University of Southern California Dissertations and Theses

Using spatial modes for data transmission through the air and through the air-water interface

(USC Thesis Other)

Using spatial modes for data transmission through the air and through the air-water interface

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content

USING SPATIAL MODES FOR DATA TRANSMISSION THROUGH THE AIR
AND THROUGH THE AIR-WATER INTERFACE

by

Haoqian Song

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

August 2022

Copyright 2022 Haoqian Song
ii

Dedication

This dissertation is dedicated to my supportive parents, Jingshan Song and Fang
Li, and my respectful advisor, Professor Alan E. Willner.

iii

Acknowledgments
First of all, I would like to thank my advisor Professor Alan E. Willner, who
guides me during my study in the Ph.D. program. He not only provides support and
guidance for my research but also teaches me how to be a good person. The wisdom I
learned from him has benefited me a lot during my study at Optics Communications
Laboratory (OCLab) and will also be greatly helpful for the rest of my life. In addition,
I would like to thank Professor Moshe Tur, who provides me with insightful and
detailed suggestions for my research. I sincerely appreciate his help with my journey
toward the Ph.D. degree. I would also like to thank my dissertation defense committee
members Professor Stephan W. Haas and Professor Mercedeh Khajavikhan, and
qualification exam committee members Professor Andrea M. Armani and Professor
Keith Jenkins.
I sincerely appreciate the generous help from my current and previous colleagues:
Dr. Ahmed Almaiman, Dr. Ahmad Fallahpour, Dr. Amirhossein Mohajerin-Ariaei, Dr.
Changjing Bao, Dr. Cong Liu, Dr. Fatemeh Alishahi, Dr. Guodong Xie, Dr. Jing Du,
Dr. Long Li, Dr. Morteza Ziyadi, Dr. Peicheng Liao, Dr. Yinwen Cao, Dr. Yongxiong
Ren, Dr. Zhe Zhao, Amir Minoofar, Hao Song, Huibin Zhou, Karapet Manukyan, Kai
Pang, Kaiheng Zou, Nanzhe Hu, Narek Karapetyan, Runzhou Zhang, Xinzhou Su,
Yuxiang Duan, Zhe Wang. Moreover, I would also be so grateful for the support from
USC staff, particularly, Ms. Corine Wong, Ms. Diane Demetras, Ms. Gerrielyn Ramos,
Ms. Susan Wiedem, Mr. Andy S. Chen, and Mr. Theodore Low.
I want to extend my deepest appreciation to my collaborators, particularly
iv

Professor Eric G. Johnson, Professor Jerome K. Miller, and Professor Richard J.
Watkins from Clemson University; Professor Daeyoung Park from INHA University;
Professor Aristide Dogariu from University of Central Florida; Professor Greg Gbur
from University of North Carolina at Charlotte; Dr. Brittany Lynn from Naval
Information Warfare Center Pacific; Dr. Robert Bock from R-DEX Systems Inc.
Finally, I want to thank my parents. It is you who raised me and make me who I
am today.
v

Table of Contents
Dedication ................................................................................................................... ii
Acknowledgments ..................................................................................................... iii
List of Figures ........................................................................................................... vii
Abstract ................................................................................................................. xiv
Chapter 1 Introduction ........................................................................................... 16
1.1 Free-space optical transmission through the atmosphere ............................ 17
1.2 Free-space optical transmission through the air-water interface ................. 19
1.3 Thesis outline ................................................................................................ 21
Chapter 2 Investigation for the causes of modal coupling when OAM beams
propagate through the dynamic atmospheric turbulence .................. 22
2.1 Introduction................................................................................................... 22
2.2 Concept and experimental setup ................................................................... 23
2.3 Simulation and experimental results ............................................................. 26
2.4 Conclusion .................................................................................................... 28
Chapter 3 Pre-compensation of atmospheric turbulence effect using
combinations of OAM modes in uni- and bi-directional OAM
multiplexed FSO links ........................................................................... 29
3.1 Introduction................................................................................................... 29
3.2 Concept and experimental setup ................................................................... 31
3.3 Method for mode combination generation ................................................... 35
3.4 Experimental results ..................................................................................... 39
3.5 Conclusion .................................................................................................... 44
Chapter 4 Using two aperture pairs combined with multiple-mode receivers
and MIMO signal processing for enhanced FSO link tolerance to
turbulence and misalignment ................................................................ 45
4.1 Introduction................................................................................................... 45
4.2 Concept ......................................................................................................... 47
4.2 Simulation results ......................................................................................... 48
4.3 Experimental setup and results ..................................................................... 50
4.4 Conclusion .................................................................................................... 54
Chapter 5 Investigation of dynamic aerosol and dynamic air-water interface
curvature effects on OAM multiplexed FSO link ............................... 55
5.1 Introduction................................................................................................... 55
5.2 Concept and experimental setup ................................................................... 57
5.3 Results for air-water interface effects on OAM beams ................................ 62
vi

5.4 Results for air-water interface effects on OAM multiplexed link ................ 68
5.5 Conclusion .................................................................................................... 70
Chapter 6 Investigation of the 2-D modal coupling of an air-water
communication link through dynamic aerosol and water surface
curvature using LG beam ...................................................................... 72
6.1 Introduction................................................................................................... 72
6.2 Concept and experimental setup ................................................................... 73
6.3 Simulation and experimental results ............................................................. 76
6.4 Conclusion .................................................................................................... 81
References ............................................................................................................... 82

vii

List of Figures
Figure 1.1 Intensity and phase in the transverse plane of LG beams. 𝐿 𝐺 00
is
the Gaussian beam. We note that the phase of the beam is at z=0
(without propagation), there could be wavefront curvature if the
beam propagation distance is none zero [8]. ...................................... 16
Figure 1.2 Concept of optical beam propagation through the atmospheric
turbulence. The turbulence effects could induce beam wandering
and beam distortion. ........................................................................... 17
Figure 1.3 Concept of free space optical link between an airborne transceiver
and an underwater transceiver. There could be multiple “layers” of
environmental effect in such a link, including but not limited to
maritime turbulence, aerosol above the water, the water surface
curvature, and the underwater effect. In this dissertation, we
mainly investigate the effect of aerosol and water surface curvature.
........................................................................................................... 19
Figure 2.1 (a) The concept of OAM beam transmission through the dynamic
random turbulent medium. Such a turbulent medium could induce
distortion of the wavefront as well as beam wandering. (b) Both
the beam distortion and beam wandering would affect the spatial
amplitude and phase profile of the received beam and thereby
result in power coupling from the transmitted mode to neighboring
modes. ................................................................................................ 24
Figure 2.2 (a) Experimental setup. BS: beam splitter; M: mirror. The
turbulence is generated by a hot plate with a temperature of
~200°C. (b) The probability distribution of received power when
transmitting and receiving a Gaussian beam. The variance of
received power is ~0.17, and we use this value to characterize the
turbulence strength. (c) The example images of received intensity
profile for a Gaussian beam with and without turbulence effects. .... 25
Figure 2.3 (a) Experimentally measured beam wandering effect with and
without atmospheric turbulence. Each blue dot in the figure
corresponds to the beam center position (weighted by spatial
intensity profile) for one measurement. The total measurement
time is ~30 s and the sampling rate is ~200 Sa/s. (b) and (c) show
the experimentally measured and the simulated modal power
viii

coupling under lateral displacement and angular error, respectively.
OAM +1 is transmitted. ..................................................................... 26
Figure 2.4 (a) Simulated modal power distribution due to beam wandering
for OAM +1. In the simulation, we assume there is only
misalignment between the receiver and the incoming beam
without beam distortion. The simulation is based on the beam
wandering measurement shown in Fig. 2.3 (a). (b) Experimentally
measured modal power coupling for OAM +1 and +2, respectively.
The power on all the modes are measured simultaneously at a
sampling rate of 50k Sa/s over 20 s. .................................................. 27
Figure 3.1 The concept of pre-compensation in a uni-directional link and post
compensation for the backward channels in a bi-directional link by
applying an inverse transmission matrix. For the forward
propagating channels, each channel transmits a combination of
multiple OAM modes. After the beams propagate through the
turbulence, each channel will have little power on a designated
OAM mode and relatively high power on the mode intended to
receive due to interference. For the backward propagating
channels in the bi-directional link, each of the channels transmits
a single OAM mode. After applying the inverse matrix at the
backward receiver, the crosstalk could be mitigated. We note that
the beams in free space are coaxial with each other. Ch: channel. .... 31
Figure 3.2 The experimental setup. QPSK: quadrature phase-shift keying;
EDFA: erbium-doped fiber amplifier; PC: polarization controller;
Col: collimator; M: mirror; BS: beam splitter; SLM: spatial light
modulator. We note that the uni-directional link corresponds to the
forward link in this setup. .................................................................. 34
Figure 3.3 An example of the transmitted beams and their OAM mode
spectrum at the receiver. (a) The SLM patterns for single OAM
beam and two-OAM beam (beam α) generation in channel A, and
the intensity profile of generated beams. (b) The turbulence effect
on the transmitted beams. .................................................................. 35
Figure 3.4 The probe beams used to measure the phase term of the
transmission matrix. 𝐸 1
and 𝐸 2
are the complex beam profile of
OAM +1 and +2, respectively............................................................ 37
ix

Figure 3.5 (a)The intensity profile for the combination of OAM +1 and +2
after propagation. (b) The phase difference between OAM 𝑙 1
and
𝑙 2
after propagation. The phase difference is designed to be 0
without propagation. 𝑙 1
=+1. ............................................................... 38
Figure 3.6 (a-c) The normalized transmission intensity matrices and (d) BER
performance for the forward channels without and with
compensation. We note that channel A receives OAM 𝑙 = +1, and
channel B receives OAM 𝑙 = +2 . In the link without
compensation, channels A and B transmit OAM 𝑙 = +1 and 𝑙 =
+2, respectively. Beam α and β are the combinations of OAM +1
and +2 transmitted by channels A and B, respectively, when the
compensation is applied. .................................................................... 39
Figure 3.7 (a-c) The normalized transmission intensity matrices and (d) BER
performance for the backward channels without and with
compensation. Channels C and D transmit OAM 𝑙 = +1 and 𝑙 =
+2, respectively. In the link without compensation, channel C
receives OAM 𝑙 = +1, and channel D receives OAM 𝑙 = +2.
When the compensation is applied, channels C and D receive beam
α and beam β, respectively. The beam α and beam β here are the
same as the ones in Fig. 3.6. .............................................................. 40
Figure 3.8 The system performance under 6 turbulence realizations with and
without the compensation. The crosstalk for (a) the forward
channels and (c) backward channels. The measured BER for (b)
the forward channels and (d) backward channels. The OSNR is
16.8dB for the BER measurement. .................................................... 41
Figure 3.9 Measured BER and constellation diagrams for (a) forward and (b)
backward channels. The OSNR for each received channel is 16.8
dB. ...................................................................................................... 42
Figure 3.10 The normalized power coupling from the transmitted beam to
OAM 0 to OAM +3 under turbulence effects (a) without and (b)
with compensation. Beam 1,2,3, and 4 are four different
combination of OAM 0, +1, +2, and +3. All the beams are transmitted
by channel A. ..................................................................................... 43
Figure 4.1 The concept of the FSO link combining aperture diversity and
multimode receiver. In this link, multiple fundamental Gaussian
x

beams are transmitted between transmitter and receiver aperture
pairs. For each aperture pair, the turbulence effects, as well as the
aperture misalignment (e.g., lateral displacement), would induce
power loss on the fundamental Gaussian mode (OAM 0) and
power coupling to its neighboring modes. At the receiver, the data
over multiple modes and multiple receiver apertures are digitally
combined using MIMO DSP. ............................................................ 47
Figure 4.2 (a) The simulated outage probability under 10,000 turbulences
with 0-mm and 2-mm lateral displacement. (b) Simulated BER
under 10 turbulence realizations with 2-mm lateral displacement
and -7.5 dBm transmitted power. Simulated outage probability
with different numbers of (c) aperture pairs and (d) recovered
modes. AP: aperture. d: lateral displacement. The noise floor at
each detector is -32 dBm, which is similar to our experimental
setup. .................................................................................................. 49
Figure 4.3 The experimental setup. EDFA: erbium-doped fiber amplifier; PC:
polarization controller; Col: collimator; BS: beam splitter; PD:
photon detector; ATT: attenuator; LO: local oscillator. .................... 50
Figure 4.4 The recovered power on OAM modes (a1) without displacement
and turbulence, (a2) with turbulence, and (a3) with displacement.
The recovered power on OAM modes 0 and +1 under lateral
displacement (b) without turbulence and (c) with turbulence. The
beam separation is 12 mm for (a-c). (d) The recovered power on
OAM modes 0 and +1 for both apertures pairs under 2-mm spatial
separation. (e) The power coupling between the two apertures
pairs with 2-mm and 12-mm separation. ........................................... 51
Figure 4.5 (a) The degradation of BER performance under turbulence and
misalignment. (b) and (c) are the BER performances of different
compensation schemes without and with turbulence, respectively.
The turbulence realization is the same as Fig. 4.4 (c). The aperture
separation is 12 mm. (d) BER performance under 8 realizations
with 0-mm and 2-mm lateral displacement, where the total
transmitted power is -7.5-dBm. AP: aperture. ................................... 53
Figure 5.1 Concept of the OAM multiplexed link through the dynamic air-
water interface. The dynamic aerosol and water surface curvature
would induce time-varying power loss of the transmitted mode and
xi

crosstalk to neighboring modes. θ: angle of incidence; Tx:
transmitter; Rx: receiver; Ch: channel. .............................................. 58
Figure 5.2 (a) The potential causes of modal power loss and power coupling
under (a1) aerosol and (a2) curvature effects. (b) The wavefront
distortion, beam wandering, and spatially dependent scattering &
absorption could affect the unique intensity and phase profile of
the received OAM beam. The example images of OAM -1 under
aerosol and curvature effects. The cross mark in the image shows
the beam center position under the no-effect case. ............................ 59
Figure 5.3 (a) The experimental setup for the OAM multiplexed link through
the dynamic air-water interface. The aerosol flow is generated by
a vaporizer, and the curvature of the interface is induced by wind.
Col: collimator; PPLN: periodically poled lithium niobate; BS:
beam splitter; SLM: spatial light modulator; FSM: fast steering
mirror; PSD; position-sensitive detector; HWP: half-wave plate;
DMD: digital micromirror device. (b) Example images of the
curvature at the air-water interface. (c) The positions of the beam
center over ~1 min under various air-water interface effects with
and without tracking. Under aerosol case 2, the received power is
too low to be measured by the camera. Moreover, the beam is out
of the camera for most of the measurements under curvature case
2 without tracking, and therefore there are fewer data points............ 61
Figure 5.4 The received power on the transmitted modes and their
neighboring modes under various curvature and aerosol conditions
for (a) OAM -1 and (b) OAM +2. The beam propagation distance
in aerosol is ~7 cm. The orange bar shows the received power
fluctuation range during the multiple measurements over >5 s, and
each measurement takes ~11 ms. The incident angle is 0 (normal
incidence). The power is normalized by the maximum received
power for the transmitted mode in the absence of interface effects.
........................................................................................................... 63
Figure 5.5 Simulated received OAM spectrum of OAM -1 under the lateral
displacement and angular error derived from the beam wandering
measurements on the left side. In this simulation, we assume there
is only beam misalignment without any other beam distortions.
The beam diameter is ~ 3 mm and the wavelength is 532 nm. .......... 65
xii

Figure 5.6 The power on each mode when (a) OAM -1 and (b) OAM +2 are
transmitted. Each measurement takes ~11 ms. The aerosol and
curvature conditions with the same measurement number are
different for different scenarios and different transmitted modes,
and therefore they can’t be compared directly. The incident angle
is 0 (normal incidence). The power is normalized by the maximum
received power for the transmitted mode in the absence of
interface effects. ................................................................................. 67
Figure 5.7 The received power on the transmitted mode and power coupling
to neighboring modes under different angles of incidence. The
orange bar shows the received power fluctuation range for each
mode. The power is normalized by the maximum received power
for the transmitted mode without curvature. There are no aerosol
effects for these measurements. ......................................................... 68
Figure 5.8 The BER performance of the OAM -1 and +2 under various effects.
The measurement of each data point takes >30 s. We note that the
interface conditions are different for all these measurements. The
incident angle is 0 (normal incidence). .............................................. 69
Figure 5.9 The BER performance for discrete measurements (each takes ~4
s) versus time under various air-water interface effects when OAM
-1 and +2 are multiplexed. The four BER curves in each plot are
not measured at the same time, and therefore should not be
compared with each other directly. The incident angle is 0 (normal
incidence). .......................................................................................... 70
Figure 6.1 (a) The concept of LG beam propagates through the dynamic
aerosol and dynamic water surface curvature. The aerosol and
curvatures could induce degradations to the transmitted beams,
including beam wandering and beam distortion. (b) The
degradation of amplitude and phase profiles under beam distortion
and beam wandering. Both effects could lead to modal power
coupling. ............................................................................................ 73
Figure 6.2 Experimental setup. Col: collimator; PPLN: periodically poled
lithium niobite; SLM: spatial light modulator; HWP: half-wave
plate; BS: beam splitter; PSD: position-sensitive detector; FSM:
fast steering mirror; The dashed black lines are electrical cables. ..... 74
xiii

Figure 6.3 The recorded beam mass center positions (weighted by spatial
intensity profile) under various air-water interface effects with and
without tracking. The beam wandering is mainly along one
direction under the curvature effect, which could be due to that our
curvature is mainly along one direction in the water tank and
thereby the beam would mainly wander along that direction. The
tracking system, which partially mitigated the misalignment at the
receiver, is always applied during the modal coupling and BER
measurements. .................................................................................... 76
Figure 6.4 The measured power for transmitted mode (𝐿 𝐺 11
) and the power
coupled to other modes with tracking. (a) The power is mainly on
the transmitted mode and there are some modal power couplings.
For these cases, we can measure a BER below the FEC limit. (b)
The power loss of the transmitted mode and power coupling to
other modes become higher. Our system can’t efficiently measure
BER for these cases. The power is normalized by the maximum
received power for the transmitted 𝐿 𝐺 11
without interface effects. ... 77
Figure 6.5 (a) The experimentally measured beam wandering effect. (b) The
simulated modal power coupling under the assumption that there
is only misalignment without beam distortion. (c) The measured
modal coupling with tracking. This modal coupling could be due
to the combination of beam wandering and beam distortion. The
power is normalized by the maximum received power for 𝐿 𝐺 11

without interface effects. .................................................................... 78
Figure 6.6 BER performance of a 1 Gbit/s OOK link carried by 𝐿 𝐺 11
with
tracking. The measurement of each data point takes >30 s. Due to
that the air-water interface effects are dynamic, the aerosol and
curvature conditions could be slightly different for all these
measurements. .................................................................................... 80

xiv

Abstract
There has been a growing interest in free-space optical (FSO) communications
due to its potential for higher capacity and higher privacy as compared with
conventional radio-frequency techniques. One potential approach that could further
enhance the capacity and robustness of an FSO link is by using structured beams with
designated spatial amplitude and phase profiles.
Using Laguerre Gaussian (LG) beams is one choice for such structured beams.
LG beams could be characterized by two modal indices l and p, l represents the number
of 2π phase shifts in the azimuthal direction of the wavefront, and p+1 represents the
number of concentric amplitude rings in the radial direction. We note that one subset
of LG modes is orbital angular momentum (OAM) modes, which could be
characterized by the index l. LG beams with different orders (with different l and/or p
values) are mutually orthogonal, which enables them to be multiplexed, coaxially
transmitted, and demultiplexed with little inherent crosstalk.
One potential scenario of interest for FSO links is the data transmission through
the atmosphere. However, a key challenge for such an FSO link is the atmospheric
turbulence, which would degrade the link performance by inducing power loss and
modal power coupling. This first part of the dissertation will investigate using spatial
modes for links through atmospheric turbulence: (i) investigation for the causes of
OAM modal coupling through a dynamic random turbulent medium; (ii) pre-
compensation of atmospheric turbulence effect using combinations of OAM modes in
uni- and bi-directional OAM multiplexed FSO links; (iii) using two aperture pairs
combined with multiple-mode receivers and multiple-input and multiple-output
xv

(MIMO) signal processing for enhanced FSO link tolerance to turbulence and
misalignment.
Another scenario of interest is the data transmission through a dynamic air-water
interface. In this case, the beam passes through the dynamic aerosol above the water
and the dynamically changing water surface curvature at the air-water interface. This
part of the dissertation will investigate the degradations induced by the dynamic air-
water interface: (i) investigation of dynamic aerosol and dynamic air-water interface
curvature effects on OAM multiplexed FSO links; (ii) investigation of the 2-D modal
coupling of an air-water communication link through dynamic aerosol and water
surface curvature using LG beam.

16

Chapter 1
Introduction
There has been a growing interest in FSO communication links because of their
potential for higher capacity and higher privacy as compared with radio frequency
techniques [1–4]. One recent technique to further increase the capacity and robustness
of FSO links is by utilizing structured beams with designated spatial amplitude and
phase profiles [5–7].
One example of such structured beams is the LG modes, which could be
characterized by two modal indices l and p [8]. Specifically, l represents the number
of 2π phase shifts in the azimuthal direction of the wavefront, and p+1 represents the
number of concentric amplitude rings in the radial direction. We note that one subset
of LG modes is OAM modes, which could be characterized by the index l [9–11].
Figure 1.1 shows the intensity and phase profiles of 𝐿 𝐺 00
(Gaussian beam), 𝐿 𝐺 01
,
𝐿 𝐺 10
and 𝐿 𝐺 11
beams as examples.

Figure 1.1 Intensity and phase in the transverse plane of LG beams. 𝐿 𝐺 00
is the Gaussian beam. We
note that the phase of the beam is at z=0 (without propagation), there could be wavefront curvature if
the beam propagation distance is none zero [8].
17

LG modes with different orders (with different l and/or p values) are mutually
orthogonal. This orthogonality enables the following: (i) LG beams with different
orders could be combined, co-axially transmitted, and separated with little inherent
crosstalk. As a result, multiple orthogonal beams, each located on a different LG mode
and carrying independent data, can be transmitted simultaneously between a single
transmitter/receiver aperture pair [6,12–14]. This form of multiplexing is known as
mode-division-multiplexing (MDM); (ii) a distorted or misaligned Gaussian beam
could be decomposed into the combination of multiple LG modes, such that one can
increase the total received power by simultaneously recovering multiple modes as
compared with single-mode receivers [15–19].
1.1 Free-space optical transmission through the atmosphere

Figure 1.2 Concept of free space optical link through the atmospheric turbulence. The turbulence effects
could induce beam wandering and beam distortion towards.
FSO communications has gained much interest due to its potential for higher
capacity and lower probability of interception [1–4]. However, one challenge for the
FSO link is the atmospheric turbulence, which is caused by the inhomogeneous
temperature of the atmosphere. Such non-uniform temperature distribution would
result in a spatial dependent refractive index of the atmosphere along the beam
18

propagation path, leading to wavefront distortion and wandering of the transmitted
beam [20–22], as shown in Fig. 1.2. For a single-channel link using a conventional
Gaussian beam, turbulence could induce power loss at the receiver due to the
inefficient coupling of a distorted or misaligned Gaussian beam into a single-mode-
fiber-based receiver [21–23]. For a mode multiplexed link, turbulence could also
induce power coupling from transmitted modes to their neighboring modes, resulting
in inter-channel crosstalk [24–28]. A laudable goal is to mitigate the turbulence effects
for both the single-channel link and mode-multiplexed muti-channel link. This thesis
focuses on the following topics:
1. Investigation for the causes of modal coupling when orbital-angular-
momentum beams propagate through the dynamic atmospheric turbulence [29]:
the contribution of beam wandering and beam distortion towards the modal
power coupling of transmitted OAM modes is investigated by simulation and
experiment. The modal power coupling variation over time is recorded and the
probability distribution of received power on each mode is analyzed. The results
present the contributions of beam wandering and beam distortion to the
experimentally measured modal coupling under turbulence effects.
2. Pre-compensation of atmospheric turbulence effect using combinations of OAM
modes in uni- and bi-directional OAM multiplexed FSO links [30]: a unique
combination of two OAM modes is generated using a designed phase pattern in
each of the two channels. Such mode combinations could perform the inverse
function of turbulence-induced crosstalk and thereby mitigate the channel
crosstalk. Moreover, this approach only needs in-fiber power detection for
19

determining the compensation phase pattern without using wavefront sensors.
3. Using two aperture pairs combined with multiple-mode receivers and MIMO
signal processing for enhanced FSO link tolerance to turbulence and
misalignment [31]: in this approach: (a) each of multiple transmitter apertures
transmits a single fundamental Gaussian beam carrying the same data stream,
(b) each of multiple receiver apertures detects the signals that are coupled to
multiple OAM modes, and (c) MIMO algorithm is utilized to recover the data
over multiple modes and receivers. The simulation and experiment show that
this approach could potentially reduce the link outage probability.
1.2 Free-space optical transmission through the air-water interface

Figure 1.3 Concept of free space optical link between an airborne transceiver and an underwater
transceiver. There could be multiple “layers” of environmental effect in such a link, including but not
limited to maritime turbulence, aerosol above the water, the water surface curvature, and the underwater
effect. In this dissertation, we mainly investigate the effect of aerosol and water surface curvature.
For similar reasons as using FSO links through the atmosphere, using FSO
communications for underwater links has also gained attention, especially when
compared to acoustic techniques [32–35]. Whereas links through the air can be
20

performed in the visible or near-infrared (IR) region, underwater links tend to be in
the blue-green region to minimize water absorption induced optical losses [32–35].
An interesting scenario is the transmission of data between a transceiver above
the water and one below the water, such as links between a drone/plane and an
underwater sensor/submarine [36–40], as shown in Fig. 1.3. In this case, the optical
beam would pass through a dynamic, complex, and potentially harsh air-water
interface, which can have dynamic aerosol above the water and dynamic curvature of
the water surface [41–43]. This thesis focuses on the following topics:
1. Investigation of dynamic aerosol and dynamic air-water interface curvature
effects on OAM multiplexed FSO links [44]: two coaxial OAM beams, each
carrying an independent data channel, are simultaneously transmitted through
the dynamic aerosol and dynamic water surface curvature. We experimentally
investigate (a) the modal power loss for the transmitted mode, and modal power
coupling between OAM modes under different aerosol and water surface
curvature conditions, and (b) the degradation of OAM multiplexed links under
air-water interface effects.
2. Investigation of the 2-D modal coupling of an air-water communication link
through dynamic aerosol and water surface curvature using LG beam [45]: one
single LG beam with both non-zero azimuthal index and non-zero radial index
is transmitted through the dynamic aerosol and water surface curvature. The
experimental results show that the interface effects would induce both beam
wandering and beam distortion. The contributions of beam wandering and beam
distortion toward the modal power loss and modal power coupling are analyzed
21

by simulation and experiment.
1.3 Thesis outline
This dissertation is organized as the following: Chapter 2 investigates the
causes of modal coupling when OAM beams propagate through the dynamic
atmospheric turbulence; Chapter 3 shows the pre-compensation of atmospheric
turbulence effect using combinations of OAM modes in uni- and bi-directional
OAM multiplexed FSO links; Chapter 4 presents using two aperture pairs
combined with multiple-mode receivers and MIMO signal processing for
enhanced FSO link tolerance to turbulence and misalignment; Chapter 5
investigates the dynamic aerosol and dynamic air-water interface curvature
effects on OAM multiplexed FSO links; Chapter 6 investigates the 2-D modal
coupling of an air-water communication link through dynamic aerosol and water
surface curvature using LG beam.

22

Chapter 2
Investigation for the causes of modal coupling when OAM
beams propagate through the dynamic atmospheric
turbulence
2.1 Introduction
OAM beams have been utilized for various applications, including sensing,
imaging, and communications [6,46–49]. An important characteristic of OAM beam
propagation is the modal purity of the beam, such that coupling of power into
neighboring modes could degrade the usefulness of the beam. A key issue for OAM
beams is to understand the beam degradation due to interaction with various types of
random medium [20]. One common type of random medium is the turbulent
atmosphere, which has a spatially dependent refractive index distribution that can
cause beam degradations [25,50,51].
Specifically, it has been reported that OAM beams passing through the turbulent
atmosphere can suffer from power coupling into other modes, thereby reducing modal
purity [26–28]. However, there is a fundamental question as to the primary causes of
the modal coupling. Two main causes might be (i) beam distortion: light-medium
interaction can vary the amplitude and phase across the transverse beam profile,
causing modal coupling [26–28], and (ii) beam wandering: random turbulent medium
can cause the beam to wander at the receiver such that the detector “measures” modal
coupling of the misaligned beam (e.g., angular tilt and/or lateral displacement) [52–
23

54]. Currently, it is not so clear as to the relative contribution of each of these effects
to the power coupling to other modes for dynamic random atmospheric turbulence.
In this chapter, we experimentally measure the relative contributions of beam
wandering and beam distortion to the modal coupling of OAM beams when propagate
through dynamic atmospheric turbulence [29]. The contribution of beam wandering is
investigated by simulation, where we (i) measure the wandering of the beam center
experimentally, and (ii) simulate the corresponding modal coupling assuming there is
only misalignment without beam distortion. Subsequently, we analyze the contribution
of modal coupling from beam distortion by comparing the experimental measurement
results (both beam distortion and beam wandering) and simulated misalignment-only
cases. For the turbulence we generated, the variance of received power is ~0.17 when
transmitting and receiving a Gaussian beam. Our simulation and experimental results
for dynamic turbulence show that: (i) the beam wandering could induce up to ~-12 dB
average modal power coupling from OAM +1 to OAM 0 and +2 (simulation); (ii) the
experimental measurement shows an increase in such average modal coupling to ~-9
dB; (iii) we believe the extra modal coupling in the experiment as compared with the
simulation results could be due to beam distortion.
2.2 Concept and experimental setup
Figure 2.1 (a) shows the concept of OAM beam propagation through dynamic
atmospheric turbulence. The inhomogeneous spatial distribution of atmosphere
temperature would lead to a spatially dependent refractive index distribution, resulting
in both beam wandering and beam distortion. Specifically, (i) the “larger-scale
24

structure” of the refractive index variation may induce random refraction of the OAM
beam and thereby induce beam wandering [4]. Such beam wandering would result in
a lateral displacement and/or angular tilt between the incoming beam and the receiver,
such that the amplitude and phase profiles of received beams are no longer azimuthally
symmetric [55]; (ii) the “smaller-scale structure” would induce spatial dependent
phase delay across the wavefront, such that the received spatial amplitude and phase
profiles would be distorted [4,25]. Both beam wandering and beam distortion would
lead to the power coupling from the transmitted modes to the neighboring modes, as
shown in Fig. 2.1 (b).

Figure 2.1 (a) The concept of OAM beam transmission through the dynamic random turbulent medium.
Such a turbulent medium could induce distortion of the wavefront as well as beam wandering. (b) Both
the beam distortion and beam wandering would affect the spatial amplitude and phase profile of the
received beam and thereby result in power coupling from the transmitted mode to neighboring modes.
To investigate the contribution of beam wandering and beam distortion to the
modal power coupling, we simulate the modal power coupling under the beam-
wandering-only cases and experimentally measure the modal coupling with turbulence
generated by a hot plate [56]. To characterize the turbulence effect, we transmit one
single Gaussian beam and measure the fluctuation of the received power over 20 s
(with a sampling rate of 50k Sa/s), and the probability distribution of received power
is shown in Fig. 2.2 (b). The received power has a variance of ~0.17, which is within
25

the regime for relatively weak turbulence [20]. The images of the received Gaussian
beam with and without atmospheric turbulence are shown in Fig. 2.2 (c) as examples.

Figure 2.2 (a) Experimental setup. BS: beam splitter; M: mirror. The turbulence is generated by a hot
plate with a temperature of ~200°C. (b) The probability distribution of received power when
transmitting and receiving a Gaussian beam. The variance of received power is ~0.17, and we use this
value to characterize the turbulence strength. (c) The example images of received intensity profile for a
Gaussian beam with and without turbulence effects.
Our experimental setup is shown in Fig. 2.2 (a). The laser at 1550 nm is coupled
into free space and converted into an OAM beam with designated order by using a
multi-plane-light-conversion (MPLC) based OAM generator [57], and the diameter of
the generated beam is ~3 mm. Subsequently, the OAM beam propagates through the
atmospheric turbulence generated by the hot plate and is captured by the receiver. At
the receiver end, we split the power into two branches by a BS. In one branch, we
utilize a camera (~200 Sa/s sampling rate and <1 ms exposure time for each sample)
to capture the intensity profile of the incoming beam for beam wandering measurement.
In the other branch, the incoming beam is coupled into fiber by the MPLC-based OAM
demultiplexer [57], which could convert different OAM components of the incoming
beam into different fiber outputs. Such that the power on multiple OAM modes could
be detected simultaneously by using photodetectors and a data-acquisition device
(with a sampling rate of 50k Sa/s).

26

2.3 Simulation and experimental results

Figure 2.3 (a) Experimentally measured beam wandering effect with and without atmospheric
turbulence. Each blue dot in the figure corresponds to the beam center position (weighted by spatial
intensity profile) for one measurement. The total measurement time is ~30 s and the sampling rate is
~200 Sa/s. (b) and (c) show the experimentally measured and the simulated modal power coupling under
lateral displacement and angular error, respectively. OAM +1 is transmitted.
To investigate the beam wandering effect on the model power coupling, we
experimentally measure the beam center variation over ~30 s for an incoming OAM
+1 beam using the camera (6000 samples in total with a sampling rate of ~200 Sa/s),
as shown in Fig. 2.3 (a). Each blue dot in the figure represents the beam center position
weighted by the spatial intensity distribution. The results show that the turbulence
generated by the hot plate induces a maximum beam offset of ~0.5 mm. The measured
beam center offset could be caused by lateral displacement, angular error, or the
combination of both effects. In our experiment, (i) the lateral displacement is
considered to be equal to the beam center offset, (ii) the angular error is considered to
be the beam center offset divided by the beam propagation distance from the turbulent
area to the receiver (~2 m), and (iii) the pointing error includes both types of
27

misalignments. We first experimentally measure the potential modal coupling due to
misalignment. Various lateral displacement and angular error are induced by tuning
the mirror M2, which is mounted on a tunable stage. The experimental results in Figs.
2.3 (b1) and (c1) show that the lateral displacement and angular error could induce the
modal power loss and modal power coupling. Moreover, the simulation results in Figs.
2.3 (b2) and (c2) show a similar trend as the experimental measurement.

Figure 2.4 (a) Simulated modal power distribution due to beam wandering for OAM +1. In the
simulation, we assume there is only misalignment between the receiver and the incoming beam without
beam distortion. The simulation is based on the beam wandering measurement shown in Fig. 2.3 (a).
(b) Experimentally measured modal power coupling for OAM +1 and +2, respectively. The power on
all the modes are measured simultaneously at a sampling rate of 50k Sa/s over 20 s. Ave: average.
To further investigate the contribution of the beam wandering effect to the modal
coupling, we simulate the potential modal coupling under the beam wandering
measured in Fig. 2.3 (a). Specifically, we (i) experimentally measure the beam
wandering effects, (ii) simulate the potential modal coupling under different beam
offsets (assuming there is only misalignment without beam distortion), and (iii) draw
the statistical distribution of received power on each mode, as shown in Fig. 2.4 (a).
The simulation results for OAM +1 show that under the lateral displacement only case,
the average modal power coupling from OAM +1 to OAM 0 and +2 are ~-22 and ~-
28

19 dB, respectively, and the modal purity of OAM +1 is degraded by < 1 dB. With the
angular error, the average modal power coupling to OAM 0 and +2 increase to ~-15
and ~-13 dB respectively, and the average modal purity decreases to ~-1 dB. The
results show that the misalignment-induced modal power coupling and modal power
loss are mainly due to angular error effects for our system.
Moreover, we also experimentally measure the modal coupling, in which both
the beam wandering and beam distortion may contribute to the modal coupling of the
incoming beam. In the experimental measurement shown in Fig. 2.4 (b), we observe
an average modal purity degradation of ~-4 dB for OAM +1, and an average modal
coupling of ~-9 dB and ~-10 dB to OAM 0 and +2, respectively. We believe that the
extra modal purity degradation and the extra modal coupling as compared with our
simulation are mainly due to the beam distortion. We note that the imperfect system
for our experiment may also affect the modal purity and modal power coupling.
2.4 Conclusion
In this chapter, we investigate the causes of modal coupling when OAM beams
propagate through dynamic atmospheric turbulence. The results show that both the
beam wandering and beam distortion could induce modal power coupling from the
transmitted mode to the neighboring modes, and we further analyze their contributions
toward the modal coupling. We note that the contribution of modal power coupling
from beam wandering and beam distortion could be dependent on the turbulence
condition, their contributions could be different for other turbulence strength or
turbulence generated by other approaches.
29

Chapter 3
Pre-compensation of atmospheric turbulence effect using
combinations of OAM modes in uni- and bi-directional
OAM multiplexed FSO links
3.1 Introduction
As mentioned in previous chapters, OAM-based multi-channel FSO links could
be degraded by atmospheric turbulence, which could induce power coupling from
transmitted modes to their neighboring modes, resulting in inter-channel
crosstalk [24–28].
Previous reports have shown several approaches for mitigating the inter-channel
crosstalk induced by atmospheric turbulence, such as by: (a) pre- and/or post-
compensation for the turbulence-induced wavefront distortion using adaptive
optics [58–62] and (b) inter-channel crosstalk mitigation at the receiver using digital
signal processing (DSP) techniques in the electrical domain, such as the algorithms
used in MIMO systems [63–67]. It might be valuable to develop an alternative
atmospheric turbulence effects mitigation technique that: (a) can compensate for the
turbulence effects at the transmitter to avoid increasing receiver complexity, (b) only
needs in-fiber power measurement instead of using wavefront sensors to measure the
spatial amplitude and phase profile of the optical beams, and (c) can mitigate the
crosstalk from other data channels without recovering all the data channels at the
receiver. Recently, one report showed an approach by simulation that “precode” each
30

data-carrying beam with multiple OAM modes [68], which is similar to beam
structuring using spatial modes [69–71]. By designing the complex weights of the
multiple modes carried by each beam, the modes could perform the inverse function
of atmospheric turbulence-induced crosstalk [68]. Such an approach is analogous to
the pre-beamforming schemes for inter-user interference mitigation in multi-user
wireless links using radio waves [72,73], as well as visible light [74–76].
In this chapter, we experimentally demonstrate the mitigation of atmospheric
turbulence-induced crosstalk using phase patterns that apply the inverse transmission
matrix for pre-compensation in the uni-directional FSO links with two 100-Gbit/s
OAM-multiplexed channels [30]. In the uni-directional link, the transmitter of each
channel transmits a combination of two OAM modes by applying designed phase
patterns to the emitted beam. To design the phase patterns, we: (i) measure the
transmission matrix based on several in-fiber power measurements, and (ii) use the
inverse transmission matrix to calculate the phase pattern for each channel. In the uni-
directional link, the crosstalk between two OAM channels is reduced by up to 21 dB
and is always below -10 dB for the 6 turbulence realizations when using the pre-
compensation phase patterns. We also investigate applying such phase patterns to
backward propagating channels in a bi-directional OAM multiplexed link for post-
compensation. For the two backward propagating OAM multiplexed channels, the
inter-channel crosstalk is reduced by up to 16 dB, when applying such phase patterns
at the backward receivers. Moreover, a BER below the 7% forward error correction
(FEC) limit is achieved under most of the 6 turbulence realizations when
compensations are applied to the forward and the backward channels.
31

3.2 Concept and experimental setup

Figure 3.1 The concept of pre-compensation in a uni-directional link and post compensation for the
backward channels in a bi-directional link by applying an inverse transmission matrix. For the forward
propagating channels, each channel transmits a combination of multiple OAM modes. After the beams
propagate through the turbulence, each channel will have little power on a designated OAM mode and
relatively high power on the mode intended to receive due to interference. For the backward propagating
channels in the bi-directional link, each of the channels transmits a single OAM mode. After applying
the inverse matrix at the backward receiver, the crosstalk could be mitigated. We note that the beams
in free space are coaxial with each other. Ch: channel.
The concepts of the uni-directional and bi-directional OAM multiplexed links
are shown in Fig. 3.1 In the uni-directional link, the inverse transmission matrix is
applied using a compensation phase pattern at the transmitter for each channel, so that
the signal from each transmitted channel is carried by the combination of two OAM
modes with designed complex weights. The weights are calculated based on the
inverse of the complex transmission matrix under the corresponding turbulence
realization, which will be discussed in section 3.3. After combining the beams from
32

the two channels at the output port of the transmitter, the data-carrying beams from
both channels become coaxial. When the beams are transmitted through the turbulence,
the signals on the two transmitted modes will be coupled to their neighboring modes
and experience interference in those modes. Thus, the channels could have little power
on the designated modes and relatively high power on the others. By receiving the
mode on which the undesired channel has little power, the desired channel could be
recovered with little inter-channel crosstalk. The same concept can be applied to
recover the second channel when receiving another mode. Moreover, in the bi-
directional link, the phase patterns used for pre-compensation in the forward link could
also be used at the receiver for post-compensation. The beam from each of the two
backward channels carries a single OAM mode. The two channels are multiplexed so
that the transmitted beams are coaxial with each other as well as with the beams from
the forward channels. With the effect of turbulence, the wavefront of the beam will be
distorted and the signal on each OAM mode will be coupled to its neighboring modes.
At the receiver, the incoming beams are demultiplexed with the phase patterns that
have the same phase distribution as the pre-compensation patterns used in the forward
link. The patterns will perform the inverse function of turbulence-induced crosstalk so
that the inter-channel crosstalk could be reduced.
Fig. 3.2 shows the experimental setup for the forward and backward links. We
note that the uni-directional link corresponds to the scenario in which the signals are
transmitted through the forward link in this setup. A 100-Gbit/s quadrature-phase-
shift-keying (QPSK) signal is generated and fed to the transmitters of both the forward
and backward links. At each of the two transmitters, the signal is split into two
33

branches by a 50/50 coupler. The two copies of signals are decorrelated by sending
them through fibers with different lengths. In the forward link, the two signals are
coupled into free space through their corresponding collimators and projected onto
two SLMs respectively. The SLMs tailor the intensity and phase profiles of the
incoming Gaussian beams and generate designed beams with a beam diameter of ~3
mm. In the absence of turbulence compensation, the generated beams from channels
A and B are OAM +1 and OAM +2, respectively. When pre-compensation is applied,
the generated beam from each of the two channels will be a weighted combination of
OAM +1 and +2. The weights for the OAM modes in each channel are calculated
based on the inverse of the complex transmission matrix. The details of the
transmission matrix measurement and phase pattern generation are discussed in the
next section. The beams generated from the two channels are then combined using a
beam splitter so that the two beams are coaxial with each other. The combined beams
are then transmitted through a phase plate that is used for turbulence emulation [25].
The Fried parameter of the emulated turbulence is 𝑟 0
=1 mm, which corresponds to
weak to moderate turbulence [25]. At the receiver of the forward channels, the
incoming coaxial beams are coupled into a multi-plane-light-conversion-based OAM
converter [77]. The converter couples the incoming beams to different fiber output
ports based on their OAM mode order. The signals on OAM +1 and OAM +2 are
received for channels A and B, respectively, and then detected with homodyne
detection. For the bi-directional link, the signals are transmitted through a backward
link that is coaxial with the forward link. The signals for the two backward channels
are fed into designated ports of the OAM converter at the backward transmitter, so that
34

channels C and D transmit OAM +1 and OAM +2, respectively. At the output of the
backward transmitter, the generated beams are coaxial with each other as well as with
the beams in the forward link. The beams are then transmitted through the same
turbulence as the forward link. In the absence of compensation, the SLM-3 at the
backward receiver will down-convert the OAM +1 and +2 to a Gaussian beam for
receiving the signals from channels C and D respectively. When the compensation is
applied, the SLM will load the beam generation patterns in channels A and B for
receiving channels C and D, respectively. For each backward channel, the phase
patterns would weight and down-convert OAM +1 and OAM +2 to the Gaussian beam
simultaneously, where the signal from the undesired backward channel will experience
destructive interference. The resulting Gaussian beam is then coupled into fiber
through a collimator for signal detection. We note that typical bi-directional links may
have similar transceivers for the forward and backward links. However, there also
might be scenarios that require asymmetric systems, where it could be desirable that
one transceiver has lower complexity than the other one (e.g., a ground-based
transceiver communicates with a flying transceiver [78,79]).

Figure 3.2 The experimental setup. QPSK: quadrature phase-shift keying; EDFA: erbium-doped fiber
amplifier; PC: polarization controller; Col: collimator; M: mirror; BS: beam splitter; SLM: spatial light
modulator. We note that the uni-directional link corresponds to the forward link in this setup.
As an example, the compensation phase patterns used for beam generation in
35

channel A and the intensity profiles of the generated beams are shown in Fig. 3.3 (a).
As can be seen from the figure, the intensity profile of the combination of OAM +1
and +2 (beam α) is no longer a donut shape because of the interference between two
OAM modes. When OAM +1 from channel A is transmitted through the turbulence,
its power will couple to their neighboring modes and have a -16.9 dBm power on
OAM +2. However, the power coupling to OAM +2 drops to -28.5 dBm when beam
α is transmitted by channel A due to the destructive interference on OAM +2.

Figure 3.3 An example of the transmitted beams and their OAM mode spectrum at the receiver. (a)
The SLM patterns for single OAM beam and two-OAM beam (beam α) generation in channel A, and
the intensity profile of generated beams. (b) The turbulence effect on the transmitted beams.
3.3 Method for mode combination generation
The design of such phase patterns is based on the inverse matrix of the
transmission matrix. In a system composed of n different channels each transmitting a
unique OAM mode, the transmission matrix could describe the complex amplitude of
crosstalk from one of the transmitted OAM modes among 𝑙 1
, 𝑙 2
, …, 𝑙 𝑛 to the other
n-1 modes during the propagation. The transmission matrix could be described by [68]:
𝐶 = (
𝑐 11
⋯ 𝑐 1𝑛 ⋮ ⋱ ⋮
𝑐 𝑛 1
⋯ 𝑐 𝑛𝑛
) (1)
where 𝑐 𝑥𝑦
is the complex amplitude for the signal coupled from OAM 𝑙 𝑦 to OAM 𝑙 𝑥 .
36

The inverse of the matrix is described by:
𝐶 −1
= (
𝑀 11
⋯ 𝑀 1𝑛 ⋮ ⋱ ⋮
𝑀 𝑛 1
⋯ 𝑀 𝑛𝑛
) (2)
where 𝑀 𝑥𝑦
is the element at the x-th row and y-th column of the inverse matrix. To
compensate for the turbulence-induced crosstalk, the complex weight of the
transmitted OAM mode 𝑙 1
, 𝑙 2
, …, 𝑙 𝑛 in the m-th channel could be described by
𝑀 1𝑚 / √∑ |𝑀 𝑘𝑚
|
2 𝑛 𝑘 =1
, 𝑀 2𝑚 / √∑ |𝑀 𝑘𝑚
|
2 𝑛 𝑘 =1
, …, 𝑀 𝑛𝑚
/ √∑ |𝑀 𝑘𝑚
|
2 𝑛 𝑘 =1
,
respectively [68]. When the beam from the m-th channel is “precoded” with such an
OAM combination and transmitted through the turbulence, it will have relatively high
power on OAM mode 𝑙 𝑚 and little power on the other n-1 OAM modes after the
transmission. By receiving OAM mode 𝑙 𝑚 , the signal from the m-th channel could be
recovered.
In this experiment, the transmission matrix of the two modes multiplexed link
(forward link) could be described by [68]:
𝐶 = (
𝑐 11
𝑐 12
𝑐 21
𝑐 22
) = (
𝑎 11
𝑒 𝑗𝜃
11
𝑎 12
𝑒 𝑗𝜃
12
𝑎 21
𝑒 𝑗𝜃
21
𝑎 22
𝑒 𝑗𝜃
22
)
= (
𝑒 𝑗𝜃
11
0
0 𝑒 𝑗𝜃
22
)(
𝑎 11
𝑎 12
𝑒 𝑗 ( 𝜃 12
−𝜃 11
)
𝑎 21
𝑒 𝑗 ( 𝜃 21
−𝜃 22
)
𝑎 22
) (3)
where 𝑎 𝑥𝑦
and 𝜃 𝑥𝑦
are the amplitude and phase of the complex coefficient 𝑐 𝑥𝑦
. The
OAM values 𝑙 1
and 𝑙 2
are +1 and +2 respectively. Because the diagonal matrix on the
left side doesn't affect the amplitude of modal coupling between OAM 𝑙 1
and 𝑙 2
, both
𝜃 11
and 𝜃 22
are set to 0 for convenience. Thus, the matrix could be constructed by
measuring values of amplitude 𝑎 11
, 𝑎 12
,𝑎 21
, 𝑎 22
as well as the phase difference 𝜃 21
−
37

𝜃 22
, 𝜃 12
− 𝜃 11
.

Figure 3.4 The probe beams used to measure the phase term of the transmission matrix. 𝐸 1
and 𝐸 2
are
the complex beam profile of OAM +1 and +2, respectively.
In this experiment, the value of 𝑎 11
, 𝑎 12
,𝑎 21
, and 𝑎 22
are calculated based on the
transmission intensity matrix:
(
𝑎 11
𝑎 12
𝑎 21
𝑎 22
) = (
√𝑃 11
√𝑃 12
√𝑃 21
√𝑃 22
) (4)
where 𝑃 𝑥𝑦
is the power coupling from OAM 𝑙 𝑦 to OAM 𝑙 𝑥 . The phase difference
𝜃 21
− 𝜃 22
, and 𝜃 12
− 𝜃 11
could be measured by transmitting four probe beams and
measuring the received power of the corresponding OAM modes [49,80,81]. The
measurement of 𝜃 12
− 𝜃 11
is shown in Fig. 3.4 as an example. As shown in the figure,
four different combinations of OAM 𝑙 1
and 𝑙 2
(i.e., OAM +1 and +2) are transmitted
by channel A as probe beams, each having a designed phase difference between the
modes. At the receiver, the power on OAM +1 is measured for each of the four
transmitted beams and the 𝜃 12
− 𝜃 11
is calculated based on the equation [49,80,81]:
𝜃 12
− 𝜃 11
= {
𝑎𝑟𝑐𝑡𝑎𝑛 (
𝐼 3𝜋 /2
−𝐼 𝜋 /2
𝐼 0
−𝐼 𝜋 ) , 𝐼 0
> 𝐼 𝜋 𝜋 + 𝑎𝑟𝑐𝑡𝑎𝑛 (
𝐼 3𝜋 /2
−𝐼 𝜋 /2
𝐼 0
−𝐼 𝜋 ) , 𝐼 0
< 𝐼 𝜋 (5)
𝐼 0
, 𝐼 𝜋 /2
, 𝐼 𝜋 and 𝐼 3𝜋 /2
are the measured intensity for the four transmitted probe
38

beams. Similarly, the value of 𝜃 21
− 𝜃 22
could also be calculated based on the power
measurement of four transmitted beams when receiving OAM +2. Based on the
measurement result, the phase pattern used to generate such beams could be designed
with the approaches for complex field generation [82–84].

Figure 3.5 (a)The intensity profile for the combination of OAM +1 and +2 after propagation. (b) The
phase difference between OAM 𝑙 1
and 𝑙 2
after propagation. The phase difference is designed to be 0
without propagation. 𝑙 1
=+1.
We note that the generated beam may “rotate” during the propagation due to the
Gouy phase [10]. Fig. 3.5 (a) shows the simulated beam profile of a combination of
OAM +1 and +2 after 0 m, 2 m, and 4 m propagation as an example. The rotation
might be caused by the variation of the phase difference between the two OAM modes.
Fig. 3.5 (b) shows a scenario where the phase difference between OAM 𝑙 1
and 𝑙 2
is
designed to be 0 without propagation. The phase difference could vary during the
propagation, depending on the value of 𝑙 2
. For this approach, the probe beams and
signal-carrying beams traverse the same optical path, such that they would experience
similar propagation effects. Therefore, the measured transmission matrix from the
probe beam would incorporate the effects of turbulence and beam propagation (e.g.,
Gouy phase [10]) experienced by the signal-carrying beams. In this scenario, where
39

probe beams and signal carrying beams are coaxially transmitted by the same distance,
the crosstalk could be mitigated without pre-knowledge of the propagation distance.
3.4 Experimental results

Figure 3.6 (a-c) The normalized transmission intensity matrices and (d) BER performance for the
forward channels without and with compensation. We note that channel A receives OAM 𝑙 = +1, and
channel B receives OAM 𝑙 = +2. In the link without compensation, channels A and B transmit
OAM 𝑙 = +1 and 𝑙 = +2, respectively. Beam α and β are the combinations of OAM +1 and +2
transmitted by channels A and B, respectively, when the compensation is applied.
In this experiment, we first measure the performance of the pre-compensation
approach in a uni-directional link (forward link). Fig. 3.6 shows the normalized
transmission intensity matrix both with and without turbulence. As can be seen in Fig.
3.6 (b), with the turbulence effect, the inter-channel crosstalk increases to -8.7 dB and
-5.5 dB for channels A and B respectively in the absence of compensation. Fig. 3.6 (c)
shows the transmission intensity matrix with pre-compensation, where beam α and β
are the combinations of OAM +1 and +2 transmitted by channels A and B, respectively.
40

As shown in the figure, the inter-channel crosstalk decreases to -22.1 dB when
receiving OAM +1, and -17.8 dB when receiving OAM +2. The BER performance for
the forward channels is shown in Fig. 3.6 (d). The figure shows that, by applying pre-
compensation phase patterns in the forward link, the BER performance could be
improved for both forward channels.

Figure 3.7 (a-c) The normalized transmission intensity matrices and (d) BER performance for the
backward channels without and with compensation. Channels C and D transmit OAM 𝑙 = +1 and 𝑙 =
+2, respectively. In the link without compensation, channel C receives OAM 𝑙 = +1, and channel D
receives OAM 𝑙 = +2. When the compensation is applied, channels C and D receive beam α and beam
β, respectively. The beam α and beam β here are the same as the ones in Fig. 3.6.

We then use the compensation phase patterns applied in the forward link for
post-compensation and demultiplexing in the backward link. Fig. 3.7 shows the
crosstalk and BER performance of the backward channels under the same turbulence
as in Fig. 3.6. Through using the compensation patterns (i.e., beam generation patterns
in the forward link) as the receiver patterns, the crosstalk decreases from -8.9 dB and
41

-4.2 dB to -19.7 dB and -22.1 dB for channels C and D, respectively. We note that the
channels C and D receive beam α and β, respectively, when the compensation is
applied. Additionally, the BER performance is also improved for both backward
channels when the compensation phase patterns are applied.

Figure 3.8 The system performance under 6 turbulence realizations with and without the compensation.
The crosstalk for (a) the forward channels and (c) backward channels. The measured BER for (b) the
forward channels and (d) backward channels. The OSNR is 16.8dB for the BER measurement.
Moreover, we rotate the turbulence emulator to different positions to further
investigate the performance of both pre- and post-compensation under various
turbulence realizations. For each turbulence realization, we re-measure the
transmission matrix and generate the corresponding phase patterns. Fig. 3.8 (a) and (b)
shows the crosstalk and BER performance for the forward channels. As can be seen,
the inter-channel crosstalk decreases for the forward channels when the compensation
phase patterns are applied. The BER performance of the channels under an OSNR of
42

16.8 dB is also improved under these turbulence realizations, such that the forward
channels realize a BER below the 7% FEC limit (3.8×10
−3
) under the 6 turbulence
realizations. Fig. 3.8 (c) and (d) show the crosstalk and BER performance of the
backward channels with and without post-compensation under the 6 turbulence
realizations. We note that the 6 turbulence realizations in Fig. 3.8 (c) and (d) are the
same as the ones in Fig. 3.8 (a) and (b). As can be seen in the figures, the crosstalk
performances of the backward channels are improved and the BER of the channels is
under the 7% FEC limit (3.8×10
−3
) for 5 turbulence realizations. The performance
difference between the forward and backward channels might be caused by the
imperfect alignment.

Figure 3.9 Measured BER and constellation diagrams for (a) forward and (b) backward channels. The
OSNR for each received channel is 16.8 dB.
43

In addition, we measure the BER performance of the forward and backward
channels with pre- and post-optical compensation or post-digital MIMO equalization
under the emulated turbulence. For this measurement, each channel transmits a 10-
Gbit/s QPSK signal and the detection scheme is heterodyne detection. As shown in
Fig. 3.9, both compensation schemes could improve the BER performance.

Figure 3.10 The normalized power coupling from the transmitted beam to OAM 0 to OAM +3 under
turbulence effects (a) without and (b) with compensation. Beam 1,2,3, and 4 are four different
combination of OAM 0, + 1, +2, and +3. All the beams are transmitted by channel A.
Finally, we investigate the potential for generating the combinations of 4 OAM
modes (OAM 0 to +3) using the approach to perform destructive interference on 3 of
the 4 OAM modes, such that it could be potentially applied in a system with more than
two channels (e.g., four channels). For this measurement, all the beams are transmitted
by channel A and we measure the power coupled to the OAM modes from 0 to +3. As
can be seen in Fig. 3.10 (a), with the turbulence effect, the power will be coupled to
the OAM modes from 0 to +3 when transmitting single OAM modes. When
transmitting beams 1, 2, 3, and 4 (i.e., different combinations of multiple OAM modes),
44

the normalized power on the desired mode is 13 dB higher than the modal power
coupling to other modes in the worst-case scenario of this measurement, as shown in
Fig. 3.10 (b).
3.5 Conclusion
In this chapter, we experimentally demonstrate the pre-compensation of
atmospheric turbulence-induced crosstalk using phase patterns that apply inverse
transmission matrix in the uni-directional FSO links for two 100-Gbit/s OAM-
multiplexed channels. We also investigate using these phase patterns for post-
compensation in a bi-directional link. Our results show that the inter-channel crosstalk
could be reduced by up to 21 dB. Moreover, the scheme could be applied to the links
with more than two channels by measuring a transmission matrix that describes the
power coupling between more modes, and each of the channels will transmit a
combination of more than two OAM modes. We note that, with increasing the matrix
size, the number of required measurements may also increase, resulting in a higher
requirement of the measurement and feedback speed.

45

Chapter 4
Using two aperture pairs combined with multiple-mode
receivers and MIMO signal processing for enhanced FSO
link tolerance to turbulence and misalignment
4.1 Introduction
As mentioned in previous chapters, FSO communication links can provide high
data throughput but are relatively sensitive to various system deleterious effects [4,85].
For a single-channel link using a conventional Gaussian beam, there could be various
degradations: (i) atmospheric turbulence can distort the wavefront or cause beam
wandering of a Gaussian beam and induce power fluctuations at the receiver [21–23],
and (ii) misalignment between the transmitter and receiver apertures can induce link
power loss [86,87]. Part of the link loss in these two scenarios is due to the inefficient
coupling of a distorted or misaligned Gaussian beam into a single-mode-fiber-based
receiver.
There have been various approaches to mitigate degradations, reduce outage
probability, and enhance the recovery of the original signal for the single-mode-fiber
receiver. One approach is to use adaptive optics, which generally requires wavefront
sensing, tunable optical elements, and a feedback loop [88]. Other approaches for link
robustness improvement include using MIMO DSP potentially combined with either
(i) aperture diversity in which multiple copies of the same data stream are transmitted
and received using multiple apertures [89], or (ii) multiple-mode receivers that recover
46

power coupled from the fundamental Gaussian mode into other modes [15–19,90].
This second multiple-mode receiver approach uses the fact that turbulence and
misalignment can induce power coupling from the fundamental Gaussian mode into
other orthogonal modes; indeed, a single-mode-fiber detector would then not
efficiently receive the power coupled into non-Gaussian modes [23]. Reports have
shown that the simultaneous recovery in the receiver of the power that has been
coupled into other orthogonal modes can help mitigate the link loss caused by
atmospheric turbulence [15–19] and aperture misalignment [90]. This was reported for
linearly polarized (LP) modes [16–19,90], and OAM modes [15].
In this chapter, we utilize aperture diversity combined with multiple-mode
receivers and MIMO DSP to demonstrate enhanced tolerance to atmospheric
turbulence and spatial misalignment in a 10-Gbit/s QPSK FSO link [31]. Specifically,
we (a) transmit multiple fundamental Gaussian beams carrying the same data channel,
(b) detect the power that is coupled to multiple OAM modes at each receiver aperture,
and (c) use MIMO DSP to recover the original data from signals recovered from
multiple receiver apertures and modes. Our simulation shows that the outage
probability could be reduced from >0.1 to <0.01. We also simulate the potential link
performance under different numbers of aperture pairs and recovered spatial modes.
Moreover, in the experimental demonstration, two Gaussian beams (OAM 0) carrying
the same data stream are transmitted and the signals on OAM 0 and OAM +1 from
both apertures are recovered. With this approach, we measure a ~10-dB power-penalty
reduction for a BER at the 7% FEC limit for a 10-Gbit/s QPSK signal.
47

4.2 Concept

Figure 4.1 The concept of the FSO link combining aperture diversity and multimode receiver. In this
link, multiple fundamental Gaussian beams are transmitted between transmitter and receiver aperture
pairs. For each aperture pair, the turbulence effects, as well as the aperture misalignment (e.g., lateral
displacement), would induce power loss on the fundamental Gaussian mode (OAM 0) and power
coupling to its neighboring modes. At the receiver, the data over multiple modes and multiple receiver
apertures are digitally combined using MIMO DSP.
The concept of our approach is shown in Fig. 4.1. At the transmitter, a single
fundamental Gaussian beam is transmitted at each of the apertures and the transmitted
beams carry the same data channel. The transmitted beams would be affected by (i)
atmospheric turbulence, and (ii) misalignment. Both effects could induce power loss
for the fundamental Gaussian mode and the power coupling to higher-order modes.
Our approach involves using OAM as a tool at the receiver. Indeed, we transmit one
fundamental Gaussian beam from each transmitter aperture. The OAM modes are
utilized as a modal basis at the receiver to recover the power that is coupled from the
fundamental Gaussian mode into higher-order modes, as might be caused by
turbulence or misalignment. Such power would normally be lost when being received
by a single-mode fiber. Additionally, for a proper implementation of the transmitter
48

and the receiver apertures, the degradation effects for each Gaussian beam (OAM 0)
would be different. Such characteristics could also be utilized for enhancing link
robustness [89]. Therefore, we recover the signals from multiple OAM modes and at
the multiple receiver apertures using MIMO DSP to improve the link robustness for a
single data channel. We note that we sum up the power from all the recovered OAM
modes at each receiver as signal power. Any recovery of the power that is coupled
from the fundamental Gaussian mode to other OAM modes is “helping” the signal
recovery since the power would otherwise have been lost and is now received as more
signal power.
4.2 Simulation results
In order to model our experiment and also explore a wider parameter space, we
simulate the atmospheric turbulence when using our approach. Specifically, we
simulate the turbulence using a single phase plate with a Fired parameter of 1 mm [25],
which has the same configuration as our experiment. The diameters of the fundamental
Gaussian beams are ~3 mm, the aperture separation is 12 mm, and the propagation
distance is ~1 m. Fig. 4.2 shows the simulated system performance under 10,000
turbulence realizations. The outage probability refers to the percentage of turbulence
realizations where the BER is above the 7% FEC limit. The BER calculation is based
on the simulated signal-to-noise ratio (SNR) instead of the simulated data sequence.
Specifically, we (i) calculate the total signal power from all the receiver apertures and
recovered modes, (ii) simulate the SNR as the total signal power divided by the total
noise power, and (iii) calculate the BER using SNR. The optical noise power (receiver
49

noise) is -32 dBm for each recovered mode at each receiver, which is similar to our
experiment.

Figure 4.2 (a) The simulated outage probability under 10,000 turbulences with 0-mm and 2-mm lateral
displacement. (b) Simulated BER under 10 turbulence realizations with 2-mm lateral displacement and
-7.5 dBm transmitted power. Simulated outage probability with different numbers of (c) aperture pairs
and (d) recovered modes. AP: aperture. d: lateral displacement. The noise floor at each detector is -32
dBm, which is similar to our experimental setup.
Fig. 4.2 (a) shows that our approach reduces the outage probability from >0.1 to
<0.01 under the turbulence effects and 2-mm lateral displacement when the
transmitted power is ~1 dBm (The threshold 0.01 is selected as an example.). The
reason might be that a lower BER is achieved by recovering the power from multiple
modes and apertures. Fig. 4.2 (b) shows the simulated BER performance under ten of
the turbulence realizations as examples. Fig. 4.2 (c) and (d) show the system
performance improvement when using more aperture pairs or recovering more OAM
modes. When using 4 aperture pairs, the required power for an outage probability
50

<0.01 is reduced by ~5 dB compared with a single multiple-mode receiver.
Additionally, ~7 dB less power is required for an outage probability <0.01 when
recovering 4 modes at each of the receiver apertures instead of covering a single
Gaussian mode. We note that the turbulence simulation and emulation approach used
in this chapter is an approximation and may not fully characterize the propagation of
OAM beams in real turbulence [20]. More advanced approaches could be applied to
further enhance the turbulence simulation and emulation accuracy [20,91,92].
4.3 Experimental setup and results

Figure 4.3 The experimental setup. EDFA: erbium-doped fiber amplifier; PC: polarization controller;
Col: collimator; BS: beam splitter; PD: photodetector; ATT: attenuator; LO: local oscillator.
Subsequently, we experimentally demonstrate a link using two aperture pairs
each recovering two OAM modes. The experimental setup is shown in Fig. 4.3. A 10-
Gbit/s QPSK signal is split into two branches and coupled into free space through
collimators, which generate fundamental Gaussian beams with diameters of ~3 mm.
After being combined by a beam splitter, the two beams are parallel to each other with
a designed spatial separation (initially 12 mm). The beams are then transmitted
through a single-phase-plate turbulence emulator as a demonstration of the concept.
The phase plate has a phase distribution that follows Kolmogorov spectrum statistics
51

with an effective Fried parameter of 1 mm [25]. At the receiver, the beams are reflected
by a mirror on the linear stage 2 (displacement controller) and then collected by the
MPLC-based multiple-mode receivers [77], where different OAM modal components
are coupled to different fiber outputs. In our experiment, the signals on OAM modes
0 and +1 from both receiver apertures are recovered. The detected signals are
processed and combined using the MIMO offline DSP.

Figure 4.4 The recovered power on OAM modes (a1) without displacement and turbulence, (a2) with
turbulence, and (a3) with displacement. The recovered power on OAM modes 0 and +1 under lateral
displacement (b) without turbulence and (c) with turbulence. The beam separation is 12 mm for (a-c).
(d) The recovered power on OAM modes 0 and +1 for both apertures pairs under 2-mm spatial
separation. (e) The power coupling between the two apertures pairs with 2-mm and 12-mm separation.
In this experiment, we first characterize the link performance under one of the
turbulence realizations as an example to show the potential performance improvement.
As shown in Fig. 4.4 (a2), with turbulence effects, the two OAM 0 beams experience
a ~10 dB and ~6 dB power loss, respectively. Moreover, their modal power coupling
52

to OAM +1 increases to -19.5 dBm and -11.3 dBm, respectively. Additionally,
misalignment could also affect the power loss of the fundamental Gaussian mode and
power coupling to other modes [55]. The beam spatial amplitude and phase profile
along the azimuthal direction of the receiver center could be described by an OAM
mode spectrum. Ideally, the received fundamental Gaussian beam has an azimuthally
symmetric beam profile. Under misalignment effects, the received beam profile is no
longer azimuthally symmetric, which could lead to a variation of the received OAM
spectrum (e.g., modal power coupling). As an example, the received OAM spectrum
under 2-mm lateral displacement is shown in Fig. 4.4 (a3). Fig. 4.4 (b) shows that the
power on OAM 0 decreases with the increase of lateral displacement and the power
coupling to OAM +1 is also affected. The difference between the two apertures might
be caused by the imperfect alignment. Fig. 4.4 (c) shows that the turbulence could
further affect the power on OAM 0 and +1, and the two apertures are affected
differently. We note that the separation between two apertures may affect the system
performance. In our experiment, the two beams are still affected differently under a 2
mm separation, as shown in Fig. 4.4 (d). This might be caused by the small turbulence
Fried parameter. Moreover, there would be power coupling between the two apertures
under a 2-mm separation, as shown in Fig. 4.4 (e). Such power coupling might affect
the link performance.
We then investigate the BER performance of the system under lateral
displacement and the turbulence of Fig. 4.4 (c) with 12-mm beam separation. The
transmitted power is defined as the total power of the transmitted channel in free space.
As shown in Fig. 4.5 (a), the 1, 2, and 3-mm lateral displacement could induce ~3, ~9,
53

and ~20-dB power penalty at the FEC limit, respectively, for a single fundamental
Gaussian beam (OAM 0). The turbulence induces an extra power penalty of up to 14
dB (with 2-mm lateral displacement). Through recovering OAM 0 and +1 from both
apertures, the power penalty is reduced by up to ~10 dB as shown in Fig. 4.5 (c).
Moreover, compared with only using aperture diversity or a multiple-mode receiver,
their combination further reduces the power penalty at the FEC limit by up to ~7 and
~5 dB, respectively. MIMO DSP is always applied for signal recovery.

Figure 4.5 (a) The degradation of BER performance under turbulence and misalignment. (b) and (c) are
the BER performances of different compensation schemes without and with turbulence, respectively.
The turbulence realization is the same as Fig. 4.4 (c). The aperture separation is 12 mm. (d) BER
performance under 8 realizations with 0-mm and 2-mm lateral displacement, where the total transmitted
power is -7.5-dBm. AP: aperture.
To further investigate the performance of our scheme, we measure the BER
under 8 different turbulence realizations (i.e., different positions of the phase plate).
The total transmitted power is -7.5 dBm. As shown in Fig. 4.5 (d), the system with
misalignment is further degraded compared with the aligned system, and the
54

combination of aperture diversity and multiple-mode receivers could potentially
provide a lower BER.
4.4 Conclusion
In this chapter, we explore using two aperture pairs combined with multiple-
mode receivers and MIMO signal processing for enhanced FSO link tolerance to
turbulence and misalignment. The results show that the system outage probability
could be reduced by using multiple aperture pairs and recovering multiple modes for
each receiver. We note that we mainly investigate the system performance under a 12
mm aperture separation, where there is little power coupling between aperture pairs.
With the decrease of aperture separation distance, there could be more power coupling
between aperture pairs, which could potentially further affect the link performance.

55

Chapter 5
Investigation of dynamic aerosol and dynamic air-water
interface curvature effects on OAM multiplexed FSO link
5.1 Introduction
An interesting scenario for FSO links is the transmission of data between a
transceiver above the water and one below the water [36–40], such that the optical
beam would pass through dynamic aerosol above the water and dynamic curvature of
the water surface [41–43]. Previous reports have investigated the aerosol and curvature
effects for a typical Gaussian beam: (i) the aerosol effect could lead to scattering and
absorption of the beam [43], and (ii) the curvature effect could induce beam wandering
and wavefront distortion [93–95]. In addition, the comprehensive effects of aerosol
and curvature have also been investigated for a Gaussian beam transmitting through
the air-water interface [43,96]. These separate and comprehensive effects could result
in system performance degradation (e.g., power loss) for a Gaussian-beam-based FSO
link [93,94,97].
These effects of the air-water interface can be further complicated when there
are multiple optical beams with unique amplitude and phase profiles instead of a single
fundamental Gaussian beam. One example is the OAM beams, which is a subset of
LG beams [8]. For an OAM beam, the distortion of the beam’s unique intensity and
phase profile could lead to power loss of the transmitted mode and power coupling to
the neighboring modes [9]. Such degradations could induce both power loss and
56

channel crosstalk in OAM multiplexed links, where multiple OAM beams are
simultaneously transmitted each carrying an independent data channel [9]. There have
been reports of transmitting OAM beams through dynamic aerosol without carrying
data [98–100] or transmitting a single data-carrying OAM beam through a relatively
flat air-water interface [101]; however, little has been reported on the transmission of
OAM modes when the comprehensive effects of aerosol and curvature are
dynamically present, nor on the OAM multiplexed link under aerosol and/or curvature
effects.
In this chapter, we experimentally investigate the dynamic aerosol and dynamic
water surface curvature effects on the OAM beam transmission, and we demonstrate
an air-to-water 2-Gbit/s on-off keying (OOK) OAM multiplexed FSO communication
link [44]. The detrimental effects of the dynamic aerosol and curvature on the
transmitted OAM beams include but are not limited to wavefront distortion, beam
wandering, scattering, and absorption. Such time-varying degradation could affect the
received intensity and phase profiles of OAM beams, resulting in the dynamic power
loss of the transmitted mode and power coupling to the neighboring modes. In this
experiment, we generate the aerosol and curvature effects in a laboratory environment
by using a vaporizer and a wind generator, respectively. Moreover, we characterize
the two aerosol cases by their attenuation coefficients (~0.1-0.6 and ~0.7-1.3 dB/cm
for aerosol cases 1 and 2, respectively, over ~7 cm), and characterize the two curvature
cases by their variances of the curvature slope over time (~6×10
-7
and ~2×10
-5
rad
2
for
curvature cases 1 and 2, respectively, with a maximum wave height of several
millimeters). Our results show the following: (i) With the increase of the aerosol
57

strength from no-aerosol to aerosol cases 1 and 2, the power coupling ratio from OAM
-1 to +2 increases by 2 and 4 dB, respectively. This might be due to the amplitude and
phase distortion induced by spatially dependent scattering and absorption. (ii) The
scattering and absorption of aerosol also induce a power loss of the transmitted beam
for >1 and >5 dB under aerosol cases 1 and 2, respectively. (iii) With the increase of
the curvature strength from no-curvature to curvature cases 1 and 2, the power
coupling ratio from OAM -1 to +2 increases by 3 and 11 dB, respectively. This could
be caused by both the wavefront distortion and the beam wandering. (iv) Under the
comprehensive effect of aerosol (~0.1-0.6 dB/cm) and curvature (~6×10
-7
rad
2
), there
is an up to 2-dB higher modal power loss as compared with the single-effect cases. (v)
The received power on OAM -1 fluctuates in a range of ~6-dB within a 220-ms
measurement time under the aerosol (~0.1-0.6 dB/cm) and curvature (~6×10
-7
rad
2
)
effects due to the dynamic degradations. We also demonstrate OAM -1 and +2
multiplexed 2-Gbit/s OOK links under the dynamic aerosol and interface curvature.
The results show a power penalty of ~3 dB for the BER at the 7% FEC limit under the
comprehensive effect of aerosol (~0.1-0.6 dB/cm) and curvature (~6×10
-7
rad
2
), when
compared with the no-effect case.
5.2 Concept and experimental setup
Figure 5.1 shows the concept of an OAM multiplexed link through the dynamic
air-water interface. Each independent data channel is carried by a unique OAM beam,
and multiple data-carrying OAM beams are multiplexed and coaxially propagate
towards the air-water interface with an angle of incidence θ. At the dynamic air-water
58

interface, the OAM beams could be degraded by the interface effects, including but
not limited to dynamic aerosol and dynamic water surface curvature. Specifically, the
curvature effect could potentially induce beam wandering and wavefront
distortion [93–95,97], and the inhomogeneous aerosol effect could induce spatially
dependent scattering and attenuation towards the beam [43,98]. When recovering the
OAM beams at the receiver, there would be (i) power loss of the transmitted modes,
which would reduce the SNR of the recovered signal, and (ii) power coupling from
the transmitted modes to their neighboring modes, resulting in crosstalk between OAM
channels. Since the interface effects are dynamic, the link would experience time-
varying degradations.

Figure 5.1 Concept of the OAM multiplexed link through the dynamic air-water interface. The dynamic
aerosol and water surface curvature would induce time-varying power loss of the transmitted mode and
crosstalk to neighboring modes. θ: angle of incidence; Tx: transmitter; Rx: receiver; Ch: channel.
Figure 5.2 (a) shows the potential reasons for the power loss of the transmitted
mode and the power coupling to neighboring modes under the dynamic water surface
curvature and aerosol effects. As shown in Fig. 5.2 (a1), non-uniform water curvature
could induce spatially dependent refraction towards the OAM beam. Specifically,
there could be a relatively larger scale “slope” that steers the beam and induce beam
59

wandering [94], and there could also be “curves” that are smaller than or similar to the
beam size that induces wavefront distortion [97]. Both the beam wandering and
wavefront distortion could affect the unique intensity and phase profiles of the
received OAM beam regarding the aperture center, resulting in modal power coupling,
as shown in Fig. 5.2 (b). We note that both types of water curvature structures may
exist in our experiment. As shown in Fig. 5.2 (a2), the aerosol droplets could scatter
and/or absorb the incident light [43], and the inhomogeneous aerosol could induce
spatially dependent scattering and attenuation. In this case, the intensity and phase
profile of the received beam could also be affected, resulting in modal power coupling.

Figure 5.2 (a) The potential causes of modal power loss and power coupling under (a1) aerosol and (a2)
curvature effects. (b) The wavefront distortion, beam wandering, and spatially dependent scattering &
absorption could affect the unique intensity and phase profile of the received OAM beam. The example
images of OAM -1 under aerosol and curvature effects. The cross mark in the image shows the beam
center position under the no-effect case.
In this experiment, we induce the aerosol and curvature of the air-water interface
in two separated containers. The dynamic aerosol flow is composed of water droplets
generated by a vaporizer, and we characterize the aerosol effect by its
attenuation [102]. Specifically, aerosol cases 1 and 2 have attenuation coefficients of
~0.1-0.6 and ~0.7-1.3 dB/cm, respectively, over a distance of ~7 cm. Such aerosol
might have less thickness and a larger attenuation coefficient as compared with the
60

ocean aerosol (several dB over several kilometers [102]) due to the limitation of our
laboratory environment. The dynamic water surface curvature is induced using a wind
generator. To characterize the curvature effects, we (i) measure the beam center offset
of the refracted beam over ~1 min to calculate the water surface slope values (φ rad)
at each moment [42], and (ii) calculate the variation of the curvature slope φ over time.
Curvature cases 1 and 2 have slope variances of ~6×10
-7
and ~2×10
-5
rad
2
, respectively,
and their maximum slopes are ~0.003 and ~0.015 rad, respectively. Such water
curvature has a height of up to several millimeters. We note that the curvature slope
could be more than 0.1 rad with a variance of >3×10
-3
rad
2
in the ocean [103], which
is stronger than that of our experiment. The potential approaches to enable OAM
transmission in stronger curvature will be discussed in the conclusion section.
Moreover, as shown in Fig. 5.3 (b), the “structure” of the curvature (i.e., the brightness
variation recorded by the camera) could have a similar size to the transmitted beam
and potentially result in wavefront distortion besides the beam wandering.
The experimental setup is shown in Fig. 5.3 (a). At the transmitter, a 1-Gbit/s
OOK signal is modulated on a laser at 1064 nm, and light is coupled into free space
through a collimator. Subsequently, the data-carrying beam is coupled into a PPLN
for frequency doubling. Through second harmonic generation (SHG), the 1064 nm
beam is converted to a 532 nm wavelength Gaussian beam (green light) with a beam
diameter of ~3 mm. The resulting beam is split into two branches by a BS, and one
branch is delayed in free space to decorrelate the two data channels. In each branch,
an SLM converts the incoming Gaussian beam into an OAM beam with a unique order.
The two OAM beams are subsequently multiplexed using a BS and combined with the
61

beacon Gaussian beam (i.e., the beam for tracking) at 520 nm. The combined beams
are transmitted through the aerosol and curvature containers and processed by a
tracking system (response speed ~1 kHz, and steering range ~±0.026 rad). Finally, the
OAM beam with the desired order is down-converted to a Gaussian beam by a DMD
or an SLM and coupled into a single-mode fiber for analysis.

Figure 5.3 (a) The experimental setup for the OAM multiplexed link through the dynamic air-water
interface. The aerosol flow is generated by a vaporizer, and the curvature of the interface is induced by
wind. Col: collimator; PPLN: periodically poled lithium niobate; BS: beam splitter; SLM: spatial light
modulator; FSM: fast steering mirror; PSD; position-sensitive detector; HWP: half-wave plate; DMD:
digital micromirror device. (b) Example images of the curvature at the air-water interface. (c) The
positions of the beam center over ~1 min under various air-water interface effects with and without
tracking. Under aerosol case 2, the received power is too low to be measured by the camera. Moreover,
the beam is out of the camera for most of the measurements under curvature case 2 without tracking,
and therefore there are fewer data points.
62

Fig. 5.3 (c) shows the beam center (i.e., the blue dots in the figure) variation
over~ 1 min recorded by a camera. The results show that the interface effects could
induce beam wandering and such an effect is partially mitigated by the tracking system.
Therefore, the measured degradations of the OAM beams are always affected by the
residual misalignment. Such residual misalignment is relatively large under curvature
case 2, which might be due to the limited tracking accuracy. Moreover, the power of
the received beam is too low to be measured by the camera under aerosol case 2. We
note that the beam could be outside the receiver aperture due to beam wandering and
thus may not be efficiently captured without beam tracking. Therefore, to investigate
the modal coupling and power loss caused by other distortions, we use a tracking
system to mitigate the beam wandering for the measurements in the following sections.
5.3 Results for air-water interface effects on OAM beams
Figure 5.4 shows the power loss of different transmitted modes and the power
coupling to their neighboring modes under various aerosol and curvature conditions.
In this measurement, we (i) transmit one beam at a time (OAM -1 or +2), (ii) quickly
change the mode demultiplexing pattern (each for extracting one OAM mode) on the
DMD at the receiver at a rate of ~1 kHz such that the received power on different time
slot represents the power coupled to different modes, (iii) repeat this measurement
multiple times and record the power variation over time using an oscilloscope, and (iv)
calculate the power fluctuation range for each OAM mode (plotted as the orange bar
in Fig. 5.4). The DMD was used in this modal spectrum measurement because its
pattern-switching rate is higher than that of our SLMs (~10 Hz) [104].
63

Figure 5.4 The received power on the transmitted modes and their neighboring modes under various
curvature and aerosol conditions for (a) OAM -1 and (b) OAM +2. The beam propagation distance in
aerosol is ~7 cm. The orange bar shows the received power fluctuation range during the multiple
measurements over >5 s, and each measurement takes ~11 ms. The incident angle is 0 (normal
incidence). The power is normalized by the maximum received power for the transmitted mode in the
absence of interface effects.
As shown in Fig. 5.4, aerosol cases 1 and 2 could reduce the maximum received
power on the transmitted mode by >1 dB and >5 dB, respectively. Moreover, as
compared with the no aerosol case, the mutual power coupling ratios (defined as power
on the received mode divided by power on the transmitted mode) between OAM -1
64

and OAM +2 increase by 2 dB and 5 dB under aerosol case 1, respectively, and
increase by 4 dB and 7 dB under aerosol case 2, respectively. The reason could be that
the inhomogeneous absorption and scattering of aerosol induce amplitude and phase
distortion to the transmitted beams [98]. The curvature effects could also degrade the
transmitted OAM beam. Specifically, the modal power loss for transmitted OAM -1
and OAM +2 is >1 dB under curvature case 1, and such loss increases to >4 dB under
curvature case 2. Moreover, the mutual power coupling ratio between OAM -1 and +2
increases by 11 dB and 13 dB under curvature case 2, respectively, as compared with
the no curvature case. This is due to: (i) the curvature induces wavefront distortion of
the transmitted beams [97], and (ii) there is residual misalignment between the
incident beam and the receiver due to the beam wandering effect, as shown in Fig. 5.3
(c). Both the wavefront distortion and misalignment could affect the amplitude and
phase profile of the beam and induce both power loss of the transmitted mode and
power coupling to its neighboring mode. With the comprehensive effect of curvature
and aerosol, there is a higher modal power coupling ratio and/or a higher modal power
loss as compared with the single-effect cases. In our experiment, the curvature effects
induce stronger beam degradation as compared with the aerosol effect, which might
be due to that the curvature induces larger beam wandering and thereby larger residual
misalignment as compared with that of the aerosol effect, as shown in Fig. 5.3 (c).
65

Figure 5.5 Simulated received OAM spectrum of OAM -1 under the lateral displacement and angular
error derived from the beam wandering measurements on the left side. In this simulation, we assume
there is only beam misalignment without any other beam distortions. The beam diameter is ~ 3 mm and
the wavelength is 532 nm.
To further investigate the potential causes of modal power loss & modal coupling
and to provide some insights into the experimental data, we simulate the power
fluctuation on each mode for transmitted OAM -1 under beam wandering effects, as
shown in Fig. 5.5. The misalignment values used for this simulation are derived from
the measured beam offsets under three different example curvature conditions.
Moreover, we assume the offset could be caused by the lateral displacement, angular
error, or pointing error without other distortions. Such pointing error includes both
lateral displacement and angular error between the receiver and the beam [55]. We
calculate the variation range of misalignment as the following: (i) the lateral
displacement is calculated as the measured beam center offset, (ii) the angular error is
calculated as lateral displacement divided by the propagation distance from the air-
66

water interface to the receiver (~2 m), and (iii) the pointing error includes both lateral
displacement and angular error. Subsequently, we simulate the power fluctuation on
each mode under the lateral displacement and angular error values, and the power is
normalized by the transmitted power. The simulation results show that if there is only
lateral displacement, there could be a modal coupling ratio of up to -8 dB, and if the
angular error exists, there could be up to -6 dB modal coupling ratio and >20 dB power
loss of transmitted mode. This is because the beam’s phase and amplitude profiles are
no longer azimuthally symmetric under misalignment [55]. Such misalignment might
contribute to the beam degradations measured in Figs. 5.4 (a-c).
Figure 5.6 shows the power loss of the transmitted mode and power coupling to
neighboring modes over time. Each measurement takes ~11 ms and there could be a
small interval between subsequent measurements. The modal power loss and power
coupling in each discrete measurement are measured by switching the demultiplexing
pattern on the DMD (similar to the measurement for Fig. 5.4). The results show that
the crosstalk and power loss vary over time within the ~220 ms measurement time.
This could be because (i) the dynamic effects induce time-varying amplitude and phase
distortion [95], and (ii) the residual misalignment varies with time due to beam
wandering [55]. We note that we take the measurements under different interface
effects sequentially and transmit one OAM mode at a time. Due to the dynamic nature
of the aerosol and curvature, their conditions for data points with the same
measurement number are not the same. Therefore, it is difficult to make a direct
comparison between different curves in the figure.
67

Figure 5.6 The power on each mode when (a) OAM -1 and (b) OAM +2 are transmitted. Each
measurement takes ~11 ms. The aerosol and curvature conditions with the same measurement number
are different for different scenarios and different transmitted modes, and therefore they can’t be
compared directly. The incident angle is 0 (normal incidence). The power is normalized by the
maximum received power for the transmitted mode in the absence of interface effects.
Figure 5.7 shows the power loss of the transmitted OAM -1 and power coupling
to its neighboring modes under various angles of incidence. Under curvature case 1,
the power loss of OAM -1 increases by up to 3 dB, and the modal power coupling ratio
68

to neighboring modes increases by up to 3-dB as the angle of incidence increases. This
might be because under a larger angle of incidence (i) the curvature induces stronger
amplitude and phase distortion to the beam [105], and (ii) the curvature-induced beam
wandering becomes stronger [106], thereby resulting in a larger residual misalignment.
We note that there is no aerosol effect for the measurements in Fig. 5.7. Moreover, we
rebuild the tracking system and receiver for measuring the data in Fig. 5.7 which may
make it difficult to compare the results in Fig. 5.7 to those in Figs. 5.4 and 5.6 directly.

Figure 5.7 The received power on the transmitted mode and power coupling to neighboring modes
under different angles of incidence. The orange bar shows the received power fluctuation range for each
mode. The power is normalized by the maximum received power for the transmitted mode without
curvature. There are no aerosol effects for these measurements.
5.4 Results for air-water interface effects on OAM multiplexed link
Figure 5.8 shows the BER performance versus the average received power when
a single OAM -1, a single OAM +2, or multiplexed OAM -1 and +2 beams are
transmitted. When only a single data channel is transmitted, the link experiences a ~2
dB power penalty for the BER at the 7% FEC limit under aerosol case 1 and curvature
case 1, when compared with the no effect case. This is because the dynamic curvature
and aerosol induce time-varying power loss, and there could be some time slots where
69

the received power is too low to efficiently recover the signal. When OAM -1 and +2
are multiplexed, the link suffers from an extra ~1 dB power penalty for the BER at the
7% FEC limit compared with the single-channel link. This is because the crosstalk
between the two channels further degrades the link. We note that due to the OAM +2
channel having a higher loss than OAM -1 channel, its maximum received power is
lower and fails to achieve a BER < 1 × 10
−9
. Moreover, we use an SLM instead of a
DMD to demultiplex the incoming OAM beams for BER measurements, because the
DMD would induce a higher power loss (>10 dB) [104].

Figure 5.8 The BER performance of the OAM -1 and +2 under various effects. The measurement of
each data point takes >30 s. We note that the interface conditions are different for all these
measurements. The incident angle is 0 (normal incidence).
Figure 5.9 shows the BER performance over time for the multiplexed OAM -1
and OAM +2 channels. Each of the BER measurements takes ~4 s and the received
power fluctuates around -18 dBm during the measurement. The BER performance for
both channels vary with time, which is due to (i) the dynamic power loss results in a
dynamic signal-to-noise ratio at the receiver, and (ii) the dynamic modal power
coupling leads to time-dependent channel crosstalk. Here, we take the measurements
for different interface conditions separately and only one of the two channels is
70

recovered at a time. Therefore, the different BER measurements with the same
measurement number only indicate the BER fluctuation trends and should not be
compared directly. Moreover, the measurement for each BER point takes ~4s, such
that the aerosol and curvature dynamics within a smaller time scale might be missed
in Fig. 5.9.

Figure 5.9 The BER performance for discrete measurements (each takes ~4 s) versus time under various
air-water interface effects when OAM -1 and +2 are multiplexed. The four BER curves in each plot are
not measured at the same time, and therefore should not be compared with each other directly. The
incident angle is 0 (normal incidence).
5.5 Conclusion
We experimentally investigate the effects of the dynamic aerosol and water
surface curvature on the propagation of OAM beams. The results show that both the
aerosol and curvature induce dynamic beam distortions, resulting in the power loss of
the transmitted beam as well as the power coupling to neighboring modes. We also
demonstrate a 2-Gbit/s OOK OAM-multiplexed link through aerosol and curvature
effects. With some power penalty as compared with the no effects case, the OAM
71

multiplexed link is achieved under aerosol case 1 and curvature case 1. To enable data
transmission under stronger aerosol and/or curvature cases, we might need to (i)
transmit higher power for the data channels, (ii) improve the accuracy and steering
range of the tracking system to mitigate the residual misalignment, and (iii) adaptively
compensate for the beam degradation, for example, by using adaptive optics [95].
Moreover, we only multiplex two OAM beams for data transmission as a proof of
concept due to limited transmitter power. It is likely possible to multiplex more than
two OAM channels if higher transmitter power is used (e.g., by using a YDFA with
higher output power).

72

Chapter 6
Investigation of the 2-D modal coupling of an air-water
communication link through dynamic aerosol and water
surface curvature using LG beam
6.1 Introduction
The previous chapter has investigated the air-water interface effects and link
degradation for the case of LG beams with only the azimuthal value l being examined
for a radial value of p=0 [44]. However, degrading modal coupling might occur for
both azimuthal and radial components of a structured beam when considering both
aerosol and water surface curvature.
In this chapter, we investigate the 2-D modal coupling of an LG beam when
propagating through dynamic aerosol and water curvature by simulation and
experiment [45]. Specifically, we investigate the contribution of beam wandering and
beam distortion to modal power coupling under the air-water interface effects. The
experimental and simulation results show that for a transmitted 𝐿 𝐺 11
: (i) the measured
modal power coupling to adjacent modes (𝐿𝐺
01
, 𝐿 𝐺 21
, 𝐿 𝐺 10
, 𝐿 𝐺 12
) increases to -7 dB
under 8 Hz sine-shaped water curvature (~1 mm peak-to-peak height). (ii) The
simulated beam wandering-only case shows an up to ~-8 dB coupling to the adjacent
modes for misalignment under the 8 Hz curvature (~1 mm peak-to-peak height); (iii)
We believe the extra modal power coupling for the experimentally measured results
(both beam wandering and beam distortion may occur) as compared with the
73

simulation results (beam wandering only) could be due to the beam distortion. We also
demonstrate a 1-Gbit/s OOK link carried by 𝐿 𝐺 11
, and the results show a power
penalty of ~3 dB for the BER at the 7% FEC limit under the aerosol (with 1-2 dB loss)
and curvature (with 4 Hz frequency and ~1 mm height) effects, compared with the no-
effect case.
6.2 Concept and experimental setup

Figure 6.1 (a) The concept of LG beam propagates through the dynamic aerosol and dynamic water
surface curvature. The aerosol and curvatures could induce degradations to the transmitted beams,
including beam wandering and beam distortion. (b) The degradation of amplitude and phase profiles
under beam distortion and beam wandering. Both effects could lead to modal power coupling.
Figure.6.1 (a) shows the concept of the transmission for a data-carrying LG beam
through the dynamic air-water interface. At the dynamic air-water interface, the LG
beam could be degraded by various effects, including but not limited to dynamic
aerosol and dynamic water surface curvature. These effects may induce beam
wandering and beam distortion towards the beam, which could affect the unique
intensity and phase profiles of the received LG beam, as shown in Fig. 6.1 (b).
Therefore, when recovering the LG beam at the receiver, the beam would experience
(i) power loss of the transmitted modes, resulting in a lower the SNR of the recovered
74

signal, and (ii) power coupling to neighboring modes, which may cause inter-channel
crosstalk if multiple modal channels are transmitted. Because the aerosol and curvature
effects are dynamic, the modal power coupling would also vary over time. Due to the
limitation of total transmitted power with our equipment, we only investigate the air-
water interface effects on a single LG beam in this chapter.

Figure 6.2 Experimental setup. Col: collimator; PPLN: periodically poled lithium niobite; SLM: spatial
light modulator; HWP: half-wave plate; BS: beam splitter; PSD: position-sensitive detector; FSM: fast
steering mirror; The black dashed lines are electrical cables.
In this experiment, we induce the aerosol and curvature of the air-water interface
in the same container, such that the aerosol is right above the water surface curvature.
The dynamic aerosol is composed of water droplets with a diameter of ~5 𝜇𝑚
generated by a vaporizer. We characterize the aerosol effect by its attenuation: the
attenuation induced by the two aerosol cases are 1-2 dB and 3-5 dB, respectively, over
a distance of ~0.3 m. Such aerosol might have a larger attenuation coefficient over a
shorter distance as compared with the aerosol at the ocean (several dB over several
kilometers [102]). The dynamic curvature is induced by a ripple generator, which
75

could generate sine-shaped curvature that propagates in one direction within the water
tank. In this experiment, we investigate the curvature with a peak-to-peak height of
~1mm and a frequency of 4 Hz (~75 mm wave period) or 8 Hz (~25 mm wave period).
We note that the ocean curvature could be composed of multiple frequency
components ranging from sub-centimeter to multiple meters and could have a higher
height as compared with our experiment [107].
The experimental setup is shown in Fig. 6.2. The signal carried by a 1064-nm
laser (l-Gbit/s OOK) is coupled into free space through a collimator. The generated
Gaussian beam is frequency-doubled to 532-nm wavelength (green light) through
SHG in PPLN. Subsequently, the light is converted by an SLM into 𝐿 𝐺 11
beam with
a diameter ~2 mm and combined with a beacon Gaussian beam (for tracking) at 520
nm. The combined beam propagates through the emulated air-water interface effects
(aerosol and water surface curvature) and is processed by the tracking system (with a
response speed of ~1 kHz). To measure the 2-D power coupling of the transmitted LG
beam, we implement the off-axis holography at the receiver [108]. Specifically, we
combine the incoming light with a reference beam, and their interference pattern is
captured by a camera (~15 Hz sampling rate and <1 ms exposure time for each sample).
Such that the amplitude and phase profile of the incoming beam could be calculated
based on the interference pattern, and thereby the power on all the modes could be
measured simultaneously. To measure the BER performance of the link, the incoming
LG beam is converted back to a Gaussian beam by an SLM and coupled into a fiber-
based detector.
76

6.3 Simulation and experimental results
To investigate the modal power coupling induced by beam wandering and beam
distortion, we first measure the beam wandering effect using a camera. The beam
center variation for >10 s is recorded by the camera, as shown in Fig. 6.3. Each “dot”
in the figure is the beam mass center position (weighted by intensity profile) for one
measurement. As shown in the figure, the beam wandering is mainly induced by the
curvature effect in our experiment, which could have >3 mm beam center offset for
the 8-Hz curvature. With our tracking system, such variation beam center offset is
reduced to be < 0.1 mm, but still greater than the without curvature case. We note that
the beam may not be efficiently captured by the receiver without beam tracking.
Therefore, we use a tracking system for most of the measurements excluding Fig. 6.3.

Figure 6.3 The variation of beam mass center positions (weighted by spatial intensity profile) under
various air-water interface effects with and without tracking. The beam wandering is mainly along one
direction under the curvature effect, which could be due to that our curvature is mainly along one
direction in the water tank and thereby the beam would mainly wander along that direction. The tracking
system, which partially mitigated the misalignment at the receiver, is always applied during the modal
coupling and BER measurements.
77

Figure 6.4 The measured power for transmitted mode (𝐿 𝐺 11
) and the power coupled to other modes
with tracking. (a) The power is mainly on the transmitted mode and there are some modal power
couplings. For these cases, we can measure a BER below the FEC limit. (b) The power loss of the
transmitted mode and power coupling to other modes become higher. Our system can’t efficiently
measure BER for these cases. The power is normalized by the maximum received power for the
transmitted 𝐿 𝐺 11
without interface effects.
Figure 6.4 shows the measured modal power coupling for 𝐿 𝐺 11
beam under
various aerosol and curvature conditions. This measurement is realized by using the
camera and off-axis holography [108]. The results show that, when there is no
interface effect, the power coupling from 𝐿 𝐺 11
to adjacent modes (𝐿𝐺
01
, 𝐿 𝐺 21
, 𝐿 𝐺 10
,
𝐿 𝐺 12
) is ~-19 dB, which is due to the imperfect system. The aerosol effects with
attenuation of 1-2 dB and 3-5 dB could increase such power coupling to ~-12 dB and
~-8 dB respectively. The curvature with a frequency of 4 Hz and 8 Hz could increase
the modal power coupling to adjacent modes to ~-11 dB and ~-7 dB, respectively.
Moreover, such modal power coupling is further increased with the combination of
both aerosol and curvature effects as compared with the single-effect cases. This could
78

be due to that, (i) the interface effects induce the distortion of amplitude and phase
profile of the beam [95], and (ii) the beam wandering leads to misalignment between
the receiver and the incoming beam [94]. Both beam distortion and misalignment
could affect the amplitude and phase profile of the received beam and induce power
coupling from the transmitted mode to its neighboring mode.

Figure 6.5 (a) The experimentally measured beam wandering effect. (b) The simulated modal power
coupling under the assumption that there is only misalignment without beam distortion. (c) The
measured modal coupling with tracking. This modal coupling could be due to the combination of beam
wandering and beam distortion. The power is normalized by the maximum received power for 𝐿 𝐺 11

without interface effects.
79

We note that, for the cases shown in Fig. 6.4 (a), where the power is mainly on
the transmitted mode, our system can achieve a BER below the FEC limit. However,
for the cases shown in Fig. 6.4 (b), the modal power coupling becomes stronger, and
our system is not able to efficiently recover the signal. It might be possible to improve
the system performance by using a better tracking system to reduce the misalignment
and using wavefront correction techniques, e.g., adaptive optics, for mitigating the
beam distortion [95].
To investigate the contribution of beam wandering and beam distortion toward
the modal power coupling, we simulate the power coupling under misalignment-only
cases. Due to that the beam wandering is mainly induced by the curvature effects for
our experiment, as shown in Fig. 6.3, we focus on the curvature only cases in this
simulation. We simulate the power coupling by (i) experimentally measuring the beam
offset variation over a period of time under the curvature effect, as shown in Fig. 6.5
(a), (ii) simulate the modal power coupling at each moment assuming there is only
misalignment without beam distortion, and (iii) calculate the power fluctuation range
(from highest to lowest power) for each recovered mode, as shown in Fig. 6.5 (b). We
note that the beam center offset could be caused by lateral displacement and/or angular
error. In our simulation, (i) the lateral displacement is calculated as the beam center
offset, (ii) the angular error is calculated as the beam center offset divided by the beam
propagation distance from the air-water interface to the receiver (~1.3 m), and (iii) the
pointing error includes both types of misalignments.
Our simulation results show that the angular error could induce stronger modal
power coupling for our system, which might be due to the specific propagation
80

distance from the air-water interface to the receiver in our case. Such results might be
different for another setup. Moreover, the misalignment could induce up to -13 dB and
-8 dB modal power coupling to adjacent modes, for curvature strength of 4 Hz and 8
Hz respectively. The experimentally measured modal power coupling, which might be
due to the combination of beam wandering and beam distortion, is shown in Fig. 6.5
(c) for comparison. We believe that the extra modal power coupling in Fig. 6.5 (c) as
compared with Fig. 6.5 (b) could be due to curvature-induced beam distortion as well
as the imperfect experimental setup.

Figure 6.6 BER performance of a 1 Gbit/s OOK link carried by 𝐿 𝐺 11
with tracking. The measurement
of each data point takes >30 s. Due to that the air-water interface effects are dynamic, the aerosol and
curvature conditions could be slightly different for all these measurements.
Figure 6.6 shows the measured BER performance for a single-channel 1-Gbit/s
OOK link carried by 𝐿 𝐺 11
. The system experiences an up to ~3 dB power penalty at
the FEC limit under the effects shown in Fig. 6.4 (a). This might be due to that the
aerosol and curvature effects induce power coupling from the transmitted mode to
neighboring modes, leading to lower received power for 𝐿 𝐺 11
. Therefore, the received
signal would have lower SNR for a given receiver. In this experiment, we only transmit
one modal channel as a demonstration of concept due to the limitation of our
81

transmitted power. We note that, if multiple mode-multiplexed channels are
transmitted simultaneously, the modal power coupling could also result in inter-
channel crosstalk and further degrade the BER performance of the link.
6.4 Conclusion
In this chapter, we investigate the 2-D modal coupling of an LG beam when
propagates through dynamic aerosol and dynamic water surface curvature by
simulation and experiment. We also demonstrate an LG-beam-based 1-Gbit/s OOK
link. It might be possible to further enhance the performance of such links by (i)
mitigating the misalignment effects by using a more accurate tracking system, and (ii)
compensating the beam distortion by wavefront correction techniques, e.g., adaptive
optics [95].

82

References
1. H. Kaushal, V. K. Jain, and S. Kar, Free Space Optical Communication
(Springer, 2017).
2. V. W. S. Chan, "Free-space optical communications," Journal of Lightwave
Technology 24, 4750–4762 (2006).
3. J. C. Juarez, A. Dwivedi, A. R. Hammons, S. D. Jones, V. Weerackody, and R.
A. Nichols, "Free-space optical communications for next-generation military
networks," IEEE Communications Magazine 44, 46–51 (2006).
4. M. A. Khalighi and M. Uysal, "Survey on free space optical communication: A
communication theory perspective," IEEE Communications Surveys &
Tutorials 16, 2231–2258 (2014).
5. A. E. Willner, K. Pang, H. Song, K. Zou, and H. Zhou, "Orbital angular
momentum of light for communications," Applied Physics Reviews 8, 41312
(2021).
6. J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y.
Yue, S. Dolinar, M. Tur, and A. E. Willner, "Terabit free-space data
transmission employing orbital angular momentum multiplexing," Nat
Photonics 6, 488–496 (2012).
7. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett,
and S. Franke-Arnold, "Free-space information transfer using light beams
carrying orbital angular momentum," Opt Express 12, 5448–5456 (2004).
8. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital
angular momentum of light and the transformation of Laguerre-Gaussian laser
modes," Physical Review A 45, 8185 (1992).
9. A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y.
Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F.
Molisch, N. Ashrafi, and S. Ashrafi, "Optical communications using orbital
angular momentum beams," Adv Opt Photonics 7, 66–106 (2015).
10. A. M. Yao and M. J. Padgett, "Orbital angular momentum: origins, behavior
and applications," Adv Opt Photonics 3, 161–204 (2011).
11. M. J. Padgett, "Orbital angular momentum 25 years on," Opt Express 25,
11265–11274 (2017).
12. A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. ben Salem, M.
Zghal, and A. Forbes, "Optical communication beyond orbital angular
momentum," Sci Rep 6, 1–6 (2016).
83

13. J. Baghdady, K. Miller, K. Morgan, M. Byrd, S. Osler, R. Ragusa, W. Li, B. M.
Cochenour, and E. G. Johnson, "Multi-gigabit/s underwater optical
communication link using orbital angular momentum multiplexing," Opt
Express 24, 9794–9805 (2016).
14. K. Pang, H. Song, Z. Zhao, R. Zhang, H. Song, G. Xie, L. Li, C. Liu, J. Du, A.
F. Molisch, M. Tur, and A. E. Willner, "400-Gbit/s QPSK free-space optical
communication link based on four-fold multiplexing of Hermite–Gaussian or
Laguerre–Gaussian modes by varying both modal indices," Opt Lett 43, 3889–
3892 (2018).
15. S. Huang, G. R. Mehrpoor, and M. Safari, "Spatial-mode diversity and
multiplexing for FSO communication with direct detection," IEEE Transactions
on Communications 66, 2079–2092 (2018).
16. M. Arikawa and T. Ito, "Performance of mode diversity reception of a
polarization-division-multiplexed signal for free-space optical communication
under atmospheric turbulence," Opt Express 26, 28263–28276 (2018).
17. D. Zheng, Y. Li, H. Zhou, Y. Bian, C. Yang, W. Li, J. Qiu, H. Guo, X. Hong,
Y. Zuo, I. P. Giles, W. Tong, and J. Wu, "Performance enhancement of free-
space optical communications under atmospheric turbulence using modes
diversity coherent receipt," Optics Express 26, 28879–28890 (2018).
18. D. J. Geisler, T. M. Yarnall, G. Lund, C. M. Schieler, M. L. Stevens, N. K.
Fontaine, B. S. Robinson, and S. A. Hamilton, "Experimental comparison of 3-
mode and single-mode coupling over a 1.6-km free-space link," in Free-Space
Laser Communication and Atmospheric Propagation XXX (2018), Vol. 10524,
p. 105240H.
19. B. Denolle, G. Trunet, D. Allioux, P. Jian, O. Pinel, and G. Labroille,
"Turbulence-mitigating free-space-optical-communication receiver using
multi-plane-light-conversion-based spatial mode demultiplexer (Conference
Presentation)," in Free-Space Laser Communications XXXI (2019), Vol. 10910,
p. 109100E.
20. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random
Media (2005).
21. M. Uysal, J. Li, and M. Yu, "Error rate performance analysis of coded free-
space optical links over gamma-gamma atmospheric turbulence channels,"
IEEE Transactions on Wireless Communications 5, 1229–1233 (2006).
22. X. Zhu and J. M. Kahn, "Free-space optical communication through
atmospheric turbulence channels," IEEE Transactions on Communications 50,
1293–1300 (2002).
84

23. Y. Dikmelik and F. M. Davidson, "Fiber-coupling efficiency for free-space
optical communication through atmospheric turbulence," Applied Optics 44,
4946–4952 (2005).
24. M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J.
Lavery, M. J. Padgett, and R. W. Boyd, "Influence of atmospheric turbulence
on optical communications using orbital angular momentum for encoding," Opt
Express 20, 13195–13200 (2012).
25. Y. Ren, H. Huang, G. Xie, N. Ahmed, Y. Yan, B. I. Erkmen, N. Chandrasekaran,
M. P. J. Lavery, N. K. Steinhoff, M. Tur, S. Dolinar, M. Neifeld, M. J. Padgett,
R. W. Boyd, J. H. Shapiro, and A. E. Willner, "Atmospheric turbulence effects
on the performance of a free space optical link employing orbital angular
momentum multiplexing," Opt Lett 38, 4062–4065 (2013).
26. R. J. Watkins, K. Dai, G. White, W. Li, J. K. Miller, K. S. Morgan, and E. G.
Johnson, "Experimental probing of turbulence using a continuous spectrum of
asymmetric OAM beams," Opt Express 28, 924–935 (2020).
27. J. Zeng, X. Liu, C. Zhao, F. Wang, G. Gbur, and Y. Cai, "Spiral spectrum of a
Laguerre-Gaussian beam propagating in anisotropic non-Kolmogorov turbulent
atmosphere along horizontal path," Optics Express 27, 25342–25356 (2019).
28. G. Funes, M. Vial, and J. A. Anguita, "Orbital-angular-momentum crosstalk
and temporal fading in a terrestrial laser link using single-mode fiber coupling,"
Opt Express 23, 23133–23142 (2015).
29. H. Song, Y. Duan, H. Zhou, R. Zhang, H. Song, X. Su, C. Acevedo, M. Eshaghi,
K. Zou, K. Pang, M. Tur, A. Dogariu, R. J. Watkins, and W. A. E,
"Experimental investigation for the causes of orbital-angular-momentum modal
coupling through a dynamic random turbulent medium," in CLEO: Science and
Innovations (2022), pp. 1–2.
30. H. Song, H. Song, R. Zhang, K. Manukyan, L. Li, Z. Zhao, K. Pang, C. Liu, A.
Almaiman, R. Bock, B. Lynn, M. Tur, and A. E. Willner, "Experimental
mitigation of atmospheric turbulence effect using pre-signal combining for uni-
and bi-directional free-space optical links with two 100-Gbit/s OAM-
multiplexed channels," Journal of Lightwave Technology 38, 82–89 (2020).
31. H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y.
Cao, A. N. Willner, A. Almaiman, R. Bock, B. Lynn, M. Tur, and A. E. Willner,
"Demonstration of using two aperture pairs combined with multiple-mode
receivers and MIMO signal processing for enhanced tolerance to turbulence and
misalignment in a 10 Gbit/s QPSK FSO link," Optics Letters 45, 3042–3045
(2020).
85

32. H. Kaushal and G. Kaddoum, "Underwater optical wireless communication,"
IEEE Access 4, 1518–1547 (2016).
33. Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, "A survey of underwater
optical wireless communications," IEEE Communications Surveys & Tutorials
19, 204–238 (2016).
34. N. Saeed, A. Celik, T. Y. Al-Naffouri, and M.-S. Alouini, "Underwater optical
wireless communications, networking, and localization: A survey," Ad Hoc
Networks 94, 101935 (2019).
35. M. F. Ali, D. N. K. Jayakody, and Y. Li, "Recent trends in underwater visible
light communication (UVLC) systems," IEEE Access 10, 22169–22225 (2022).
36. X. Sun, M. Kong, O. A. Alkhazragi, K. Telegenov, M. Ouhssain, M. Sait, Y.
Guo, B. H. Jones, J. S. Shamma, T. K. Ng, and B. S. Ooi, "Field demonstrations
of wide-beam optical communications through water-air interface," IEEE
Access 8, 160480–160489 (2020).
37. S. Karp, "Optical communications between underwater and above surface
(satellite) terminals," IEEE Transactions on Communications 24, 66–81 (1976).
38. C. Li, H. Lu, Y. Huang, Q. Huang, J. Xie, and S. Tsai, "50 Gb/s PAM4
underwater wireless optical communication systems across the water-air-water
interface," Chinese Optics Letters 17, 100004 (2019).
39. L.-K. Chen, Y. Shao, and Y. Di, "Underwater and water-air optical wireless
communication," Journal of Lightwave Technology 40, 1440–1452 (2022).
40. H. Lu, C. Li, X. Huang, P.-S. Chang, Y. Chen, Y. Lin, C. Liu, and T. Ko, "A
400-Gb/s WDM-PAM4 OWC system through the free-space transmission with
a water–air–water link," Scientific Reports 11, 1–9 (2021).
41. M. S. Islam and M. F. Younis, "Analyzing visible light communication through
air-water interface," IEEE Access 7, 123830–123845 (2019).
42. Y. Shao, Y. Di, and L. Chen, "Adaptive loading for water-air SIMO OWC
system based on the temporal and spatial properties of waves," in Optical Fiber
Communication Conference (2021), pp. Th5E–2.
43. R. F. Lutomirski, "An analytic model for optical beam propagation through the
marine boundary layer," in Ocean Optics V (1978), Vol. 160, pp. 110–122.
44. H. Song, R. Zhang, N. Hu, H. Zhou, X. Su, H. Song, K. Zou, K. Pang, C. Liu,
D. Park, B. Lynn, G. Gbur, A. Dogariu, R. J. Watkins, J. K. Miller, E. Johnson,
M. Tur, and A. E. Willner, "Dynamic aerosol and dynamic air-water interface
86

curvature effects on a 2-Gbit/s free-space optical link using orbital-angular-
momentum multiplexing," Nanophotonics 11, 885–895 (2022).
45. H. Song, R. Zhang, H. Zhou, K. Zou, N. Hu, X. Su, H. Song, K. Pang, Y. Duan,
D. Park, B. Lynn, G. Gbur, A. Dogariu, R. J. Watkins, J. K. Miller, E. G.
Johnson, M. Tur, and A. E. Willner, "Demonstration of an air-water
communication link through dynamic aerosol and water curvature when
considering the 2-D modal coupling of a spatially structured beam," in Optical
Fiber Communication Conference (2022), p. M4I.5.
46. K. Dai, J. K. Miller, R. J. Watkins, A. Dogariu, and E. G. Johnson,
"Demonstration of a real-time orbital angular momentum (OAM) sensor for
probing variable density fog clouds," in 2021 Conference on Lasers and
Electro-Optics (CLEO) (2021), pp. 1–2.
47. Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan,
"Optical vortices 30 years on: OAM manipulation from topological charge to
multiple singularities," Light: Science & Applications 8, 1–29 (2019).
48. M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M.
Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, "High-
dimensional quantum cryptography with twisted light," New Journal of Physics
17, 33033 (2015).
49. N. Cvijetic, G. Milione, E. Ip, and T. Wang, "Detecting lateral motion using
light’s orbital angular momentum," Sci Rep 5, 1–7 (2015).
50. M. A. Cox, N. Mphuthi, I. Nape, N. Mashaba, L. Cheng, and A. Forbes,
"Structured light in turbulence," IEEE Journal of Selected Topics in Quantum
Electronics 27, 1–21 (2020).
51. A. H. Ibrahim, F. S. Roux, M. McLaren, T. Konrad, and A. Forbes, "Orbital-
angular-momentum entanglement in turbulence," Physical Review A 88, 12312
(2013).
52. V. P. Aksenov, V. v Kolosov, and C. E. Pogutsa, "Random wandering of laser
beams with orbital angular momentum during propagation through atmospheric
turbulence," Applied Optics 53, 3607–3614 (2014).
53. Y. Yuan, T. Lei, Z. Li, Y. Li, S. Gao, Z. Xie, and X. Yuan, "Beam wander
relieved orbital angular momentum communication in turbulent atmosphere
using Bessel beams," Scientific Reports 7, 1–7 (2017).
54. M. Hulea, Z. Ghassemlooy, S. Rajbhandari, and X. Tang, "Compensating for
optical beam scattering and wandering in FSO communications," Journal of
Lightwave Technology 32, 1323–1328 (2014).
87

55. G. Xie, L. Li, Y. Ren, H. Huang, Y. Yan, N. Ahmed, Z. Zhao, M. P. J. Lavery,
N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, A. F. Molisch, and A. E. Willner,
"Performance metrics and design considerations for a free-space optical orbital-
angular-momentum-multiplexed communication link," Optica 2, 357–365
(2015).
56. X. Zhang, T. Wang, J. Chen, and H. Yao, "Scintillation index reducing based
on wide-spectral mode-locking fiber laser carriers in a simulated atmospheric
turbulent channel," Opt Lett 43, 3421–3424 (2018).
57. G. Labroille, P. Jian, N. Barré, B. Denolle, and J.-F. Morizur, "Mode selective
10-mode multiplexer based on multi-plane light conversion," in Optical Fiber
Communication Conference (2016), pp. Th3E–5.
58. Y. Ren, G. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. Bao, M. P. J. Lavery,
M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, "Adaptive-
optics-based simultaneous pre-and post-turbulence compensation of multiple
orbital-angular-momentum beams in a bidirectional free-space optical link,"
Optica 1, 376–382 (2014).
59. X. Yin, H. Chang, X. Cui, J. Ma, Y. Wang, G. Wu, L. Zhang, and X. Xin,
"Adaptive turbulence compensation with a hybrid input-output algorithm in
orbital angular momentum-based free-space optical communication," Appl Opt
57, 7644–7650 (2018).
60. S. Li and J. Wang, "Compensation of a distorted N-fold orbital angular
momentum multicasting link using adaptive optics," Opt Lett 41, 1482–1485
(2016).
61. G. Xie, Y. Ren, H. Huang, M. P. J. Lavery, N. Ahmed, Y. Yan, C. Bao, L. Li,
Z. Zhao, Y. Cao, M. Willner, M. Tur, S. J. Dolinar, R. W. Boyd, J. H. Shapiro,
and A. E. Willner, "Phase correction for a distorted orbital angular momentum
beam using a Zernike polynomials-based stochastic-parallel-gradient-descent
algorithm," Opt Lett 40, 1197–1200 (2015).
62. S. Fu, S. Zhang, T. Wang, and C. Gao, "Pre-turbulence compensation of orbital
angular momentum beams based on a probe and the Gerchberg-Saxton
algorithm," Optics Letters 41, 3185–3188 (2016).
63. H. Huang, Y. Cao, G. Xie, Y. Ren, Y. Yan, C. Bao, N. Ahmed, M. A. Neifeld,
S. J. Dolinar, and A. E. Willner, "Crosstalk mitigation in a free-space orbital
angular momentum multiplexed communication link using 4 4 MIMO
equalization," Opt Lett 39, 4360–4363 (2014).
64. Y. Zhang, P. Wang, L. Guo, W. Wang, and H. Tian, "Performance analysis of
an OAM multiplexing-based MIMO FSO system over atmospheric turbulence
88

using space-time coding with channel estimation," Opt Express 25, 19995–
20011 (2017).
65. Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N.
Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner,
"Atmospheric turbulence mitigation in an OAM-based MIMO free-space
optical link using spatial diversity combined with MIMO equalization," Opt
Lett 41, 2406–2409 (2016).
66. T. Sun, M. Liu, Y. Li, and M. Wang, "Crosstalk mitigation using pilot assisted
least square algorithm in OFDM-carrying orbital angular momentum
multiplexed free-space-optical communication links," Opt Express 25, 25707–
25718 (2017).
67. M. Krenn, R. Fickler, M. Fink, J. Handsteiner, M. Malik, T. Scheidl, R. Ursin,
and A. Zeilinger, "Communication with spatially modulated light through
turbulent air across Vienna," New Journal of Physics 16, 113028 (2014).
68. S. Huang and M. Safari, "Spatial-mode multiplexing with zero-forcing
beamforming in free space optical communications," in 2017 IEEE
International Conference on Communications Workshops (ICC Workshops)
(2017), pp. 331–336.
69. B. Lü and H. Ma, "Coherent and incoherent off-axis Hermite-Gaussian beam
combinations," Applied Optics 39, 1279–1289 (2000).
70. G. Xie, C. Liu, L. Li, Y. Ren, Z. Zhao, Y. Yan, N. Ahmed, Z. Wang, A. J.
Willner, C. Bao, Y. Cao, P. Liao, M. Ziyadi, A. Almaiman, S. Ashrafi, M. Tur,
and A. E. Willner, "Spatial light structuring using a combination of multiple
orthogonal orbital angular momentum beams with complex coefficients,"
Optics Letters 42, 991–994 (2017).
71. M. W. Beijersbergen, L. Allen, H. der Veen, and J. P. Woerdman, "Astigmatic
laser mode converters and transfer of orbital angular momentum," Optics
Communications 96, 123–132 (1993).
72. Q. H. Spencer, A. L. Swindlehurst, and M. Haardt, "Zero-forcing methods for
downlink spatial multiplexing in multiuser MIMO channels," IEEE
Transactions on Signal Processing 52, 461–471 (2004).
73. M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F.
Romanato, R. A. Ravanelli, P. Coassini, and B. Thidé, "Space-division
demultiplexing in orbital-angular-momentum-based MIMO radio systems,"
IEEE Transactions on Antennas and Propagation 63, 4582–4587 (2015).
89

74. H. Ma, L. Lampe, and S. Hranilovic, "Coordinated broadcasting for multiuser
indoor visible light communication systems," IEEE Transactions on
Communications 63, 3313–3324 (2015).
75. Y. Hong, J. Chen, Z. Wang, and C. Yu, "Performance of a precoding MIMO
system for decentralized multiuser indoor visible light communications," IEEE
Photonics Journal 5, 7800211 (2013).
76. B. Li, J. Wang, R. Zhang, H. Shen, C. Zhao, and L. Hanzo, "Multiuser MISO
transceiver design for indoor downlink visible light communication under per-
LED optical power constraints," IEEE Photonics Journal 7, 1–15 (2015).
77. G. Labroille, B. Denolle, P. Jian, P. Genevaux, N. Treps, and J.-F. Morizur,
"Efficient and mode selective spatial mode multiplexer based on multi-plane
light conversion," Opt Express 22, 15599–15607 (2014).
78. X. Wang, X. Feng, P. Zhang, T. Wang, and S. Gao, "Single-source bidirectional
free-space optical communications using reflective SOA-based amplified
modulating retro-reflection," Optics Communications 387, 43–47 (2017).
79. I. B. Djordjevic, "Deep-space and near-Earth optical communications by coded
orbital angular momentum (OAM) modulation," Opt Express 19, 14277–14289
(2011).
80. G. Milione, T. Wang, J. Han, and L. Bai, "Remotely sensing an object’s
rotational orientation using the orbital angular momentum of light," Chinese
Optics Letters 15, 30012 (2017).
81. C. Schulze, A. Dudley, D. Flamm, M. Duparre, and A. Forbes, "Measurement
of the orbital angular momentum density of light by modal decomposition,"
New Journal of Physics 15, 73025 (2013).
82. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, "Pixelated phase computer
holograms for the accurate encoding of scalar complex fields," JOSA A 24,
3500–3507 (2007).
83. J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, "Vortex knots in light,"
New Journal of Physics 7, 55 (2005).
84. D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparré, "Mode analysis
with a spatial light modulator as a correlation filter," Opt Lett 37, 2478–2480
(2012).
85. D. Kedar and S. Arnon, "Urban optical wireless communication networks: the
main challenges and possible solutions," IEEE Communications Magazine 42,
S2–S7 (2004).
90

86. S. Arnon, "Effects of atmospheric turbulence and building sway on optical
wireless-communication systems," Opt Lett 28, 129–131 (2003).
87. A. A. Farid and S. Hranilovic, "Outage capacity optimization for free-space
optical links with pointing errors," Journal of Lightwave Technology 25, 1702–
1710 (2007).
88. T. Weyrauch and M. A. Vorontsov, "Free-space laser communications with
adaptive optics: Atmospheric compensation experiments," in Free-Space Laser
Communications (Springer, 2004), pp. 247–271.
89. J. H. Shapiro, "Imaging and optical communication through atmospheric
turbulence," in Laser Beam Propagation in the Atmosphere (Springer, 1978),
pp. 171–222.
90. T. M. Yarnall, D. J. Geisler, C. M. Schieler, and R. B. Yip, "Analysis of free-
space coupling to photonic lanterns in the presence of tilt errors," in 2017 IEEE
Photonics Conference (IPC) (2017), pp. 723–724.
91. V. P. Aksenov, V. v Dudorov, V. v Kolosov, and V. Y. Venediktov,
"Probability distribution of intensity fluctuations of arbitrary-type laser beams
in the turbulent atmosphere," Opt Express 27, 24705–24716 (2019).
92. V. P. Aksenov, V. v Kolosov, G. A. Filimonov, and C. E. Pogutsa, "Orbital
angular momentum of a laser beam in a turbulent medium: preservation of the
average value and variance of fluctuations," Journal of Optics 18, 54013 (2016).
93. O. Alharbi, W. Xia, M. Wang, P. Deng, and T. Kane, "Measuring and modeling
the air-sea interface and its impact on FSO systems," in Laser Communication
and Propagation through the Atmosphere and Oceans VII (2018), Vol. 10770,
p. 1077002.
94. A. K. Majumdar, J. Siegenthaler, and P. Land, "Analysis of optical
communications through the random air-water interface: feasibility for under-
water communications," in Laser Communication and Propagation through the
Atmosphere and Oceans (2012), Vol. 8517, p. 85170T.
95. P. Land and A. K. Majumdar, "Demonstration of adaptive optics for mitigating
laser propagation through a random air-water interface," in Ocean Sensing and
Monitoring VIII (2016), Vol. 9827, p. 982703.
96. Y. Dong and X. Qingji, "Atmosphere-ocean laser communication channel
simulation and modeling," in 2009 ISECS International Colloquium on
Computing, Communication, Control, and Management (2009), Vol. 4, pp.
554–557.
91

97. T. Lin, C. Gong, J. Luo, and Z. Xu, "Dynamic optical wireless communication
channel characterization through air-water interface," in 2020 IEEE/CIC
International Conference on Communications in China (ICCC Workshops)
(2020), pp. 173–178.
98. A. P. Porfirev, M. S. Kirilenko, S. N. Khonina, R. V. Skidanov, and V. A. Soifer,
"Study of propagation of vortex beams in aerosol optical medium," Applied
Optics 56, E8–E15 (2017).
99. T. Qu, H. Li, Z. Wu, Q. Shang, J. Wu, and W. Kong, "Scattering of aerosol by
a high-order Bessel vortex beam for multimedia information transmission in
atmosphere," Multimedia Tools and Applications 79, 34159–34171 (2020).
100. S. N. Khonina, S. v Karpeev, and M. A. Butt, "Spatial-light-modulator-based
multichannel data transmission by vortex beams of various orders," Sensors 21,
2988 (2021).
101. A. Wang, L. Zhu, Y. Zhao, S. Li, W. Lv, J. Xu, and J. Wang, "Adaptive water-
air-water data information transfer using orbital angular momentum," Opt
Express 26, 8669–8678 (2018).
102. S. S. Prijith, K. Rajeev, B. v Thampi, S. K. Nair, and M. Mohan, "Multi-year
observations of the spatial and vertical distribution of aerosols and the genesis
of abnormal variations in aerosol loading over the Arabian Sea during Asian
summer monsoon season," Journal of Atmospheric and Solar-Terrestrial
Physics 105, 142–151 (2013).
103. F. M. Bréon and N. Henriot, "Spaceborne observations of ocean glint
reflectance and modeling of wave slope distributions," Journal of Geophysical
Research: Oceans 111, (2006).
104. M. Mirhosseini, O. S. Magana-Loaiza, C. Chen, B. Rodenburg, M. Malik, and
R. W. Boyd, "Rapid generation of light beams carrying orbital angular
momentum," Opt Express 21, 30196–30203 (2013).
105. B. Walter, S. R. Marschner, H. Li, and K. E. Torrance, "Microfacet models for
refraction through rough surfaces," Rendering Techniques 2007, 18th (2007).
106. T. hua Zhou, Y. He, X. lei Zhu, and W. biao Chen, "Influence of sea-air
interface on upward laser beam propagation," in International Symposium on
Photoelectronic Detection and Imaging 2013: Laser Communication
Technologies and Systems (2013), Vol. 8906, pp. 345–351.
107. T. Elfouhaily, B. Chapron, K. Katsaros, and D. Vandemark, "A unified
directional spectrum for long and short wind-driven waves," Journal of
Geophysical Research: Oceans 102, 15781–15796 (1997).
92

108. Y. Zhou, B. Braverman, A. Fyffe, R. Zhang, J. Zhao, A. E. Willner, Z. Shi, and
R. W. Boyd, "Vectorial phase conjugation for high-fidelity mode transmission
through multimode fiber," in Photonic Networks and Devices (2020), pp.
NeW2B–5.

Abstract (if available)

Abstract There has been a growing interest in free-space optical (FSO) communications due to its potential for higher capacity and higher privacy as compared with conventional radio-frequency techniques. One potential approach that could further enhance the capacity and robustness of an FSO link is by using structured beams with designated spatial amplitude and phase profiles.
Using Laguerre Gaussian (LG) beams is one choice for such structured beams. LG beams could be characterized by two modal indices l and p, l represents the number of 2π phase shifts in the azimuthal direction of the wavefront, and p+1 represents the number of concentric amplitude rings in the radial direction. We note that one subset of LG modes is orbital angular momentum (OAM) modes, which could be characterized by the index l. LG beams with different orders (with different l and/or p values) are mutually orthogonal, which enables them to be multiplexed, coaxially transmitted, and demultiplexed with little inherent crosstalk.
One potential scenario of interest for FSO links is the data transmission through the atmosphere. However, a key challenge for such an FSO link is the atmospheric turbulence, which would degrade the link performance by inducing power loss and modal power coupling. This first part of the dissertation will investigate using spatial modes for links through atmospheric turbulence: (i) investigation for the causes of OAM modal coupling through a dynamic random turbulent medium; (ii) pre-compensation of atmospheric turbulence effect using combinations of OAM modes in uni- and bi-directional OAM multiplexed FSO links; (iii) using two aperture pairs combined with multiple-mode receivers and multiple-input and multiple-output (MIMO) signal processing for enhanced FSO link tolerance to turbulence and misalignment.
Another scenario of interest is the data transmission through a dynamic air-water interface. In this case, the beam passes through the dynamic aerosol above the water and the dynamically changing water surface curvature at the air-water interface. This part of the dissertation will investigate the degradations induced by the dynamic air-water interface: (i) investigation of dynamic aerosol and dynamic air-water interface curvature effects on OAM multiplexed FSO links; (ii) investigation of the 2-D modal coupling of an air-water communication link through dynamic aerosol and water surface curvature using LG beam.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Spatial modes for optical communications and spatiotemporal beams

PDF

optical communication systems and space-time wave packet generation using frequency combs and spatial modes

PDF

Multiplexing techniques and reconfigurable networking functions for optical communications using orbital angular momentum beams

PDF

Orbital angular momentum based spatially multiplexed optical and millimeter-wave communications

PDF

Free-space optical communications and probing through turbulent links using structured light

PDF

Using beams carrying orbital angular momentum for communications and remote sensing

PDF

High-capacity optical communications using structured light in random and disturbed media

PDF

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

PDF

Applications of orbital angular momentum in high-capacity free-space optical communications

PDF

Optical and mm-wave orbital-angular-momentum beam generation and its applications in communications

PDF

High capacity optical and RF/mm-wave communications utilizing orbital angular momentum multiplexing

PDF

Integrated silicon waveguides and specialty optical fibers for optical communications system applications

PDF

Optical signal processing for enabling high-speed, highly spectrally efficient and high capacity optical systems

PDF

Spectrally efficient waveforms for coherent optical fiber transmission

PDF

Topological and non-Hermitian semiconductor lasers

PDF

Modeling and analysis of parallel and spatially-evolving wall-bounded shear flows

PDF

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

PDF

Resonant light-matter interactions in nanophotonic structures: for manipulating optical forces and thermal emission

PDF

Development of novel techniques for evaluating physical, chemical and toxicological properties of particulate matter in ambient air

PDF

A framework for comprehensive assessment of resilience and other dimensions of asset management in metropolis-scale transport systems

Asset Metadata

Creator Song, Haoqian (author)

Core Title Using spatial modes for data transmission through the air and through the air-water interface

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2022-08

Publication Date 05/20/2022

Defense Date 04/26/2022

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

Tag air-water interface,free-space optical communication,OAI-PMH Harvest,spatial mode,turbulence,vortex beam

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Willner, Alan E. (committee chair), Haas, Stephan Wolfgang (committee member), Khajavikhan, Mercedeh (committee member)

Creator Email haoqians@usc.edu,haoqiansong0221@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC111333311

Unique identifier UC111333311

Document Type Dissertation

Rights Song, Haoqian

Internet Media Type application/pdf

Type texts

Source 20220523-usctheses-batch-943 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu