently tuned from 0 to 1.
36
Generated
beam at
top of the
device
-π
π
0
1
Normalized
intensity
profile
Phase
profile
Generated
beam after
propagation
Normalized
intensity
profile
Phase
profile

,

,

$,

$,

%,

%,
Figure 2.24: The simulated intensity and phase profiles of the generated beam. By tuning the azimuthal
phase delay of each UCA, the ℓ order of the generated beam can be tuned. By tuning the amplitude
distribution and phase delay among different concentric UCA, the p order of the generated beam can be
tuned.
2.9 Experimental Characterization of the LG Beam Generation
using the Integrated Circular Antenna Arrays
To characterize the LG generation beams generated by concentric UCA, an experimental setup is built as
shown in Figure 2.25. A CW laser is split into two arms. One is sent to the chip, and the other is sent
to generate a reference Gaussian beam for off-axis holography. The off-axis holography approach is utilized
to measure the spatial intensity and phase profile of the generated beam with an IR camera [71]. The PIC
is controlled by a 14-channel DAC driver. Moreover, a 5-Gbaud QPSK signal is fed to the PIC and the
generated data-carrying LG beam is down-converted by the SLM and coupled into single-mode fiber for
coherent detection.
Figure 2.26(a1-a4) shows the measured intensity and phase profiles of the generated LG beams. A single
Gaussian-like beam (LG
ℓ=0,p=0
) is generated as shown in Fig. 2.26(a1). By tuning the amplitude and phase
distribution between the two UCAs, an additional circular intensity ring is formed to carry LG
ℓ=0,p=1
mode
37
Collimator
DAC
IR Camera
90%
10%
...
SLM
EDFA
Col.
Col.
BS
CW laser/
Data stream
Flip
mirror
Mirror
PIC
HWPPol.
Coherent
receiver
PC
Figure 2.25: Experimental setup of the tunable LG beam generation.
Intensity Phase
1
0

−
0 dB <-30 dB
(a1)
(a2)
(a3)
(a4)
LG
ℓ"#, %"#
Mode purity:38.1%
LG
ℓ"#, %"&
Mode purity:23.9%
LG
ℓ"'&, %"#
Mode purity:30.2%
LG
ℓ"'&, %"&
Mode purity:33.9%
Intensity Phase
Intensity Phase
Intensity Phase

0
4
1
2
3
ℓ
+2 -2 -1 0 +1
ℓ
+2 -2 -1 0 +1
ℓ
+2 -2 -1 0 +1
ℓ
+2 -2 -1 0 +1
(b1)
(b2)
(b3)
(b4)

0
4
1
2
3
Measured beam profiles Measured LG mode spectrum
Figure 2.26: Measured intensity profiles, phase profiles and the LG modal power spectrum of the generated
(a1-b1) LG
ℓ=0,p=0
(a2-b2) LG
ℓ=0,p=1
(a3-b3) LG
ℓ=+1,p=0
(a4-b4) LG
ℓ=+1,p=1
.
38
as shown in Fig. 2.26(a2). By tuning the phase inside each UCAs, a 2π phase change in the azimuthal
direction is induced to form OAM (LG
ℓ=+1,p=0
) as shown in Fig. 2.26(a3). By further tuning the amplitude
and phase distribution between the two UCAs, two circular intensity rings are formed, and the generated
beam is tuned to carry LG
ℓ=+1,p=1
mode as shown in Fig. 2.26(a4). The measured mode purity is ranging
from 23% to 38%. It could be potentially due to the unwanted interference patterns induced by the UCAs.
ThecorrespondingLGmodalpowerspectraaremeasuredasshowninFig. 2.26(b1-b4), anditisnormalized
by the power of the desired mode. The intermodal modal power coupling to the neighboring mode is <-5
dB.
2.10 CommunicationLinkusingaSingleLGBeamwith2-DTunable
Spatial Indices
12 14 16 18 20
OSNR(dB)
10
-5
10
-4
10
-3
10
-2
BER
5-Gbaud QPSK
7% FEC threshold
12 14 16 18 20
OSNR(dB)
10
-5
10
-4
10
-3
10
-2
BER
data1
data2
data3
data4
data5
data6
Tx & Rx: ℓ = 0, = 0
Tx & Rx: ℓ = 0, = 1
Tx & Rx: ℓ = +1, = 0
Tx & Rx: ℓ = +1, = 1
Back-to-back
Tx & Rx:
ℓ = 0, = 0
EVM: 23.8%
Tx & Rx:
ℓ = 0, = 1
EVM: 24.1%
Tx & Rx:
ℓ = +1, = 0
EVM: 23.8%
Tx & Rx:
ℓ = +1, = 1
EVM: 24.1%
(a)
(b)
Figure 2.27: Measured (a) data constellation diagram and (b) BER performance of the 5-Gbaud QPSK
data channel carried by a signal LG beam with tunable modal indices. A single beam is transmitted and
received one at a time. The constellation diagram is measured with the OSNR of 18 dB. EVM: error vector
magnitude. FEC: forward error correction.
A 10-Gbit/s communication link carried the tunable LG beam generated by the concentric-UCA-based
LG emitter is experimentally demonstrated. A single data-carrying LG beam is transmitted and received
one at a time. The data constellation diagrams of the 5-Gbaud QPSK signal carried by the generated LG
beams are measured as shown in Figure 2.27(a). The data channels carried by the different LG beams show
similar EVM performance with each other. Moreover, the data channels carried by the generated LG beams
have similar BER performance compared with the case of the back-to-back link as shown in Fig. 2.27(b).
39
It should be noted that, such link demonstration is done for a single LG-carrying data channel and the
OSNR penalty could be potentially increased when there are multiple channels and the above-mentioned
inter-modal crosstalk could affect the recovered LG-carrying channel.
40
Chapter 3
Free-space Optical Communication under Atmospheric
Turbulence Effects
3.1 Background and Motivation
For FSO communication links, one of the key challenges is atmospheric turbulence [23, 72, 73, 74, 75].
Typically, an intensity modulation/direct detection system suffers from turbulence-induced scintillation and
power loss [73, 74]. The challenge is potentially greater for systems that have phase-based data, such as in
efficientphase-and-amplitude-encodedmodulationformats[75,76]asshowninFig. 3.1. Thisisbecause: (a)
the turbulence can induce power coupling of the data-carrying beam from the fundamental Gaussian mode
to higher-order spatial modes [75], (b) these higher-order spatial modes tend not to efficiently mix with the
receiver-based local oscillator (LO) which typically is limited only the fundamental Gaussian mode, and (c)
inefficient mixing between the data and LO causes significant power loss and difficulty in phase recovery
[76, 77, 78].
Recently, a turbulence-resilient FSO link for the recovery of phase-and-amplitude-encoded data was
demonstrated by utilizing a pilot-assisted self-coherent detection approach [79]. In that approach, a data-
carryingGaussianbeamistransmittedtogetherwithanadditionalpilotGaussianbeam. Whenpropagating
through the turbulence, the two coaxial beams experience similar turbulence-induced distortion [79]. At the
receiver, bothbeamsarecapturedandmixedbyasinglefree-spacedetector. Duringmixing, theturbulence-
induced modal coupling of the data beam is automatically compensated by the conjugate modal coupling
41
Tx
Rx
200 400 600 800 1000 1200 1400 1600 1800 2000
200
400
600
800
1000
1200
1400
1600
1800
2000
Rx distorted beam
Othermodes
…
Gaussian
Tx beam
200 400 600 800 1000 1200 1400 1600 1800 2000
200
400
600
800
1000
1200
1400
1600
1800
2000
Aperture Aperture
q Beam wandering
q Coupling loss to an aperture
Time
Rx power
q Power scintillation
Distorted mode spectrum
Gaussian
Gaussian
Spatial
mode
Tx mode spectrum
LO mode spectrum
×
O/E
Mixing
Other modes would not
efficiently mix with
Gaussian LO
Coherent detection λ
Data Ch.
f
Data Ch.
Atmospheric
turbulence
Direct detection
Coherent detection
Atmospheric
turbulence
Turbulence-induced
low mixing efficiency
Figure 3.1: Atmospheric turbulence effects on free-space optical communication links.
of the pilot beam. In this approach, a free-space photodetector (PD) is used for efficiently mixing the
corresponding pairs of higher-order modes of the turbulence-distorted data and pilot beams. Therefore,
the two beams are efficiently mixed and thus the amplitude and phase of the data ( e.g., 16-QAM) can be
recovered.
In the approach above, the single free-space PD typically requires a sufficient PD area to capture a
sufficient fraction of the beams [79]. However, the bandwidth of PDs tends to decrease when the PD size
increases [80]. One potential approach to overcome the beam collection and bandwidth response tradeoff
is to utilize an array of smaller free-space PDs with both a sufficient aggregate PD area yet with a larger
bandwidthforeachsub-element. SuchPDarrayshavebeenusedinamplitude-encodeddirect-detectionFSO
links for bandwidth enhancement in the absence of turbulence [80, 81, 82].
As for OAM-multiplexed FSO links, turbulence effects could induce additional channel crosstalk. Specif-
ically, turbulence-induced distortion on the OAM beam’s unique spatial modal structure can cause power
coupling from the transmitted mode to other modes, as shown in Fig. 3.2. This modal power coupling effect
cansignificantlyreducethechannelpoweronthedesiredmodeandinduceinter-channelcrosstalkifmultiple
modes are multiplexed for data transmission [26]. In addition, a typical OAM-multiplexed link requires a
mode demultiplexer to efficiently separate orthogonal mode-multiplexed channels.
42
Tx-1
Tx-2
Tx-n
...
OAM
Mode
Mux.
OAM
Mode
DeMux.
...
Rx-1
Rx-2
Rx-n
Atmospheric
turbulence
Turbulence-induced
inter-channel crosstalk
Figure 3.2: Atmospheric turbulence effect on OAM-multiplexed links.
Multi-plane light convertor (MPLC) is a technique for spatial transformation of optical fields by multiple
cascaded phase planes separated in free space [83, 84, 85, 86, 87, 88, 89]. It has been theoretically shown
that MPLC could perform a unitary transformation given an adequate number of discrete phase planes [90].
One type of such unitary transformation is “mode sorting” which converts coaxial orthogonal spatial modes
from a modal basis set to Gaussian modes with different transverse spatial locations [90, 91]. Such a “mode
sorting”functionhasbeenusedtoachievechanneldemultiplexinginanMDMFSOcommunicationlink[92].
Separately, the MPLC-related multi-mode-receiver approach has been applied for turbulence mitigation in a
single-channel FSO link [93]. In an FSO communication link, the atmospheric turbulence could distort the
wavefrontorcausebeamwandering[72,73]. ThiscouldleadtopowercouplingfromafundamentalGaussian
mode to higher-order modes and thus induce power fluctuation at the receiver [94, 95]. With the help of
the MPLC-based “mode sorting” function, the signal power in higher-order modes is captured, sorted into
separate receivers, combined digitally, and thus the turbulence-induced power fluctuation of a single channel
is reduced [93]. It would be interesting to extend the MPLC-based spatial transformation to correct the
turbulence-distorted wavefront and thus reduce inter-channel crosstalk in an MDM FSO link. Moreover,
using the same MPLC, the wavefront correction function and “mode sorting” function could be combined
and applied [96, 97].
In this section, two topics will be discussed as shown in Fig. 3.3 :(a) a turbulence-resilient free-space
opticalcommunicationlinkusingaPDarrayforbandwidthenhancement[98,99](b)simultaneousturbulence
mitigation and channel demultiplexing using a single MPLC [100, 97].
43
Free-space optical
communications under
atmospheric turbulence effects
Turbulence-resilient Free-space
Optical Communication using a
Photodetector Array
Simultaneous Turbulence
Mitigation and Channel Demux.
using a Single MPLC
Challenges
Approaches
q Turbulence-induced low
mixing efficiency between
data and LO beams
q Single free-space PD with
sufficient detection area is
typically limited in bandwidth
q OAM-multiplexed link needs
OAM demultiplexer to efficiently
separate Rx. channels
q Turbulences distorted optical
beams and therefore induces
inter-channel crosstalk
Amplitude-and-phase-encoded
Free-space Optical link
OAM-multiplexed
Free-space Optical link
Figure 3.3: Overview of the mitigation approaches for FSO links under turbulence effects (discussed in this
dissertation). LO: local oscillator. PD: photodetector. MPLC: multi-plane light convertor.
3.2 Turbulence-resilient Free-space Optical Communication using
a Photodetector Array
,
∗
(−Δ)*
∗

#$∑ &'!
"
!#$
Gaussian pilot
(LO) from the Tx
Similar distortion
(,) for the data
and LO
∆
Optical Freq.
I
Q
Gaussian beam
carrying coherent
data channel
20 40 60 80 100 120 140 160 180 200
20
40
60
80
100
120
140
160
180
200 0
500
1000
1500
2000
2500
3000
3500
4000
4500
0
1

,
Optical Freq.

,
(,)
(−)
Atmospheric
turbulence
20 40 60 80 100 120 140 160 180 200
20
40
60
80
100
120
140
160
180
200 0
500
1000
1500
2000
2500
3000
3500
4000
4500
0
1

20 40 60 80 100 120 140 160 180 200
20
40
60
80
100
120
140
160
180
200 0
500
1000
1500
2000
2500
3000
3500
4000
4500
0
1 , modal
coupling

20 40 60 80 100 120 140 160 180 200
20
40
60
80
100
120
140
160
180
200 0
500
1000
1500
2000
2500
3000
3500
4000
4500
0
1
Similar LG
modal
coupling

Amplitude and
phase recovery
SPB
Electrical Freq.

SSBI
PD 4
PD 3
PD 2
PD 1
$

PD

+
PD 1 PD 2
PD 3 PD 4
Array of smaller PDs
Electrical
sum
I
Q

Optical Freq.
Pilot
Single larger PD
Electrical Freq.
Relatively small
bandwidth

Optical Freq.
Pilot
Single smaller PD
Electrical Freq.
Relatively large
bandwidth
Electrical mixing
power loss
induced by
limited PD size

Optical Freq.
Pilot
Array of smaller PDs
Electrical Freq.
Relatively large
bandwidth
(a)
(b)
Optical Freq. Optical Freq. Optical Freq.
+
(,)=
( ( ℓ, ℓ,(,)
ℓ
Figure 3.4: (a) Concept of turbulence-resilient self-coherent FSO communications using a pilot tone and
an array of smaller photodiodes. SSBI: signal–signal beating interference; SPB: signal–pilot beating. (b)
ConceptofutilizinganarrayofsmallerPDstoenhancethesystembandwidth. Ingeneral,alargerfree-space
PD tends to have a relatively narrower frequency response, while a single smaller PD might have a relatively
higher electrical mixing power loss under turbulence distortion. Utilizing an array of smaller PDs could
potentially enhance the system bandwidth while maintaining a relatively large PD area.
44
The concept of the PD-array-based self-coherent scheme is shown in Fig. 3.4(a). At the transmitter,
the Gaussian data beam (S(t,f)) is sent together with a coaxial Gaussian pilot beam (C(f− ∆ f)) with a
frequency offset ∆ f. As the frequency offset is orders of magnitude smaller than their carrier frequencies,
the coaxial data and pilot beam are likely to experience similar turbulence-induced distortion, and therefore
they have similar modal coupling to higher-order spatial modes [23, 26]. This can be represented by a
spatial modal basis, such as the Laguerre-Gauss modes, {LG
ℓ,p
}, namely: U(x,y)=
P
ℓ
P
p
c
ℓ,p
LG
ℓ,p
(x,y),
where the indices ℓ and p correspond to the beam’s spatial distributions along with the azimuthal and radial
directions, respectively. In each PD, the generated photocurrent can be expressed as an area integral over
the detector area of the optical intensity of the combined data and pilot beams. Thus, the sum of the
photocurrent generated from the four PDs is given by,
I ∝
4
X
i=1
ZZ
A=PDi
|C(f− ∆ f)U(x,y)+S(t,f)U(x,y)|
2
dxdy (3.1)
The desired signal-pilot beating (SPB), which is centered around the frequency ∆ f as a sub term of the
photocurrent, can be represented as,
I
SPB
∝Re[S(t,f)C
∗ (f− ∆ f)]
ZZ
A=
P
4
i=1
PDi
UU
∗ dxdy (3.2)
Importantly, a conjugate U
∗ is generated from the pilot to compensate for the turbulence distortion
of the data beam. When the photodetection area is sufficient to collect the whole of the two beams,
RR
A=
P
4
i=1
PDi
UU
∗ dxdy =
P
ℓ
P
p
|c
ℓ,p
|
2
≈ 1. Subsequently, the amplitude and phase information is re-
covered from the photocurrent carrying the SPB component at ∆ f. We note that there are different ways to
achieve an M-QAM link, including (i) M-QAM sub-carrier modulation scheme in IM/DD systems [101, 102]
and (ii) our pilot-assisted self-coherent scheme [79]. For M-QAM subcarrier modulation, the electrical spec-
trum is roughly equal to the data bandwidth [101, 102]. For our pilot-assisted self-coherent scheme, the
frequency gap (approximately equal to the data bandwidth) between the pilot and data beams is used to
avoid SSBI while in turn the electrical spectrum is around 2× the data bandwidth [79]. This frequency gap
couldbepotentiallyreducedtoincreasetheelectricalspectralefficiencybyusingSSBImitigationtechniques
45
(e.g.,Kramers-Kronigdetection)withthetrade-offbetweenpowerefficiencyandelectricalspectralefficiency
[79, 103].
Furthermore, Figure 3.4(b) shows that (i) a single larger free-space surface-illuminated PD tends to have
anarrowerbandwidth,(ii)decreasingthePDareamightinduceahigherelectricalmixingpowerlossbecause
part of the turbulence-distorted optical beam could be truncated by the limited PD size, and thus (iii) an
arrayofsmallerPDs, whichhassufficientlylargeaggregatedPDarea, couldpotentiallyalleviatethetradeoff
between the PD area and PD bandwidth [80, 81, 82].
FM
Laser

AWG
EDFA
Mod
Lens
Lens
I
Q
Laser

FM
Lens
EDFA
FM
PC
PC
Turbulence
emulator
Retro-reflector
PC
Laser

PC
Laser

Camera
SMF SMF
SMF
PD
Col
Col
FM
Array of
smaller PDs
Single
smaller PD
Single
larger PD
430 µm
215 µm
500 µm
Beam
center
Single
larger PD
Single
smaller PD
Array of
smaller
PDs
Figure 3.5: Experimental setup of the PD-array-based turbulence-resilient FSO link. AWG: Arbitrary
Waveform Generator; EDFA: Erbium-doped Fiber Amplifier; PC: Polarization Controller; FM: flip mirror;
SMF: single-mode fiber; DSP: Digital Signal Processing; LO: local oscillator. Pilot λ 2
is switched off for the
LO-based SMF-coupled receiver. The inset shows the sizes of the free-space PDs used in our experiment.
The experimental setup is shown in Fig 3.5. We experimentally emulate the turbulence-induced distor-
tion by utilizing rotatable thin glass plates whose refractive index distributions are based on Kolmogorov
spectrum statistics [23]. By using a retroreflector, the beam propagates through two independent areas of
theturbulenceplate,anditexperiencesarelativelystrongerturbulencedistortion(r
0
∼ 0.26mm). Thewhole
transmission distance from the emulated turbulence plate to the receiver aperture is ∼ 1 m. We transmit a
pair of data-carrying and pilot beams with a beam size D of 2.2 mm. A 16-QAM data channel at a wave-
lengthofλ 1
≈ 1550nmisgenerated. Thepilottoneatawavelengthof λ 2
hasafrequencyoffsetwitharange
from ∼ 0.8 GHz to ∼ 1.6 GHz compared to λ 1
. At the receiver, a flip mirror is used to control the path of
the optical beam towards different free-space-coupled and single-mode fiber (SMF)-coupled detectors. The
46
amplitude and phase profiles of the beam are measured by off-axis holography [16]. The inset shows the
sizes of the free-space PDs used in our experiment. For the array of smaller PDs, a four-quadrant InGaAs
PD with a 3-dB bandwidth of ∼ 1.5 GHz and a total photodetection area of ∼ 0.14 mm
2
is used. For the
single smaller PD, one quadrant of the array is used. For the single larger PD, a single InGaAs PD with a
3-dB bandwidth of∼ 140 MHz and a PD area of∼ 0.19 mm
2
is used. For our free-space coupling, the focal
length of the lens is fixed at 75 mm, and the diameter of the focused beam without the turbulence effect is
∼ 70 µ m. We note that one could consider using a lens with a reduced focal length to further decrease the
size of the focused beam [73] and thus reduce the PD size requirement to achieve a higher PD bandwidth.
By combining both a smaller-focal-length lens and the PD array, it is conceptually possible that the beam
collectionandbandwidthresponsetradeoffcouldbefurtheralleviated[23,73,74,104]. FortheSMF-coupled
receiver, the free-space optical beam is firstly coupled into an SMF by a fiber collimator, pre-amplified by an
EDFA, and subsequently sent for LO-based heterodyne detection where the laser λ 2
is used as an LO and
the pilot λ 2
is switched off. The SMF-coupled PD has a 3-dB bandwidth of ∼ 33 GHz.
We firstly characterize the electrical mixing power loss of an FSO link under 1000 random turbulence
realizations (D/r
0
=8.4) as shown in Fig. 3.6. The electrical mixing power of the beating terms between two
CW lasers (∆ f =1GHz) is measured. For each case, the electrical mixing power loss is normalized by the
corresponding electrical mixing power without turbulence. Figure 3.6(a) shows that the LO-based coherent
detection system could suffer from an average electrical power loss of ∼ 18 dB. This could be due to that
the SMF does not efficiently capture the power coupled to higher-order modes. The pilot-assisted system
utilizing (i) a single smaller PD, (ii) a single larger PD, and (iii) an array of smaller PDs has an average
electrical mixing power loss of ∼ 5.5 dB, ∼ 1.2 dB, and ∼ 1.6 dB respectively, as shown in Fig. 3.6(b-d).
The measured electrical mixing power loss is normalized by the electrical mixing power for each receiver
without turbulence. For each receiver, the beam center is aligned at the central area of corresponding free-
space PDs as shown in Fig. 3.5. It should be noted that the single smaller PD tends to have a relatively
larger mixing power loss compared with an array of smaller PDs and a single larger PD. This could be due
to the larger impact of the turbulence-induced beam spreading and beam wandering [23] over a relatively
smaller photodetection area (i.e., 1/4 photodetection area of PD array). Besides the effect of the different
47
Figure 3.6: Measured electrical mixing power loss of the two beating terms between two CW lasers (∆ f=1
GHz) in an FSO link under 1000 turbulence realizations (D/r
0
=8.4). (a) LO-based coherent detection
utilizing an SMF PD. (b-d) pilot-assisted self-coherent detection utilizing (b) a single smaller PD, (c) a
single larger PD, and (d) an array of smaller PDs. The electrical mixing power loss is normalized by the
corresponding electrical mixing power without turbulence.
photodetector sizes, the difference of the average electrical mixing power loss for different cases could also
be related to (a) the shape of the photodetection area (i.e., “fan-shaped” or “round-shaped”) and (b) the
gap between different PDs of the PD array.
Utilizing the off-axis holography [71], the spatial amplitude and phase profiles of the received Gaussian
beam without turbulence effects are measured as shown in Fig. 3.7(a1). Figure 3.7 (b1) shows that the
main received power is contributed to a Gaussian mode without the turbulence effects. In such a case, both
the LO-based heterodyne coherent receiver and self-coherent PD-array receiver can recover the 1-Gbaud 16-
QAM signal with an EVM of 8%-9% as shown in Fig. 3.7(c1, d1). With turbulence (D/r
0
=8.4), the spatial
48
0
1

−
ℓ
-5 0 +5
0
10
Amplitude
Phase

0
1
−
0 dB
-30 dB
Amplitude

Phase
ℓ
-5 0 +5
0
10

EVM = 8.1%
EVM >20% EVM = 9.9%
EVM = 9.6%
LO-based heterodyne
coherent receiver
Pilot-assisted self-coherent
PD-array receiver
(a1) LG spectrum
Without turbulence With turbulence
(b1) (c1) (d1)
(a2) (b2) (c2) (d2)
Turbulence realization
BER
10
-1
10
-2
10
-3
10
-4
LO-based heterodyne coherent detector
Pilot-assisted self-coherent PD-array detector
(e)
1-Gbaud 16-QAM
FEC
Electrical frequency (GHz)
Normalized power
(20dB/div) 0 1 2 3 4
0 dB
-30 dB Electrical frequency (GHz)
Normalized power
(20dB/div) 0 1 2 3 4
Electrical frequency (GHz)
Normalized power
(20dB/div) 0 1 2 3 4
Electrical frequency (GHz)
Normalized power
(20dB/div) 0 1 2 3 4
Figure 3.7: Measured (a1-a2) amplitude and phase profiles, (b1-b2) LG spectrum with/without turbulence
(oneturbulence realization). Measuredelectrical spectra andrecovered1-Gbaud 16-QAMdata constellation
for (c1-c2) the LO-based heterodyne coherent detector and (d1-d2) the pilot-assisted self-coherent PD-array
receiver with/without turbulence (one turbulence realization). (e) Measured BER of the 1-Gbaud 16-QAM
signal under 100 turbulence realizations (D/r
0
=∼ 8.4). FEC: forward error correction.
amplitudeandphaseprofilesofthereceivedGaussianbeamaredistorted,andthepoweriscoupledtohigher-
orderspatialmodesasshowninFig. 3.7(a2-b2). Undersuchaturbulencerealization(D/r
0
=8.4), thepower
of the data beam cannot be efficiently coupled to the SMF and thus the data recovery using the LO-based
heterodyne coherent receiver fails as shown in Fig. 3.7(c2). Figure 3.7(d2) shows that the performance of
thepilot-assistedself-coherentPD-arrayreceiverisnotseverelyaffectedandthe16-QAMdataarerecovered
with an EVM of 9.9%. Figure 3.7(e) shows the measured BERs for the pilot-assisted self-coherent PD-array
detector under 100 turbulence realizations. The PD-array receiver can achieve BER values below the 7%
forward error correction (FEC) limit for all turbulence realizations. The variation of the measured BER for
the PD-array receiver under different turbulence realizations could be because of the remaining turbulence-
induced power fluctuation of the distorted optical beam due to the limited photodetector size as shown Fig.
49
3.5(d). Such remaining power fluctuation could potentially affect the signal SNR and therefore affect the
BER performance [80].
0.5-Gbaud
16-QAM
1-Gbaud
16-QAM
EVM = 9.7%
EVM = 9.3%
EVM = 9.6%
EVM = 9.5%
EVM = 13.8%
EVM = 9.7%
EVM = 9.9% EVM = 13.1%
EVM = 9.8%
EVM = 16.9%
EVM = 16.8%
EVM = 9.7%
With
turbulence
Without
turbulence
Array of
smaller PDs
Single
smaller PD
Single
larger PD
0.5-Gbaud
16-QAM
1-Gbaud
16-QAM
Electrical frequency (GHz)
0 1 2 3 4
0 1 2 3 4
0 1 2 3 4
Normalized power (20dB/div)
Normalized power (20dB/div)
0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
Normalized power (20dB/div)
Normalized power (20dB/div)
Normalized power (20dB/div)
Normalized power (20dB/div)
(a1) (b1)
(c1)
(a2)
(b2)
(c2)
Electrical frequency (GHz) Electrical frequency (GHz)
Electrical frequency (GHz) Electrical frequency (GHz) Electrical frequency (GHz)
Figure 3.8: Measured electrical spectrum and constellation diagram of the 0.5-Gbaud and 1-Gbaud pilot-
assisted FSO link utilizing (a1-a2) array of smaller PDs, (b1-b2) single larger PD, (c1-c2) single smaller PD
without and with the turbulence effects.
Inaddition,wevarythedatarateofthepilot-assistedFSOlinkwhendifferenttypesoffree-space-coupled
detectorsareutilized. Figure3.8showsthemeasuredelectricalspectraandrecoveredconstellationdiagrams.
The frequency spacing ∆ f is chosen as∼ 0.8 GHz and∼ 1.6 GHz for 0.5-Gbaud and 1-Gbaud 16-QAM data
transmission,respectively. Fordifferenttypesoffree-space-coupleddetectors,thesameturbulencerealization
is applied when the signal with the same baud rate is transmitted. For the array of smaller PDs, the EVMs
of the recovered 0.5-Gbaud and 1-Gbaud 16-QAM signal remain at <10% without and with turbulence
effects ( D/r
0
=8.4) as shown in Fig. 3.8(a1-a2). For the single larger PD, when the baud rate of the data
transmission increases from 0.5 Gbaud to 1 Gbaud, the EVM of the recovered signal increases to∼ 13% and
∼ 16%withoutandwithturbulenceeffects, respectively(Fig. 3.8(b1-b2)). ThemeasuredEVMinthecaseof
asinglelargerPDwithturbulence(Fig. 3.8(b2))isworsethanthatofasinglelargerPDwithoutturbulence
(Fig. 3.8(b1)). The difference of measured EVM could be probably due to that (i) there is a spatial non-
uniformityoftheresponsivityoverthephotodetectionarea[105], andthus(ii)thegeneratedphotocurrentof
50
the distorted optical beam under the specific turbulence realization is relatively lower than the undistorted
beam. For the single smaller PD, compared to the cases without turbulence effects (Fig. 3.8(c1)), the EVMs
oftherecovered0.5-Gbaudand1-Gbaud16-QAMsignalincreaseto∼ 13%and∼ 16%withturbulenceeffects
as shown in Fig. 3.8(c2). This could be because, for the single smaller PD, the turbulence-distorted beam is
more likely to be truncated by the limited PD size. This leads to a higher electrical power mixing loss and
thus affects the data recovery. It should be noted that the recovered constellation points in Fig. 3.8 show an
“oval-like” distribution as compared to that in Fig. 3.8. This could be potentially due to the IQ imbalance
of the generated signal for the drifted working condition of modulator [104].
For an FSO link that extends over significantly longer distances than our lab, beam wander and pointing
error could potentially induce beam misalignment [74, 75]. Such misalignment could lead to extra power
loss and reduced SNR if the misaligned beam is truncated by the sub-mm-scale photodetection area [74].
Such truncation might be mitigated by (a) utilizing beam tracking techniques to adaptively mitigate the
transmitter/receiver misalignment [106], and (b) increasing the aggregated photodetector size for efficiently
capturingthemisalignedbeam(e.g.,increasingthenumberofPDs)[82]. Specifically,whenconsideringaPD-
array-based receiver, the beam misalignment could further induce the power imbalance of the photocurrent
generatedbyeachindividualPDwhichcouldaffecttheSNRofthecombinedsignal[80]. SuchanSNReffect
might be alleviated by using various signal combining techniques (e.g., selection combining or maximum
ratio combining) [75, 80, 107].
3.3 SimultaneousTurbulenceMitigationandChannelDemux. using
a Single Multi-Plane Light Convertor
Figure3.9showstheconceptofutilizingoneMPLCtosimultaneouslymitigateturbulence-inducedcrosstalk
anddemultiplexOAMchannels. TwoOAMbeams,eachcarryinganindependentdatachannel,aretransmit-
tedcoaxially. ThewavefrontsofthecoaxialOAMbeamsaredistortedbytheatmosphericturbulence, which
introduces the power coupling among multiple neighboring modes and leads to inter-channel crosstalk. Sub-
sequently, thespatialprofilesofthedistortedcoaxialOAMbeamsareshapedwhilepropagatingthroughthe
51
Gaussian beam 1
(Channel 1)
Gaussian beam 2
(Channel 2)
Multi-plane light convertor
... ...
Distorted beam 1
(Channel 1)
Distorted beam 2
(Channel 2)
Inter-channel
crosstalk
OAM
ℓ
! ℓ
"
OAM ℓ
! ℓ
"
OAM
ℓ
#
OAM
ℓ
#
Crosstalk
monitor
Genetic-algorithm-
based crosstalk
mitigation
Wavefront-matching-
based channel
demultiplexing
+
Feedback
Demultiplexed channels with
low crosstalk
Coaxial
Spatially
seperated
phase patterns
Figure 3.9: Concept of utilizing one MPLC to simultaneously mitigate turbulence-induced crosstalk and
demultiplex OAM channels. The turbulence distorts the coaxial OAM beams and introduces power cou-
pling among multiple neighboring modes before coupling into the MPLC. The phase patterns of MPLC are
initialized for channel demultiplexing without considering turbulence distortion. With the feedback of the
monitored inter-channel crosstalk, the genetic algorithm is applied to adaptively update the phase patterns
of MPLC. Subsequently, each distorted beam propagates through the cascaded phase patterns and gets con-
verted to the corresponding Gaussian beam with relatively low inter-channel crosstalk.
cascaded phase planes in the MPLC. The phase planes are adaptively generated to simultaneously mitigate
turbulence-induced crosstalk and demultiplex OAM channels. After propagating through the MPLC, the
twodistortedOAMbeamsareconvertedtotwodifferentlypositionedGaussianbeamswithlowinter-channel
crosstalk.
Plane 1 Plane 2 Plane 3 Plane 4 Plane 5 Plane 6
Plane 1 Plane 2 Plane 3 Plane 4 Plane 5 Plane 6
0
2
Phase patterns for channel demultiplexing
Mitigation + demux. Patterns for one turbulence realization
(a)
(b)
Figure3.10: Examplesofthe(a)phasepatternsforchanneldemultiplexingand(b)superimposedmitigation
and demultiplexing patterns for a turbulence realization.
52
The phase patterns of the MPLC are generated by utilizing the wavefront matching method [88] and
the genetic algorithm (GA) [108, 109]. Figure 3.10(a) shows the phase patterns for channel demultiplexing.
Figure 3.10(b) shows the phase patterns which are superimposed of demultiplexing patterns and mitiga-
tion patterns for one turbulence realization. A wavefront matching method is utilized to pre-calculate the
demultiplexing phase patterns [88]. The wavefront matching method works as an optimization process to
point-to-point match the phase of each pair of input (i.e., the OAM beam with a specific mode order) and
output (i.e., the Gaussian beam with a specific position) with multiple phase patterns. For demultiplexing
two modes (k=2) using MPLC, five phase plates (2k+1=5) are typically needed to achieve a relatively high
mode purity [90]. As proof of concept, we utilize six phase plates to achieve two-mode demultiplexing. By
increasing the number of phase plates, the MPLC could potentially achieve a higher conversion efficiency
[88]. The pattern-to-pattern spacing is chosen as 31.5 mm. We choose such a pattern-to-pattern spacing by
considering several experimental limitations, including the width of the mirror and the incident angle of the
light beam. On the one hand, if a larger pattern-to-pattern spacing is chosen, there could be larger beam
divergence, and thus the output beam might be truncated by the mirror. On the other hand, for a smaller
pattern-to-pattern spacing, a larger incident angle might be required to keep the same number of reflections
which might reduce the phase modulation efficiency of the SLM [110].
Subsequently, the GA is applied iteratively to search for the optimized mitigation patterns in order to
minimizethehighestcrosstalkamongtheOAMchannels. TheGAstopswhenreachingacrosstalkthreshold
of < − 18 dB or the maximum iterations as 1000. It should be noted that all the mitigation patterns and
demultiplexingpatternsareallocatedinthesameSLM.However,thedemultiplexingpatternsandmitigation
patternsconsistofadifferentnumberofelements( i.e.,theminimumcomponentsofeachphasepattern). The
pixelsizeoftheSLMis9.2µ m. TofullyutilizethespatialresolutionoftheSLM,eachdemultiplexingpattern
has 300× 300 elements. Each element occupies one pixel of the SLM (9.2 µ m for each element). However,
the optimization time of the GA used to optimize the mitigation patterns partially depends on the number
of elements. To optimize the mitigation patterns at a faster speed for different turbulence realizations, each
mitigation pattern has a smaller number of elements compared to the demultiplexing pattern. In this case,
each mitigation pattern has 10× 10 elements, and each element occupies 30× 30 pixels of the SLM (276 µ m
53
for each element). In general, an increasing number of pixels or an increasing number of mitigation patterns
could potentially provide more degrees of freedom, while it might also require a more efficient optimization
algorithm.
As proof of concept, we set the locations of the two mitigation planes at plane 1 and plane 2. It
should be noted that the performance of turbulence mitigation might be different when there is a different
arrangement of the mitigation planes. For example, when two mitigation planes are set at plane 5 and plane
6orevenseparatelyatplane4andplane6,thedistortedcoaxialbeamsarefirstpartiallyseparatedandthen
spatially modulated by the mitigation planes. Compared to the arrangement used in our experiment, larger
mitigation patterns might be needed due to the beam separation. This could potentially induce different
crosstalk performance and require a different number of iterations [108].
PM PM
SLM
Mirror
Coherent
receiver
6-plane MPLC
Feedback
100Gbit/s
QPSK
@1550nm
Turbulence
emulator
Fiber array Mirror
Collimator
EDFA
PC
PC
50/50
coupler
OAM
Channel
MUX.
~0.5-m
propagation
~250 symbol
delay
Coaxial OAM beams
Plane 1 2 3 4 5 6 Camera
FM
Figure 3.11: Experimental setup of using MPLC for turbulence-induced crosstalk mitigation and channel
demultiplexing in an OAM-multiplexed link. QPSK: quadrature phase-shift keying. EDFA: erbium-doped
fiber amplifier. PC: polarization controller. Mux: multiplexer. SLM: spatial light modulator. PM: power
meter. FM: flip mirror.
The experimental setup is shown in Fig. 3.11. At the transmitter side, the 100-Gbit/s QPSK signal
with the center wavelength of 1550 nm is equally split by a 50/50 coupler, and the two signal copies are
decorrelated by passing through fibers with different path lengths. The two fiber branches are fed into two
input ports of a channel multiplexer, whose free-space output comprises two multiplexed OAM beams. The
54
polarization controllers are used to maximize the polarization-sensitive modulation efficiency of the SLM-
based MPLC. It is also possible to use a polarization-insensitive configuration [111]. A channel multiplexer
is used to generate different coaxial OAM beams by feeding different fiber ports. The channel multiplexer
itself is an MPLC-based device where the beams are reflected multiple times at different locations on a fixed
reflective phase plate. Subsequently, the OAM beams with a beam size D of <1.7 mm are normally incident
on the emulated turbulence plate with an effective Fried parameter (coherence length scale of turbulence) of
r
0
=1mm[26,112,23]. TheturbulenceplatehasapseudorandomphasedistributionthatobeysKolmogorov
spectrum statistics. After ∼ 0.5-m free-space propagation, the distorted beams are projected onto the first
plane (with the equivalent aperture size of ∼ 2.7 mm) of the SLM (Meadowlark Optics). Serving as an
MPLC, the SLM is positioned parallel to a silver mirror with a spacing of 15.7 mm.
The beams are bounced between the mirror and the SLM to go through six different phase planes with
anadjacentfree-spacepropagationdistanceof31.5mm. Afterpassingthroughthesix-planeMPLC,thetwo
beams are separated spatially and coupled into different ports of the fiber array with a spacing of 127 µ m
using a single collimator (NA = 0.35). After the power collection of both ports, a feedback loop is designed
tomonitorthecrosstalkbetweenthetwochannels. Giventhemeasuredcrosstalk,aGAisappliedinorderto
updatethepatternsforturbulencemitigation. AftertheMPLCpatternsareoptimized,thesignalscarriedby
the two transmitted OAM beams are received for coherent signal detection with low inter-channel crosstalk.
Intheexperiment, wefirstcharacterizethechanneldemultiplexingusingMPLC.Atthetransmitterside,
a single OAM beam is generated and transmitted one at a time. At the receiver side, the demultiplexing
patterns are generated for two different cases, i.e., OAM-multiplexed channels ℓ= {-1, +1} and {-1, +2}.
Figure3.12(a1, b1)showsthattheinter-channelcrosstalkis <-22dBand<-19dBfortheOAM-multiplexed
channels of ℓ={-1, +1} and{-1, +2}, respectively. To investigate the turbulence mitigation of the MPLC,
we put a rotatable turbulence emulator in the free-space optical path. After passing through the turbulence
emulator, the distorted coaxial OAM beams are demultiplexed by the MPLC. Figure 3.12(a2, b2) shows
that, compared with the cases without turbulence, the crosstalk degradation in the cases with turbulence
and without crosstalk mitigation is > 13.1 dB and > 9.2 dB for the transmitted OAM channels ℓ = {-1,
+1} and{-1, +2}, respectively. After applying crosstalk mitigation, the crosstalk is mitigated by >11.4 dB
55
Tx
OAM -1 OAM +1
Ch 1 Ch 2
Rx
Ch 1 Ch 2
Rx
Tx
OAM -1 OAM +1
Tx
OAM -1 OAM +1
Tx
OAM -1 OAM +2
Tx
OAM -1 OAM +2
（a1）（a2）（a3）
（b1）（b2）（b3）
OAM
ℓ = {−,+}
OAM
ℓ = {−,+}
Tx
OAM -1 OAM +2
W/ turbulence
W/ mitigation
W/ turbulence
W/O mitigation
W/O turbulence
W/O mitigation
Figure 3.12: Measured crosstalk matrix. The MPLC can be reconfigured to demultiplex different OAM
beams, e.g., ℓ = {− 1,+1} or ℓ = {− 1,+2}. Before applying the mitigation patterns, the turbulence
introducedextracrosstalk. Afterapplyingthemitigationpatterns,theintermodalcrosstalkcanbemitigated.
and >7.2 dB for the transmitted OAM channels ℓ = {-1, +1} and {-1, +2}, respectively, as shown in Fig.
3.12(a3, b3). The turbulence-induced power loss is also reduced simultaneously. It should be noted that, for
both ℓ ={-1, +1} and{-1, +2}, the insertion loss of the MPLC is <-19 dB, >-23 dB and <-20 dB without
turbulence, without and with turbulence mitigation, respectively. The insertion loss of the designed mode
might be limited by the reflection coefficient and the grating efficiency of the SLM. With a lossless SLM
without blaze gratings [88, 90], the insertion loss of the MPLC could be∼ -2 dB with turbulence mitigation.
It should be noted that the insertion loss of the MPLC-based device might be related to the number of
phase plates [88]. In general, the insertion loss related to the reflection coefficient and the grating efficiency
could be decreased by utilizing a smaller number of phase plates. However, reducing the number of phase
plates tends to achieve less adiabatic spatial phase modulation and could potentially decrease the conversion
efficiency [88].
56
OAM -1
OAM +2
W/O
turbulence
Turbulence
realization 1
Turbulence
realization 6
(a) OAM channels ℓ = {−,+} are transmitted
Crosstalk (dB)
Realization
0
-10
-20
-30
2 4 6 8 10
w/o mitigation
w/ mitigation
w/o turbulence
(b)
Figure 3.13: (a) Measured Beam profiles of and without turbulence and with turbulence under different
realizations. (b) Measured crosstalk without (dashed line) and with (solid line) mitigation for the channels
carried by ℓ=− 1 (black line) and ℓ=+2 (red line) under 10 turbulence
Furthermore, different realizations of turbulence are emulated by rotating the turbulence emulator. For
each measurement under different realizations, the turbulence phase plate is fixed, and the beams are trans-
mitted through a different part of the turbulence emulator [26, 23]. As a proof of concept, the OAM-
multiplexed channels of ℓ=-1 and +2 are transmitted. Figure 3.13(a) shows the beam profiles of the OAM
ℓ=-1 and +2 are distorted differently under different turbulence realizations, which could lead to varying
inter-channel crosstalk. Such beam profiles are captured at the input side of the MPLC. It should be noted
that, the beam profiles are not perfect without turbulence. The intermodal crosstalk between ℓ = -1 and
ℓ = +2 without turbulence is <-25 dB. This might be due to the imperfect performance of the channel
multiplexer. Figure 3.13(b) shows that under 10 different turbulence realizations before applying turbulence
mitigation, the crosstalk of channel 1 (ℓ = -1) and channel 2 (ℓ=+2) varies from -0.8 dB to -16.2 dB and
from -12.8 dB to 2.0 dB, respectively. After applying turbulence mitigation, the crosstalk under -18 dB
and a crosstalk reduction of up to 26 dB are achieved for both channels. Under some specific turbulence
realizations, the inter-channel crosstalk after turbulence mitigation is lower than that without turbulence.
This might be due to that the MPLC mitigates the crosstalk induced by not only the turbulence but also
residual misalignment [109, 113].
Under turbulence realization 1, the BER performance is measured by simultaneously transmitting the
OAM-multiplexed (ℓ ={-1,+2}) channels. As shown in Fig. 3.14(a), the measured crosstalks for channel 1
(ℓ=-1)andchannel2(ℓ=+2)modearedecreasedfrom-12dBand-2.6dBto-19.2dBand-27dB,andthe
57
EVM: 58.2%
OSNR: 22.5 dB
XT: -2.6 dB
XT: -12 dB XT: -19.2 dB
EVM: 31.4%
OSNR: 22.5 dB
W/ turbulence
W/ mitigation
W/ turbulence
W/O mitigation
Ch. 1
Ch. 2
EVM: 25.4%
OSNR: 20.4 dB
OSNR: 20.4 dB
EVM: 24.3%
XT: -27 dB
BER
OSNR (dB)
7%
FEC threshold
(a) (b)
50-Gbaud QPSK
Figure 3.14: Measured transmission matrix of OAM-multiplexed channels. (a1-a3) ℓ= -1 and +1, (b1-b3) ℓ
= -1 and l=+2 for channel demultiplexing without turbulence, without and with crosstalk mitigation (miti.)
under the turbulence (turb.). (c) Beam profiles of ℓ =-1 and +2 without turbulence and with turbulence
under different realizations. (d) Measured crosstalk without (dashed line) and with (solid line) mitigation
for the channels carried by ℓ = -1(black line) and ℓ = +2( (red line) under 10 turbulence realizations.
EVM is improved from 31% and 58% to 25% and 24%, respectively, by applying the turbulence mitigation.
Figure 3.14(b) shows that without turbulence mitigation, there is ∼ 4.8 dB OSNR penalty for channel 1 to
achieve BER of 3.8× 10
− 3
(i.e., 7% FEC threshold) compared with that of back-to-back case. For channel 2
(ℓ = +2) without turbulence mitigation, the coherent detection algorithm does not readily recover the I-Q
information. After applying turbulence mitigation, there is∼ 0.5 and∼ 1.5 dB OSNR penalty to achieve the
7% FEC threshold compared with that of the back-to-back case for channel 1 and channel 2, respectively.
The difference in the OSNR penalty might be due to the different crosstalk of different channels.
As the generation of demultiplexing patterns and mitigation patterns is relatively independent, the num-
ber of mitigation patterns is not necessarily the same as that of demultiplexing patterns. To explore the
effect of the number of mitigation patterns, the number of mitigation patterns is varied from 1 to 6. Fig.
3.15 shows that the cases with a different number of mitigation patterns achieve similar crosstalk mitigation
performance while the two-plane case takes the lowest number of iterations. This might be due to that,
with the increasing number of mitigation patterns, the increased degree of freedom tends to increase the
optimization speed while also increasing the search space that might limit the optimization speed.
58
Figure3.15: Measuredcrosstalkwithadifferentnumberofmitigationpatternsappliedunderoneturbulence
realization in the experiment for OAM-multiplexed channels ℓ={− 1,+2}.
In addition, we further explore turbulence mitigation using different numbers of mitigation planes under
200turbulencerealizationsinsimulation. Fig. 3.16(a, b)showthat(i)thecrosstalkcouldbeachievedbelow
the crosstalk threshold of -18 dB and sometimes ¡-25 dB, and (ii) the number of iterations could range from
50 to 700. The average number of iterations could partially depend on the number of mitigation planes.
The simulation result shows that, when the number of mitigation planes increases from 1 to 6, the average
number of iterations taken to reach the crosstalk level under -18 dB is ∼ 250,∼ 160,∼ 170,∼ 180,∼ 200 and
∼ 200, respectively. The case with two mitigation planes could achieve the crosstalk below -18 dB with the
smallest average number of iterations. This might be due to that, when the number of mitigation patterns
increases, the increased degrees of freedom tend to increase the optimization speed but could also increase
59
the search space, which might limit the optimization speed. Moreover, we use two turbulence simulation
approaches: (a)singlephaseplateinordertoreplicateourexperimentaldemonstration,(b)twophaseplates
in order to have better accuracy for thicker turbulent layers [113, 114]. For the case with two turbulence
plates, we use the same Fried parameter as the case of a single turbulence plate (red-dashed line) [114]. In
such a scenario, the two cases with different turbulence plates show a similar trend of crosstalk performance
and average iteration number. It should be noted that the number of iterations might be related to various
parameters that include but are not limited to the crosstalk threshold and the optimization algorithm [115].
To investigate the scalability of the MPLC for turbulence mitigation, we apply the same method to the
OAM mode sets with a different number of modes in simulation under 100 turbulence realizations. It should
benotedthatthepowerlossinducedbyMPLCmightdependon(i)thespatialmodulationefficiencyrelated
to the reflection coefficient and the grating efficiency of the SLM, (ii) the channel demultiplexing, and (iii)
the turbulence mitigation [26, 116]. In our simulation, to separate the influence of the SLM’s modulation
efficiency from channel demultiplexing and turbulence mitigation, each phase plate is assumed to be lossless.
Therefore, the modulation efficiency of the SLM is not included in the simulated power loss. As a proof of
concept, the first N (N < 10) OAM modes are selected from the sequence of OAM = (0, +1, -1, +2, -2, +3,
-3, +4, -4) and two mitigation patterns are adaptively applied in the MPLC. Fig. 3.16(c) shows that the
turbulence-induced power losses of 6–9 dB are induced on average under 100 turbulence realizations with-
out applying turbulence mitigation. After the corresponding turbulence mitigation is applied, the average
insertion loss of MPLC is reduced. This could be due to that the mitigation patterns not only reduce the
inter-channel crosstalk but also mitigate the power coupling to the other higher-order modes [117].
To mitigate the turbulence effects on an MDM FSO link, there have been various approaches, including
(i) adaptive optics, which applies an inverse phase function of turbulence to mitigate inter-modal crosstalk
[117, 118, 119, 120, 121] and (ii) electronic digital signal processing based on multiple-input-multiple-output
(MIMO)equalization[122,123]. Wenotethattherearesomechallengesinminimizingthesystemcomplexity
for the proposed MPLC-based approach. It would be valuable to develop a more efficient method for the
MPLC system.
60
Number of mitigation planes
Iterations Crosstalk (dB)
Average crosstalk/iterations
with its standard deviation
Average crosstalk/iterations
with its standard deviation
Crosstalk/iterations Crosstalk/iterations
Two turbulence plate: Single turbulence plate:
Power loss(dB)
-5
-10
-15
0
2
W/O turbulence
W/ turbulence
W/ mitigation
W/ turbulence
W/O mitigation
Number of modes N
4 6 8
(c)
(a)
(b)
Figure 3.16: Simulated (a) crosstalk and (b) number of iterations under 200 turbulence realizations for
OAM-multiplexed channel ℓ = {− 1,+2}. Each red/black dot represents the simulated crosstalk and the
simulated number of iterations under one turbulence realization emulated by a single turbulence plate/two
turbulence plates. The circles/squares represent the simulated average crosstalk and the simulated average
number of iterations under 200 turbulence realizations emulated by a single turbulence plate/two turbulence
plates. The bars show the corresponding standard deviation values. (c) Simulated average insertion loss of
the MPLC without turbulence, without and with mitigation under 100 turbulence realizations.
In our demonstration, we need to periodically update the phase patterns and measure the mode trans-
mission matrix of the two channels. During the measurement of the transmission matrix, we: (a) interrupt
the transmitted data flow of the two data channels, (b) sequentially transmit only one OAM beam at a
time, and (c) for each OAM beam, we measure the power in each part of the full mode transmission matrix.
Subsequently, the two data channels can then be transmitted simultaneously. Importantly, this periodic
interruption of data transmission can potentially be avoided by utilizing probe beams that: (i) experience a
similar turbulence effect, and (ii) could be separated from the transmitted data channels with little power
coupling. Possible methods include (a) utilizing coaxial OAM probe beams at different wavelengths [117]
or (b) transmitting coaxial backward-propagating probe beams from the receiver to the transmitter and
measuring the crosstalk at the transmitter [124] .
61
Additionally, wenotethatreal-timeturbulencemitigationapproachesinanFSOlinkshouldbeoperated
as fast as the dynamic decoherence effects of the turbulence, perhaps at a rate of kHz [23]. In our demon-
stration, it takes 5 s for each iteration and 200 iterations to mitigate the turbulence-induced crosstalk. This
would be too slow in a practical link, but the speed could be significantly increased by various methods. In
order to decrease the operation time of each iteration and increase the speed of turbulence mitigation, one
might consider: (i) applying a more efficient optimization algorithm to reduce the number of iterations, such
as a parallel wavefront optimization method [115] and (ii) utilizing a high-speed wavefront modulator [125].
62
Chapter 4
Underwater Optical Ranging through Underwater Scattering
4.1 Background and Motivation
There has been an increased interest in using optical approaches for ranging applications in underwater
moving platforms [126, 127] [1,2]. This is motivated by the relatively limited accuracy of low-loss sonar
approaches, andtheabilityforblue-greenlighttohavelowbeamdivergenceandsmallwavelengthresolution
over a distance of many meters [128, 129].
Various approaches have been reported in the underwater optical ranging system to reduce the contri-
bution of environmental effects including, (a) optical spatial filtering at the receiver (single spatial mode or
single polarization) to filter out the scattered light [130, 32], (b) hybrid radar/lidar approach (laser carrier
intensity-modulated by an RF sub-carrier) to discriminate the returned optical signal against the scattering-
induced background noise which has relatively lower frequency response at a higher modulation frequency
[131], and (c) time gating method (transmit a pulsed beam and receive the signal in a given time slot) to
reduce the collection of backscattered light in time-of-flight measurement system while it could be limited
by the tradeoff between ranging resolution and dynamic range [132].
A potential ranging approach might be to use the spatial domain as opposed to the temporal domain,
with the possibility that the amplitude and phase spatial distribution of the beam might be more tolerant
to highly scattering media [133, 130]. The concept of using a spatially structured beam for ranging could
involve the feature that the angular rotation of the spatial structure changes with different propagation
scenarios [134, 135].
63
4.2 Concept of z-dependent Angular Rotation of a Structured
Beam
Figure 4.1: Concept of the z-dependent angular rotation of the spatially structured beam. The generated
spatially structured beam carries two Bessel modes with different OAM orders and different longitudinal
wavenumbers.
The concept of the z-dependent angular rotation of a spatially structured beam is shown in Figure 4.1.
The transmitted spatially structured beam consists of two Bessel modes (J
ℓi
(k
ℓi
r
r)e
iliθ e
ik
ℓ
i
z
z
), i=1 or 2) with
different OAM orders ( ℓ
1
and ℓ
2
) as well as different longitudinal wavenumbers k
ℓ1
z
and k
ℓ2
z
. The value of
OAM order indicates the number of 2π phase shifts around the center of the beam’s phase profile. Due to
spatial interference between the two modes with the different OAM orders, a petal-like intensity profile is
obtained. Theangularrotationofthepetalislinearlyproportionaltotherelativephasedelaybetweenthese
two modes [128, 129]. To generate z-dependent angular rotation, the longitudinal wavenumber difference
64
Figure4.2: Conceptofutilizingangularrotationofspatiallystructuredbeamforunderwateropticalranging.
The reflector distance is retrieved by measuring the rotating angle of the petal-like intensity profile of the
reflected beam.
∆ k
z
= |k
ℓ1
z
− k
ℓ2
z
| is introduced between the two modes. When the beam propagates, such ∆ k
z
induces a
z-dependent relative phase delay between the two modes and thus leads to a z-dependent angular rotation
of the intensity profile [136]. The relationship between the angular rotation (∆ θ ) and reflector distance (z)
can be represented as,
∆ θ =
2z∆ k
z
n
water
|ℓ
1
− ℓ
2
|
(4.1)
where n
water
is the refractive index of the underwater medium [128, 136].
Based on the spatial feature of the z-dependent rotating pattern, a structured-light-based underwater
opticalrangingsystemcanbeachievedasshowninFigure4.2. Thespatiallystructuredbeamthatcombines
twoBesselmodeswithdifferentOAMordersanddifferentlongitudinalwavenumbersisgenerated,propagates
through an underwater medium, and is reflected back. Subsequently, the reflector distance is retrieved by
measuring the petal-like intensity profile of the reflected beam using a camera.
65
∆z (up to 0.4 m)
Laser
(520 nm )
Col
PC
SLM
Camera
Iris
lens lens
0.5 m
Water tank (clean water)
BS
BS
Figure 4.3: Experimental setup of the underwater ranging utilizing z-dependent angular rotation of the
spatially structured beam. PC: polarization controller. Col: collimator. BS: beam splitter. SLM: spatial
light modulator. PM: optical power meter.
Figure 4.4: Measured (a) intensity profiles and (b) rotating angle of the generated spatially structured beam
(∆ k
z
= 6.2m
− 1
) propagated through the air or clean water at different reflector distances. The solid black
lines indicate the linear relationship between the angular rotation (θ ) and reflector distance (z) in the air
and clean water.
4.3 Optical Ranging using a Single Structured Beam in Clean
Water
Figure 4.3 shows the experimental setup that utilizes the z-dependent angular rotation of a spatially struc-
turedbeamforopticalrangingincleanwater. Aspatiallightmodulatorisprogrammedwithaspecificphase
pattern to convert a free-space Gaussian beam (beam size of ∼ 7 mm) to the desired spatially structured
beam. In our experiment, ℓ
1
,ℓ
2
, and ∆ k
z
, are set to +1, -1 and 6.2 m
− 1
, respectively. A 4-f spatial filter is
66
usedtofilterouttheunmodulatedlightfromthespatiallightmodulator(SLM).Subsequently,thegenerated
spatiallystructuredbeamissenttoawatertank, propagatesthroughtheunderwatermedium, getsreflected
byareflector, andpropagatesbackalongthesameopticalpath. Thereflectedbeamiscapturedbyacamera
for angular rotation detection. The reflector can be moved along the optical path with a traveling range of
up to 0.4 m. The step size of the moveable reflector distance is fixed as 5 mm. The optical power of the
spatially structured beam before entering the water tank is set to ∼ -30 dBm.
Figure4.4(a)showsthemeasuredbeamprofilesatdifferentreflectordistances. Therotatingangleofthe
reflectedspatiallystructuredbeamchangesatdifferentreflectordistances. Atthesamereflectordistance,the
rotating angle of a transmitted beam in air is different from the rotating angle of the same beam ( i.e., same
∆ k
z
). Figure4(b)showsthatthemeasuredslopeofthedistance-dependentrotatinganglebetweenthecase
of air and clean water is∼ 147
◦ /400mm and∼ 106
◦ /400mm, respectively. The difference in rotating angles
between these two cases indicates that angular rotation (∆ θ ) at a given propagation distance changes in the
medium of different refractive indices [134]. Given the z-dependent angular rotation (∆ θ = |
2z∆ kz
nwater|ℓ1− ℓ2|
|
[134, 135]., the ranging information of the reflector can be obtained. The measured ranging error is <10 mm
with reflector distances varying from 0 to 0.4 m.
4.4 Optical Ranging using a Single Structured Beam in Turbid
Water
Furthermore, the scattering medium is emulated using a diluted commercial antacid solution (Maalox
®
)
[137] as shown in Fig. 4.5. Different concentration of the Maalox
®
solution results in different extinction
coefficient γ of the scattering medium. The value of γ can be measured by propagating a collimated beam
throughthescatteringmediumwithapathlengthofLandsubsequentlymeasuringthecorrespondingoptical
power(P
out
=P
in
e
− γL
)basedonBeer’slaw[137]. Duringtheangularrotationmeasurement,thecollimated
beam for extinction coefficient characterization is blocked out to reduce the background noise detected by
the camera.
67
Figure 4.5: Experimental setup of the underwater ranging utilizing z-dependent angular rotation of the
spatially structured beam. The scattering medium is emulated by a diluted commercial antacid solution.
The value of extinction ratio γ is characterized by measuring the optical power loss of a collimated Gaussian
beam.
Figure 4.6 (a) shows the measured beam profiles through underwater scattering with different extinction
coefficients γ . Whentheextinctioncoefficient γ increasesfrom1.8m
− 1
to9.4m
− 1
, theangularrotationand
the corresponding measured distance of the reflected beam remain similar at the same propagation distance
as shown in Figure 4.6 (b). This is to be expected since in our scattering cases with a small-field-of-view
system, the ballistic scattering dominates, leading to that (a) the relative phase delay between the two
modes tends not to be distorted during propagation and thus (b) the petal-like intensity profiles maintain
their shape and angular rotation [37, 133, 138].
Figure 4.7 (a) shows the measurement error under various scattering strengths. In clean water, the
measurement error at the reflector distance from 0 to 400 mm is ¡10 mm. Through underwater scattering
withincreasingscatteringstrength(e.g.,γ increasesorzincreases),themeasurementerrortendstoincrease.
With the extinction coefficient γ up to 9.4 m
− 1
and reflector distance up to 400 mm, the measurement
error is ¡20 mm. It should be noted that the camera’s exposure time is automatically adjusted during the
range measurement. When the extinction coefficient ( γ ) increases or propagation distance (2z) increases
the increased measurement error is potentially caused by the following: (i) scattering-induced power loss
increases; (ii) longer exposure time is needed to ensure sufficient beam detection; (iii) the beam wandering
affects the beam detection ( e.g., “blurred” intensity profile in measurement) for a longer exposure time, and
thus (iv) a relatively higher measurement error is observed. Figure 4.7 (b) shows the measured beam center
68
z =0.3 m
z = 0.05 m
= 9.4 m
!"
= 6.2 m
!"
= 1.8 m
!"
Clean water
0
1
Measured distance (m)
0
0.4
0.3
0.2
0.1
Reflector distance z (m)
0 0.1 0.2 0.3 0.4
Clean water
= 1.8 m
!"
= 6.2 m
!"
= 9.4 m
!"
Ideal
(a)
(b)
Figure4.6: (a)Measuredintensityprofiles ofthereflectedspatiallystructuredbeamthroughscatteringwith
different extinction coefficients ( γ ) at different reflector distances (z). (b) Measured distance with different
extinction coefficients.
when the reflector moves from z =0 m to 0.4 m. Such beam wandering effect is mostly compensated after
the beam detection.
Figure 4.9 (a) shows the adjusted exposure time under various extinction coefficients. When γ increases
from1.8m
− 1
to9.4m
− 1
,themaximumexposuretimeofthecameradetectorincreasesfrom∼ 1.6msto∼ 800
mswithafixedtransmittedopticalpowerof ∼ -30dBm. Itshouldbenotedthattheincreasedexposuretime
could potentially affect the refresh rate of the measurement in a practical ranging system. Figure 8 shows
69
Clean water
=
1.8 m
!"
=
6.2 m
!"
=
9.4 m
!"
Measurement error (mm)
Reflector distance z (mm)
0 400 0 400 0 400 0 400
0
20
10
(a)
~0.75mm
(b)
Figure 4.7: (a) Measurement error as a function of reflector distance. (b) Measured beam center when the
reflector is moving. Such beam wandering is measured and compensated after beam detection.
Adjustable
exposure time
Fixed
exposure
time

!"#
=0.4 ms

!"#
=0.2 ms

!"#
=0.2 ms

!"#
=0.2 ms

!"#
=0.2 ms

!"#
=1.6 ms
!"#
=12.8 ms
!"#
=6.4 ms
z = 0.05 m
(~3 dB loss)
z = 0.15 m
(~8 dB loss)
z = 0.2 m
(~11 dB loss)
z = 0.3 m
(~16 dB loss)
0
1
Figure4.8: Measuredintensityprofilesofthereflectedspatiallystructuredbeamwithandwithoutadjusting
exposure time. The inset number shows the exposure time for capturing the intensity profile.
the measured beam profile (normalized) through underwater scattering ( γ = 6.2 m
− 1
) with and without the
adjusting exposure time. As the reflector distance increases and the corresponding scattering-induced power
loss increases, the beam profile is less likely to show a petal-like shape if the exposure time is not sufficient
70
Measured distance (mm)
0
400
300
200
100
Reflector distance z (mm)
0 100 200 300 400
Fixed exposure
time (0.2 ms)
Adjustable exposure time
= 1.8 m
!"
= 6.2 m
!"
= 1.8 m
!"
= 6.2 m
!"
500
600
700
Exposure time (ms)
0.1
1
10
1000
100
= 1.8 m
!"
= 6.2 m
!"
= 9.4 m
!"
Reflector distance z (mm)
0 100 200 300 400
(a)
(b)
Figure 4.9: (a) Exposure time (adjustable) of the camera for different extinction coefficients at different
reflector distances. (b) Comparison of the distance measurement with and without adjusting exposure time.
for beam detection. Figure 4.9 (b) shows that, through underwater scattering (γ = 6.2 m
− 1
), the case with
a fixed exposure time of 0.2 ms tends to fail to retrieve the distance when z increases to ∼ 200 mm.
71
Chapter 5
Optical Half-adder of Phase Encoded Channels
5.1 Background and Motivation
Thedigitalhalf-adderisconsideredtobeanessentialbuildingblockofdigitalsignalprocessingandarithmetic
operations [139]. In general, a digital half-adder has two inputs (S
A
and S
B
) and generates two outputs
(Sum and Carry)[139] . Such a half-adder can be binary or M-ary (M>2), with M-ary being more spectrally
efficient [140, 141].
Several demonstrations of an optical half-adder have been reported, including (i) Sum and Carry genera-
tionwithtwomutuallycoherentbinaryinputswithamplitude-encodedsignalsatthesamecarrierwavelength
usingalinearinterferometer[142,143,144],(ii)SumandCarrygenerationwithtwobinaryinputsatdifferent
carrierwavelengthsusingnonlinearwavemixing[145,146],and(iii)Sumgenerationwithtwophase-encoded
M-ary (M≥ 4) inputs using four-wave mixing [147, 148]. It would be interesting to experimentally implement
an optical half-adder (both Sum and Carry generation) with M-ary phase-encoded inputs [70].
5.2 Nonlinear Wave Mixing
Nonlinear wave mixing is one of essential techniques enabling the optical signal processing [40]. One of
such wave mixing approaches is to utilize second-order χ (2)
nonlinear process which results in three wave
mixing and could manifests in the form of cascaded sum frequency generation (SFG), different frequencey
generation (DFG) as shown in Fig. 5.1. Specifically, such process works as follows, (a) SFG: pump and
72
c
(2)
SFG
pump signal SFG
f f f + =
dummy SFG converted
f f f - =
f
dummy
f
pump
f
SFG
QPM
c
(2)
DFG
f
signal
f
idler
Wavelength converted copy:
E
idler
~ E
signal
x E
pump
x E*
dummy
f
idler
~ f
signal
+ f
pump
-f
dummy
SFG: Sum frequency generation,
DFG: Difference frequency generation,
QPM: Quasi-phase matching
Cascaded SFG and DFG in PPLN
Figure 5.1: Concept of second-order χ (2)
nonlinear process of cascaded sum frequency generation and differ-
ence frequency generation (cSFG-DFG). PPLN: period-poled lithium niobate.
signal in the same frequency band (e.g., C-band) are firstly mixed together to generate a SFG term in a
differnet frequency band, subsequently (b) DFG: the generated SFG term interacts with the dummy pump
and converted in the original frequency band. In such process, the phase of the pump and the signal are
added together during the cascaded SFG-DFG process. One popular device for implementing χ (2)
nonlinear
process is period-poled lithium niobate (PPLN) waveguides [149].
5.3 Concept of Phase-encoded Optical Half Adder
Figure 5.2 shows the concept of the optical half-adder. A typical half-adder has two inputs (i.e., S
A
andS
B
)
and two outputs (i.e.,Sum and Carry) as shown in Fig. 5.2(a1). For a 4-ary half-adder, the possible input
and output states include S
A
{0, 1, 2, 3}, S
B
{0, 1, 2, 3}, Sum {0, 1, 2, 3}, and Carry {0, 1}. The truth
table of our 4-ary half-adder is shown in Fig. 5.2(a2).
Our optical half-adder is divided into two parallel processes [70]: (i) Sum generation, and (ii) Carry gen-
eration as shown in Fig. 5.2(b). For the Sum generation, a modulo addition is needed [141, 148]. As inputs,
two phase-doubled subcarrier signals (A
2
,B
2
) are encoded with four phase levels {π /4, 3π /4,5π /4,7π /4}.
Subsequently, the corresponding output (A
2
B
2
) is generated by adding together the phase of A
2
and B
2
(φ
A
2
B
2 = φ
A
2 +φ
B
2) with nonlinear wave mixing. The resultant output (i.e., Sum) is represented by four
phase levels{π /2,π ,3π /2,2π }. When the symbol state of addition is <4 (e.g., 1+2=3), the output phase of
A
2
B
2
will be simply added. When the symbol state of addition is ≥ 4 (e.g., 2+3=5), the output phase of
73
0 1 2 3
0 0 1 2 3
1 1 2 3 0
2 2 3 0 1
3 3 0 1 2
Sum
Carry
0 1 2 3
0 0 0 0 0
1 0 0 0 1
2 0 0 1 1
3 0 1 1 1
Input
!
Input
"
Input
!
Input
" Output Carry
Output Sum
Half
adder
012320...
012310...
001100...
Carry
020230...
Sum

!

!
(Sum)

!

!
0
1
2 3
0
1
2 3
0
1
2
3
×
+
∗

∗
(Carry)

∗

∗

∗

∗

0
1
2
3
0
1
2
3
0
1
2 3
0
1
2
3
4
5
6
3
2
1
0
4
5
6
0
1
2 3
+
1 0
×
×

#

$
(a1)
(a2)
(b)
Figure 5.2: Concept of optical half-adder. (a1) Schematic diagram of the 4-ary half-adder applying symbol-
to-symbol addition operation to the inputs. (a2) Relationship between the inputs and outputs of the 4-ary
half-adder. (b) Concept of a 4-ary phase-encoded optical half-adder. To generate Sum, Two inputs (A
2
,B
2
)
are encoded with four phase levels π /4, 3π /4,5π /4,7π /4 and the corresponding output (A
2
B
2
) is generated
by accumulating the phase of A
2
and B
2
with nonlinear wave mixing. The resultant output (i.e., Sum)
is represented by four phase levels π /2,π ,3π /2,2π .To generate Carry, two inputs (A, B) are encoded with
four phase levels ((-3π )/16, π /16,5π /16,9π /16), two inputs (A
∗ , B
∗ ) are simultaneously encoded with four
conjugate phase levels (3π /16, (-π )/16,(-5π )/16,(-9π )/16) and are fed together with A and B for nonlinear
wave mixing. The output (AB+A
∗ B
∗ ) is generated by combining the corresponding mixing terms AB and
A
∗ B
∗ . The resultant output (i.e., Carry) is represented by two phase levels (0,π ).
A
2
B
2
will be added and “wrap around”. For instance, with the two inputs being as 2 and 3 (corresponding
phase levels of 5π /4 and 7π /4), the phase of output A
2
B
2
will be added and “wrap around” to be π which
correspondstothestateof1. FortheCarrygeneration,thephase“wraparound”processneedstobetracked
[141]. In our approach, we utilize two input pairs (A, B) and (A
∗ , B
∗ ) as follows, (i) two inputs (A, B) are
encoded with four phase levels (-3π /16, π /16,5π /16,9π /16), and the phases of A and B are added where
the resulting states of AB are separated into the left and right half of the phase diagram, (ii) to squeeze the
added phase into two phase levels, A
∗ B
∗ with the conjugate phase is simultaneously generated with the two
phase-conjugate inputs (A
∗ and B
∗ ), and (ii) by coherently combining the optical field of AB and A
∗ B
∗ ,
the phase of the output (AB +A
∗ B
∗ ) are squeezed into two phase levels {0, π } which corresponds to two
states{0, 1}.
74
Outputs Phase Frequency

!"
=
!
+
"
−
#
$

!"
=
!
+
"
−
#
=
!
+
"
∗−∆−
#

∗

∗

!
∗
"
∗ =
!
∗+
"
∗−
#
$
=−(
!
+
"
)−
#
$

!
∗
"
∗ =
!
∗+
"
∗−
#
=
!
+
"
∗−∆−
#

&

&

!
"
"
" =
!
"+
"
"−
#
$
=2(
!
+
"
)−
#
$

!
"
"
" =
!
"+
"
"−
#
=
!
+
"
∗+2∆−
#
(b)
Inputs Phase Frequency

!

!

"

"

∗

!
∗ =−
!

!
∗ =
!
−∆

∗

"
∗ =−
!
'

"
∗ =
"
+∆

&

!
" =2
!

!
" =
!
+∆

&

"
" =2
"

"
" =
"
−∆
(c)
×
×
×
+
Carry
Sum

!

"

∗

∗

+
∗

∗
(Carry)
×
×
+
∆ ∆

$

$

$

$
(Sum)
×
QPM
(a)
∆ ∆
Wavelength
Figure 5.3: (a) Concept of utilizing nonlinear wave mixing to generate Sum and Carry simultaneously with
(b) the input subcarriers of S
A
and S
B
and (c) the output mixing terms AB,A
∗ B
∗ ,A
2
B
2
. φ
N
P
indicates the
phase noise of the pump. QPM: quasi-phase-matching.
The optical half-adder with phase-encoded inputs and outputs is implemented using nonlinear wave
mixing (e.g., using PPLN) as shown in Fig. 5.3. The input S
A
(S
B
) contains three phase-encoded subcarrier
signals A,A
∗ ,A
2
(B,B
∗ ,B
2
) which are encoded with the same data sequence and are generated with a
frequency offset ∆ f between the neighboring subcarrier copies. A,A
∗ and A
2
(B,B
∗ and B
2
) are generated
with a frequency offset of ∆ f. Through the cascaded SFG and DFG process of the inputs S
A
, S
B
and pump
P, the Sum and Carry can be generated simultaneously at different wavelengths. Specifically, the Carry is
generated by coherently combining the mixing terms AB and A
∗ B
∗ which requires AB and A
∗ B
∗ to share
the same phase noise. One way to implement this is to generate A and A
∗ (B and B
∗ ) from the same laser
source which shares the laser phase noise.
Wenotethat,inourproof-of-conceptdemonstration,thephase-conjugatesignals(A
∗ andB
∗ )andphase-
doubled signals (A
2
and B
2
) are generated together with the original phase-encoded signals (A and B) in
the electrical domain. In such a scheme, the electrical bandwidth of the modulator could be compromised.
75
One possible way to increase the electrical bandwidth utilization is to (i) only modulate the original phase-
encodedsignals,andsubsequently(ii)generatethosesignalcopiesintheopticaldomain(e.g.,usingfour-wave
mixing) [39].
5.4 Experimental Demonstration of Optical Half Adder for 5/10-
Gbaud 4-PSK Inputs
IQ
Mod.
AWG
OSA
Coh.
Rx
0.2 nm
PPLN
WDM
Mux
PC
Variable
delay line

!

"
!

"
"
IQ
Mod.
EDFA

∗

$

"
!

"
"

∗

$
99%
1%
Optical half-adder
Figure 5.4: Experimental setup of the optical half adder. AWG: arbitrary waveform generator. EDFA:
Erbium-doped fiber amplifier. PC: polarization controller. PPLN: periodically poled lithium niobate. OSA:
optical spectrum analyzer.
The experimental setup is shown in Fig. 5.4(a). We generate a 5-Gbaud (or 10-Gbaud) phase-encoded
subcarrier signal A in one IQ modulator together with the two subcarrier signal copies (phase-conjugate
signal A
∗ and phase-conjugate signal A
∗ ) with a frequency offset ∆ f. The frequency spacing ∆ f is chosen
as 15 GHz for the 5-Gbaud signal and 20 GHz for the 10-Gbaud signal. A similar signal-generation process
is applied to generate S
B
with an independent data sequence. The two generated phase-encoded signals are
amplified and combined with an amplified pump P. The center wavelengths of S
A
, S
B
and P are chosen
as ∼ 1546.5 nm, ∼ 1552.1 nm, and ∼ 1548.1 nm, respectively. Subsequently, the combined S
A
(A,A
∗ ,A
2
),
S
B
(B,B
∗ ,B
2
), P are sent to the PPLN with quasi-phase-matching (QPM) wavelength λ QPM
=∼ 1549.3
76
nm. The QPM wavelength is tuned by changing the temperature of PPLN to achieve maximum conversion
efficiency. The optical power at the PPLN input is ∼ 17 dBm for P, ∼ 14 dBm for S
A
, and ∼ 14 dBm for
S
B
. As the outputs, the Sum (A
2
B
2
) and Carry (AB +A
∗ B
∗ ) are generated with the frequency spacing
of 3∆ f=45 GHz for 5-Gbaud signals (3∆ f=60 GHz for 10-Gbaud signals). To select the desired output
generated in the nonlinear wave mixing process, an optical bandpass filter ( ∼ 0.2-nm bandwidth) is used at
theoutput. Thefilteredoutputchannels(SumandCarry)areseparatelysenttoacoherentreceiverfordata
recovery. As the operation of the optical half-adder is symbol-to-symbol, the symbol delay between S
A
and
S
B
is tuned and aligned by a variable delay line.

∗

"

∗

"
+
∗

∗

"

"

Wavelength (nm)
10 dB/div
1545 1550 1555
5 Gbaud(∆f = 15 GHz)
1 0
2 3

"

"
1 0
2 3
1
0
2
3

"

"
(sum)
0
1
2 3
1 0
+
∗

∗
(carry)
0
1
2
3
0
1
2 3

∗

∗
0
1
2
3
(a)
(b)
Figure 5.5: (a) Measured optical spectrum at the output of PPLN with 5-Gbaud 4-PSK channels. The
wavelength resolution is 0.1 nm. (b) Recovered constellation diagrams of the 5-Gbaud phase-encoded inputs
and outputs.
The optical power spectrum at the output of the PPLN is measured by an optical spectrum analyzer
(OSA) as shown in Fig. 5.5(a). The resolution of OSA is 0.1 nm. The Sum (A
2
B
2
) and Carry (AB+A
∗ B
∗ ) are generated at the wavelengths of ∼ 1550.2 nm and ∼ 1550.6 nm. The measured conversion efficiency is
∼ -23.9dBfortheSumgenerationand-19.9dBfortheCarrygeneration. Suchdifferencecouldbepotentially
due to the limited QPM bandwidth of the PPLN [150].
The recovered constellation diagrams of the 5-Gbaud inputs (A,A
∗ ,A
2
,B,B
∗ ,B
2
) and outputs (AB +
A
∗ B
∗ ,A
2
B
2
) are shown in Fig. 5.5(b). The input phase-encoded signals (A,B,A
∗ ,B
∗ ) and (A
2
,B
2
) are
77
recovered based on 8-PSK and 4-PSK constellations, respectively. The output Sum (A
2
B
2
) and Carry
(AB+A
∗ B
∗ ) are recovered based on the 4-PSK and BPSK modulation format, respectively.The measured
EVMs of the input signals (A,A
∗ ,A
2
,B,B
∗ ,B
2
) are <6%. The measured EVM of the output Sum (A
2
B
2
)
and Carry (AB+A
∗ B
∗ ) is <18% and <40%, respectively. The degradation of the output signals could be
due to the accumulated phase noise of S
A
and S
B
in nonlinear wave mixing.
(input)
(input)
Phase Phase
Measured phase levels Target phase levels

!

!
(Sum output)
Phase
+
!

!
(Carry output)
Phase
Figure 5.6: Receovered phase levels and the date sequence of 5-Gbaud inputs ( and ) and outputs (Sum and
Carry). The corresponding target phase levels are calculated based on the input data sequence.
Figure 5.6 shows the recovered phase levels and the data sequences of the 5-Gbaud input and output
channels. Every distinct phase level represents a specific symbol (numbers shown in the x-axis of Fig. 5.5).
The symbol-to-symbol arithmetic function of the optical half-adder is demonstrated by comparing the input
78
and output phase-encoded data sequences. It should be noted that there is phase ambiguity in the recovered
phase which could be potentially solved by using pilot sequence or differential coding [151].
10 Gbaud(∆f = 20 GHz)

∗

"

∗

"
+
∗

∗

"

"

Wavelength (nm)
10 dB/div
1545 1550 1555
(a)
10
#"
10
#$
10
#%
BER
10 15 20 25
OSNR (dB)
Sum
(5 Gbaud)
Carry
(5 Gbaud)
Sum
(10 Gbaud)
Carry
(10 Gbaud)
(b)
Figure 5.7: (a) Measured optical spectrum at the output of PPLN with 10-Gbaud 4-PSK channels. (b)
Measured BER performance of the 5-Gbaud/10-Gbaud channels.
Furthermore, the symbol rates of the input 4-PSK channels are varied from 5 Gbaud to 10 Gbaud. The
frequencyoffset∆ f ischangedfrom15GHzto20GHz, whichtakesintoconsiderationthetrade-offbetween
(a)theincreasedinter-channelcrosstalkduetotheincreasedchannelbandwidthwitharelativelysmaller∆ f,
(b) the reduced modulation efficiency due to the limited the electrical bandwidth of electrical IQ modulator
with a relatively larger ∆ f. Figure 5.7(a) shows the measured optical spectrum of the 10-Gbaud channels.
The conversion efficiency of the 10-Gbaud channels is ∼ -26 dB for Sum and∼ -20 dB for Carry. Compared
to the case of the 5-Gbaud signal, the conversion efficiency of the Sum is reduced, which could be due to the
limited QPM bandwidth in the PPLN [150].
The BER performance of the 5-Gbaud/10-Gbaud output channels is measured as shown in Fig. 5.7(b).
The bit error rate is measured by comparing the recovered data sequences (i.e., the output of optical half-
adder)withthecalculatedoutputbasedonthetwoinputdatasequencesof S
A
andS
B
. ThemeasuredBERs
of 5-Gbaud/10-Gbaud channels can be <3.8e-3. The estimated OSNR penalty of the 10-Gbaud outputs is
<5 dB for Sum and <10 dB for Carry compared with that of the 5-Gbaud output channels at the BER of
3.8e-3. Compared with the 5-Gbaud channels, the increased OSNR requirement of the 10-Gbaud channels
could be potentially due to that (a) the increased ASE noise with a larger channel bandwidth, and (b) the
increased channel crosstalk with less sufficient channel separation. Compared with the Sum generation, the
79
increased OSNR penalty of the Carry generation could be due to that (i) the input 4-PSK signals for Carry
generation with a phase difference of π /4 requires a larger euclidean distance than that of Sum generation
(phase difference of π /2), (ii) the Carry generation (AB+A
∗ B
∗ ) requires the coherent combination of two
mixing terms (AB and A
∗ B
∗ ) which is harder to optimize using the nonlinear mixing and is more sensitive
to the phase noise, and (iii) there are more adjacent channels to Carry as a by-product of the nonlinear wave
mixing which could induce higher inter-channel crosstalk.
80
Chapter 6
Conclusion
This thesis discusses various tunable and reconfigurable approaches for different optical systems. It covers
multiple topics including photonic integrated circuits, structured light, free-space optical communications,
andopticalsignalprocessing, mostofwhicharestillyoungandemergingresearchfields. Theresearchefforts
focused on these topics could potentially help enrich the fields of high-capacity optical communication, high-
resolution optical ranging, and flexible optical network.
81
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91

Abstract (if available)

Abstract There is a growing interest in structured light, especially beams carrying orbital angular momentum (OAM), for its unique spatial structure. OAM beams are characterized by a twisting phase front having an angular-dependent term exp(j*ℓ*theta), where theta is the azimuthal angle and ℓ is the OAM order and counts the number of 2pi phase shifts in the azimuthal directions. There are different types of OAM beams including (a) Laguerre-Gaussian (LG) beams which typically carry two discrete azimuthal and radial indices (ℓ, p), and (b) Bessel beams which have one discrete azimuthal index l and a continuous radial wavenumber kr.

On the one hand, OAM-carrying structured light provides a new degree of freedom and toolkit for the potential optical systems (e.g., high-capacity coherent communication, free-space optical link through a turbulent medium, or optical ranging). On the other hand, the manipulation of the structured light necessities the development of tunable and reconfigurable techniques (e.g., photonic integrated circuits or mitigation of free-space beam distortions).

This thesis will discuss (i) OAM-multiplexing links with tunable ℓ indices using an integrated pixel-array-based device, (ii) LG beam generation with both tunable ℓ and p induces using an integrated concentric circular antenna array, (iii) turbulence mitigation approaches for single-channel and multi-channel FSO links, (iv) optical underwater ranging through turbid water using a structured beam with OAM-carrying Bessel modes, and (v) optical half adder of 4-ary phase-encoded channels.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Song, Hao (author)

Core Title Optical communications, optical ranging, and optical signal processing using tunable and reconfigurable technologies

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2023-05

Publication Date 02/27/2023

Defense Date 02/23/2023

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

Tag OAI-PMH Harvest,optical communications,optical ranging,optical signal processing,structured light

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Willner, Alan (committee chair), Brun, Todd (committee member), Nakano, Aiichiro (committee member)

Creator Email samjohnbobjack@gmail.com,songhao@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC112755722

Unique identifier UC112755722

Identifier etd-SongHao-11487.pdf (filename)

Legacy Identifier etd-SongHao-11487

Document Type Dissertation

Format theses (aat)

Rights Song, Hao

Internet Media Type application/pdf

Type texts

Source 20230228-usctheses-batch-1008 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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Repository Name University of Southern California Digital Library

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