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Applications in optical communications: quantum communication systems and optical nonlinear device

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Applications in optical communications: quantum communication systems and optical nonlinear device

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APPLICATIONS IN OPTICAL COMMUNICATIONS: QUANTUM
COMMUNICATION SYSTEMS AND OPTICAL NONLINEAR DEVICE

by
Cong Liu

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
(PHYSICS)

May 2021

Copyright 2021 Cong Liu

ii

Dedication

To my parents, Zhaoli Liu and Xiuzhen Zhang,
for their selfless love and care.

iii

Acknowledgements
The journey of PhD is long, and I deeply feel that the PhD period is the most
memorable time in my life up to now. During this time, I have learned so much from
my PhD advisor Prof. Alan E. Willner and also from my colleagues in Optics
Communications Laboratory (OCLab) and Department of Physics and Astronomy,
University of Southern California (USC). Without their help and devotion, it would
not be possible for me to complete this dissertation.
First, I would like to deeply thank my PhD research advisor Prof. Alan E.
Willner who is always supporting, encouraging, and instructing me. I always feel so
lucky because I have been studying my PhD under the supervision of Prof. Willner at
USC and I have gained invaluable experience and knowledge to study in a well-
known lab. Prof. Willner's knowledge, experience, and vision help me overcome all
the difficulties in my PhD period. I have also learned a lot from him about many
personal lessons, which I believe will be greatly helpful for my future life.
I would like to express my gratitude to Prof. Stephan Wolfgang Haas, for his
support for my PhD study, Prof. Krzysztof Pilch for his academic advice for this
PhD program. I also thank Prof. Robert W. Boyd from University of Rochester, Prof.
Moshe Tur from Tel Aviv University, I cannot accomplish my research projects
without their advice and instructions. I also appreciate our collaborators Dr. M
Zahirul Alam, Dr. Orad Reshef, Dr. Jeremy Upham and Mohammad Karimi from
University of Ottawa, Jiapeng Zhao, Dr. Yiyu Zhou, Dr. Mohammad Mirhosseini
and Saumya Choudhary from University of Rochester for their help with our
research projects.
I would also like to thank my colleagues Dr. Yongxiong Ren, Kai Pang and
Karapet Manukyan for their insightful discussions and collaborations in this
dissertation. My grateful thanks are also extended to other current and past OCLab
members, Dr. Yan Yan, Dr. Nisar Ahmed, Dr. Morteza Ziyadi, Dr. Bishara Shamee,
Dr. Guodong Xie, Dr. Ahmed Almaiman, Dr. Amirhossein Mohajerin-Ariaei, Dr.
Changing Bao, Dr. Yinwen Cao, Dr. Long Li, Dr. Zhe Zhao, Dr. Peicheng Liao, Zhe
Wang, Ahmad Fallahpour, Fatemeh Alishahi, Runzhou Zhang, Haoqian Song,

iv

Kaiheng Zou, Hao Song, Huibin Zhou, Nanzhe Hu, Amir Minoofar, and Xinzhou Su
for all their helpful discussions. I also want to appreciate the tremendous support
from USC staff, particularly, Dr. Gökhan Esirgen, Mr. Joseph Vandiver, Ms. Betty
Byers, Ms. Lisa Moeller, Ms. Allison Bryant, Ms. Corine Wong, Ms. Gerrielyn
Ramos, and Ms. Susan Wiedem. Last but not least, I am also thankful to other USC
friends who have helped me in the past years.
Finally, I would like to express my deepest love and sincere appreciation to
my parents Zhaoli Liu and Xiuzhen Zhang, my boyfriend Zhihao Jiang, who are
always supporting and encouraging me spiritually and providing me with their
selfless love.
PhD life is memorable for me, while challenging, it was undoubtedly exciting
and made me a better researcher and person. 人生如逆旅，我亦是行人。I was here,
I am looking forward to the next chapter in life.

v

Table of Contents
Dedication ................................................................................................................... ii
Acknowledgements .................................................................................................... iii
Abstract ................................................................................................................. vii
Chapter 1 Introduction .............................................................................................. 1
1.1 Orbital Angular Momentum (OAM) for Quantum Communications ............ 1
1.2 High Nonlinear Epsilon-near-zero (ENZ) Material and Metasurface ............ 3
1.3 Thesis Outline ................................................................................................. 4
Chapter 2 Switchable Detector Array Scheme to Reduce the Effect of Single-
photon Detector’s Deadtime in a Multi-bit/photon Quantum Link .... 6
2.1 Introduction .................................................................................................... 6
2.2 Concept of the Switchable Detection Scheme ................................................ 8
2.3 Simulation Results ........................................................................................ 10
2.4 Conclusion and Discussion ........................................................................... 15
Chapter 3 Adaptive Optics (AO) Compensation in an OAM-encoded Quantum
Link ......................................................................................................... 17
3.1 Introduction .................................................................................................. 17
3.2 Atmospheric Turbulence and AO Compensation to OAM-Based Links ..... 18
3.3 Concept and Experimental Setup ................................................................. 20
3.4 Experimental Results .................................................................................... 23
3.5 Conclusion and Discussion ........................................................................... 28
Chapter 4 Photon Acceleration using a Time-varying Epsilon-near-zero (ENZ)
Metasurface ............................................................................................ 29
4.1 Introduction .................................................................................................. 29
4.2 ENZ Metasurface Device and Its Linear Characterization ........................... 32
4.3 Nonlinear Characterizations of the ENZ Metasurface ................................. 35
4.4 Conclusion and Discussion ........................................................................... 37
Chapter 5 Tunable Doppler Shift Using a Time-varying Epsilon-near-zero
(ENZ) Thin Film near 1550 nm ............................................................ 38
5.1 Introduction .................................................................................................. 38
5.2 Concept and ENZ Material Design .............................................................. 39
5.3 Experimental Setup and Results ................................................................... 41
5.4 Influence of Pump Pulse Duration on the Doppler Shift Effect of ITO-
ENZ Material ................................................................................................ 43
5.5 Conclusion and Discussion ........................................................................... 46
Chapter 6 Nonlinear Response of Epsilon-Near-Zero (ENZ) Plasmon Modes in
Indium-Tin-Oxide (ITO) Thin Films near 1550 nm ........................... 47

vi

6.1 Introduction .................................................................................................. 47
6.2 Concept of ENZ Mode Coupling and Dispersion Relation in ITO Thin
Film 48
6.3 Simulation Results ........................................................................................ 50
6.4 Conclusion and Discussion ........................................................................... 54
References ................................................................................................................. 55

vii

Abstract
The first part of this dissertation will study orbital-angular-momentum (OAM)
modes for high-dimensional quantum communications. In the case of a quantum
communication system, an individual photon can carry one of the many different
OAM values, similar to digital data taking on one of many values. A binary signal
has 2 values of “0” and “1” data bits, whereas an M-ary signal may have many more
possibilities ranging from “0” to “M-1” values. The number of data bits per unit time
would be log2M. If each photon can be encoded with a specific OAM value from M
possibilities, the photon efficiency in bit/photon can be increased. This has the
potential to be useful for quantum communication systems which are typically
photon “starved” and of which qubits commonly can be encoded on one of only two
orthogonal polarization states. Therefore, a larger alphabet for each qubit is, in
general, highly desirable for enhancing system performance. In this dissertation,
research issues about high-dimensional, OAM-encoded quantum communication
systems, such as: (i) developing quantum detection methods for high-dimensional
quantum system and (ii) mitigating coupling among multiple orthogonal states due to
distortions (e.g., atmospheric turbulence effects) will be addressed and discussed.
The second part of this dissertation is the investigation of epsilon-near-zero
(ENZ) material and metasurface. ENZ materials can exhibit ultra-fast (sub-ps) and
unit-order time-dependent refractive index change, therefore perform strong
nonlinear effects in a relatively short (sub-𝜇𝑚) light-matter interaction length. Firstly,
we experimentally demonstrate photon acceleration effect which is one example of
nonlinear effect induced by the time-varying refractive index in an ENZ metasurface.
Then, we characterize the Doppler shift in light utilizing an indium tin oxide (ITO)
film with a zero-permittivity wavelength of 1550 nm for potential benefits in telecom
applications. We also numerically investigate the nonlinear response of ENZ
plasmon modes in ITO thin films near 1550 nm, which might be helpful to further
enhance the nonlinearity of ENZ materials.

1

Chapter 1 Introduction
This chapter will first introduce the basic concept of orbital angular
momentum (OAM) for quantum communication systems. Then a brief overview of
high nonlinear epsilon-near-zero (ENZ) material and metasurface for optical
functional device which has potential applications in optical communications.
Finally, the outline of the rest of the dissertation will be explained.
1.1 Orbital Angular Momentum (OAM) for Quantum
Communications
A light beam carrying OAM has a helical phasefront and its wave vector
spirals around the beam axis. The phase term of an OAM beam is described as
exp (𝑖ℓ𝜃) in the transverse plane, where θ refers to the azimuthal coordinate, and ℓ
defines the “charge” carried by the OAM mode. ℓ describes the number of 2π phase
shifts occurring in the azimuthal direction, and could be a positive, negative, or a
zero-value integer, corresponding to clockwise, counterclockwise phase helices, or a
conventional non-OAM Gaussian beam with power in the beam center, respectively
[1-3], as shown in Fig. 1.1.

Figure 1.1 The wavefronts, intensity profiles, and phase profiles of OAM modes l = 0, 1, 2, and 3.
The OAM mode with a nonzero order has a donut-shaped intensity profile and helical phasefront. The
size of the ring in the intensity profile grows with l.

An OAM beam or OAM-carrying photon can be generated at the transmitter
by inverting a Gaussian beam or Gaussian carrying photon into a certain OAM-
carrying beam or photon. For example, this could be achieved by using spiral phase
plates [2] or phase holograms [4, 5]. To detect an OAM beam/photon at the receiver,
an OAM beam/photon can be converted back to a Gaussian-like beam/photon by
-10 -8 -6 -4 -2 0 2 4 6 8
x 10 -4
-10
-8
-6
-4
-2
0
2
4
6
8
x 10 -4
[m]
[m]
-10 -8 -6 -4 -2 0 2 4 6 8
x 10
-4
-10
-8
-6
-4
-2
0
2
4
6
8
x 10
-4
[m]
[m]
-10 -8 -6 -4 -2 0 2 4 6 8
x 10
-4
-10
-8
-6
-4
-2
0
2
4
6
8
x 10
-4
-10 -8 -6 -4 -2 0 2 4 6 8
x 10
-4
-10
-8
-6
-4
-2
0
2
4
6
8
x 10
-4
l = 0
‘No OAM’
Wavefront
Intensity profile
Phase profile
Wavefront
Intensity profile
Phase profile
Intensity profile
Phase profile
Intensity profile
Phase profile
l = 1 l = 2 l = 3
# of states possible = infinite , …. ( theoretically) (l = …. -3, -2, -1 ,+1, +2, +3 ….)
Wavefront
Wavefront

2

passing it through a phase distribution that is a conjugate of the transmitter. The
concept of OAM beam or photon generation is shown in Fig. 1.2.

Figure 1.2 OAM-carrying photon generation and detection using holographic phase filter.

The orthogonality of OAM modes can be utilized for communications: (i) by
multiplexing, in which multiple independent data-carrying beams each having a
different OAM value can be transmitted simultaneously; (ii) by encoding, in which
each data symbol is represented by one of many different OAM values.
OAM multiplexing could be beneficial for increasing the capacity in
communication links [3, 6]. Since each OAM-carrying beam has an independent data
stream, the total link capacity could be multiplied by the number of transmitted
beams. Orthogonality of the beams could enable efficient multiplexing at the
transmitter, co-propagation of overlapping beams, and demultiplexing of the beams
at the receiver with inherently low crosstalk.
Incoming
Gaussian
photon
Incoming
OAM-carrying
photon
Converted into
OAM-carrying
photon
Holographic
phase filter
Wave plates, spatial light
modulator (SLM), multi-
plane mode converter …
Re-converted into
Gaussian photon
Generator
Detector

3

Figure 1.3 Concept of OAM-based quantum data encoding. Within each symbol period, a
Gaussian photon is converted to one of the M OAM states, resulting in information encoding of up to
log2M bit/photon.

OAM-based data encoding could also be beneficial for increasing efficiency
in a communication link as shown in Fig. 1.3. M different data symbols of {0, 1, …,
M-1} could be encoded onto M different OAM states, thus increase the photon
efficiency of the communication link. OAM data encoding could be implemented
using: (a) a tunable OAM mode converter with time-varying phase patterns [8], or (b)
multiple fixed OAM mode converters together with an optical switch, such that the
beam is switched among the different converters to carry time-varying OAM states
[9]. OAM encoding could be used for either classical or quantum communication
links [9-11].
1.2 High Nonlinear Epsilon-near-zero (ENZ) Material and
Metasurface
Efficient nonlinear optical responses are desired for many optical photonics
applications. However, these nonlinear responses typically require intense laser
sources and long interaction lengths, requirements that often render nonlinear optics
incompatible with new nanophotonic architectures in integrated optics and
metasurface devices [12]. Materials with stronger nonlinear properties becomes a
key point for applications that require lower powers and smaller footprints. Recently,
a new class of materials with a vanishing permittivity, known as ENZ materials, has
been reported to exhibit unprecedented ultrafast nonlinear effects within sub-
wavelength light-matter-interaction lengths [13].
Phase
structure
Accumulated
intensity structure
+1ℏ
Time
T1 T2
T3 T4 …
…
OAMℓ
!
OAMℓ
"
OAMℓ
"
OAM
Converter
Gaussian photons
v A quantum communication system
encoded by M orthogonal OAM
states can encode information up
to#$%
!
& bits/photon.
OAMℓ
#

4

Figure 1.4 The light-induced change in refractive index as large as 0.7 was reported for sub-μm
thick ITO [18].

Recently, it has been established that ENZ materials can enable efficient
nonlinear optical phenomena [14-18] and display a wealth of exotic properties [19-
22]. Current research interest is motivated by the observation that degenerate
semiconductors (semiconductors with such a high level of doping that they start
showing metallic behavior) such as indium tin oxide (ITO) and aluminium-doped
zinc oxide (AZO), which both possess a zero-permittivity wavelength in the near-IR
(NIR) range, exhibit a huge enhancement of the nonlinear optical response
associated with the ENZ spectral region. Especially, a light-induced ultrafast (i.e.,
sub-picosecond) change in refractive index as large as 0.7 was reported for ITO [18]
(Fig. 1.4). Such a change is unprecedentedly large and thus renders these materials
promising for new applications in photonics [23], particularly for systems with
limited interaction lengths such as nonlinear photonic metasurfaces [24]. Moreover,
numerous fundamental studies have been reported that demonstrate ENZ-
enhancement of other nonlinear optical processes, such as harmonic generation [25-
27], wave mixing [28-30], frequency conversion [31-33] and electro-optical effects
[34-36]. Efficient practical devices such as all-optical and electro-optical modulators
have also been proposed that exploit such enhanced nonlinear effects [37-39].
1.3 Thesis Outline

5

This dissertation is organized with the following structure: Chapter 2 presents
the switchable detector array scheme to reduce the effect of single-photon detector’s
deadtime in a multi-bit/photon quantum link. This detection scheme could be applied
to high-dimensional quantum communication systems, for example, OAM-encoded
quantum links, and have the potential to benefit the detection speed of a quantum
system. Numerical simulation results of the quantum detection process are shown.
Chapter 3 describes the experimental demonstration of adaptive optics (AO)
compensation for atmospheric turbulence effects in an OAM-encoded quantum link,
the quantum symbol error rate is reduced with the help of AO mitigation. Chapter 4
investigates the photon acceleration using a time-varying ENZ metasurface, which is
composed with an ITO-ENZ thin layer and nanoantenna on top of the ITO layer.
Chapter 5 is about the experimental study of the tunable Doppler shift using a time-
varying ENZ thin film near 1550 nm, and the exploration of pump pulse duration to
the Doppler shift amount is also shown. Chapters 6 presents the numerical study of
the nonlinear response of ENZ plasmon modes in ITO thin films near 1550 nm.

6

Chapter 2 Switchable Detector Array Scheme to
Reduce the Effect of Single-photon Detector’s
Deadtime in a Multi-bit/photon Quantum Link
2.1 Introduction
Quantum information systems have the ability to protect the information
channels against eavesdropping [40, 41]. This security is derived from the quantum
non-cloning theorem that any eavesdropping made by a third party would inevitably
leads to errors that can be detected by the sending and receiving parties [42, 43].
Typical qubits encoding on photon’s two polarizations can provide one bit/photon of
information [44, 45]. However, since each photon has only two orthogonal
polarizations, quantum system capacity might be increased if a basis set having more
than two orthogonal states is used for data encoding. One example may be through
the use of a set of orthogonal spatial modes, for which the photon can occupy one of
the many states at a given time [46]. A potential spatial basis set that has recently
received increasing interest is the OAM mode set, which is a subset of Laguerre
Gaussian (LG) modes [8, 47-52].
A light beam’s phasefront that has an azimuthal (𝜙) dependence of exp (𝑖ℓ𝜙)
will “twist” in a helical fashion as it propagates. Such a beam carries OAM
corresponding to ℓℏ per photon, in which the OAM charge ℓ represents the number
of 2π phase shifts in the azimuthal direction. An OAM beam will be orthogonal to
other OAM beams depending on its ℓ value. Since a single photon can carry a
distinct OAM charge, photons can be encoded on more orthogonal OAM states than
those provided by polarization states [6, 9, 53, 54]. Typically, a quantum system
encoded in 𝑀 OAM states (𝑀 =1,2,3,…) of photons could transmit up to 𝑙𝑜𝑔
!
𝑀
quantum bits per photon [8].
A key limitation for the incident photon rate in a quantum system is the
deadtime of a single photon detector (SPD). This deadtime is defined as the length of
time that the detector must recover after “firing” from one detected photon before it

7

is ready to detect and accurately register another incoming photon. This limitation on
incident photon rate would be present to a larger or smaller extent depending on the
deadtime of different SPDs. In typical avalanche photodiode (APD) based SPDs, the
deadtime ranges from ~50 ns for actively quenched APDs to ~10 µs for passively
quenched ones [55]. Gated APD based SPDs have the potential to be operated at
higher incident photon rate because their deadtimes only exist in some of the clock
cycles [56]. Some free-running superconducting single-photon detectors could also
achieve a shorter deadtime (about tens of picosecond) with a reduced dark count rate
than the APD-based SPDs [57-59].
For two-polarization-state quantum encoding systems, the deadtime
limitation on the incident photon rate of SPDs could be reduced by using a
switchable detection scheme [55, 60]. In this approach, more SPDs are used in the
receiver than are strictly necessary, and a controllable optical switch routes an
incoming photon away from an SPD that is still within its deadtime to a “fresh” SPD.
Previous reports have shown that a switchable SPD array with 𝑁 SPDs can
potentially operate at more than 𝑁 times the incident photon rate that a single SPD
can achieve for a single quantum channel [55, 60]; we note that this result was for a
goal of missing no more than 10 % of photon-containing incident pulses, which
could be considered as a limit for some quantum detection applications. In addition,
they show that a switchable 𝑁-SPD array can potentially operate at a higher incident
photon rate than that of a single SPD that has a deadtime reduced to 1 𝑁 ⁄ .
This chapter will firstly introduce the concept of using a switchable SPD
array in a multi-bit/photon quantum link where bits are encoded on 𝑀 OAM states.
The method explained in this chapter uses 𝑁 SPDs with a controllable 𝑀 × 𝑁
optical switch to route the incoming photon from an SPD within its deadtime to a
fresh active SPD awaiting a new photon. Then the Monte Carlo-based simulation
results are presented to show that the switchable SPD array scheme with 𝑁 SPDs
could operate at an increased incident photon rate under the same deadtime when the
same detection limitation is applied. For the case of 𝑀 = 4, 𝑁 = 20, the SPDs’
individual deadtime of 50 ns, an average photon number per pulse of 0.1, and under

8

the limitation that missing at most 10 % of the photon-containing pulses, the
switchable SPD array can operate at an incident photon rate of 2250 million counts/s
(Mcts/s). This is 25 times the 90 Mcts/s incident photon rate that a non-switchable,
4-SPD array will allow. The increase in incident photon rate is more than the 5 times,
which is the simple increase in the number of SPDs (𝑁) over the number of OAM
encoding states (𝑀).
2.2 Concept of the Switchable Detection Scheme

Figure 2.1 Concept of the detection schemes for a multi-bit/photon quantum link. (a) The 𝑀-
OAM-state-encoding; (b1-b3) the traditional detection scheme; (b4-b6) the switchable SPD array
scheme. In the traditional detection scheme, the incoming photon would be ignored when it arrives
during the deadtime of the SPD. In the switchable SPD array, the controllable 𝑀 × 𝑁 switch routes
the incoming photon to the first available fresh backup SPD when its primary SPD is dead and routes
the incoming photon back to its primary SPD once it becomes fresh.

Figure 2.1 illustrates the concept of the switchable detection scheme [61, 62].
The photons are generated by an attenuated, pulsed, weak-coherent-state laser source,
encoded in 𝑀 OAM states according to the information sequence. The transmitted
information, which is a sequence of integers ranging from 1 to 𝑀, is created using a
random number generator with each number having an equal probability of 1 𝑀 ⁄ .
Without loss of generality in the analysis, we ignore channel loss between the
sending and receiving parties in our model, as channel loss and detection efficiency
always appear as a product and are thus indistinguishable. Based on this assumption,

9

the incident photon rate at the receiving party equals the pulse frequency of the
single photon source (e.g., attenuated laser source) at the sending party. The pulse
frequency is varied in our simulation by varying the incident photon rate to show its
influence on the detection system. The amount of photons coming to the detection
array in a certain time period would be determined by the pulse frequency and the
average photon number per pulse of the single photon source (𝜇).
At the receiver part, an incoming photon having an OAM charge of ℓ will be
demultiplexed and sent to the corresponding ℓ
"#
SPD. The photon would be ignored
if it arrived during the SPD’s deadtime and the information it carries would be lost,
as shown in Fig. 2.1. (b1-b3). To achieve a higher information efficiency, we use a
switchable SPD array with 𝑁 SPDs and an 𝑀 × 𝑁 optical switch (𝑁 >𝑀). Among
the 𝑁-SPD pool, the first 𝑀 SPDs work as primary SPDs corresponding to each of
the 𝑀 OAM states, and the remaining 𝑁 − 𝑀 SPDs work as backups. The switch
dynamically routes incoming photons from a dead SPD to the next available fresh
backup SPD, as shown in Fig. 2.1. (b4-b6). At the start of the operation all SPDs are
fresh and ready to detect photons. The optical switch is set to route the first incoming
photon to its primary SPD. The control electronics monitors the output of every SPD
to check whether it fires. Once an SPD fires, the switching algorithm searches for the
first available fresh backup SPD and the switch routes the incoming photon(s) to this
backup SPD. By doing this, during the deadtime of the primary SPD, the assigned
backup SPD can replace it. If an SPD does not fire, then the switch state remains
unchanged. The input is always switched back to its corresponding primary SPD
when the latter becomes available. This process repeats for every pulse. The
switching algorithm is computer-programming based, so the search-and-route time
could be small compared to the switching time of the optical switch. In addition, the
switching time of a given optical switch could be described as constant in the scheme.
Therefore, this effect might be mitigated by using an offline digital signal processing
method after the detection process if the switching time is shorter than the time
period between two incoming photons. When working at high incident photon rates,
multiple SPDs might fire in a short time period and subsequently go into their “dead”

10

states. However, if enough backup SPDs are available, the detection system can
always detect the incoming photons with an acceptable percentage of missed photon-
containing pulses. This also allows for optimum use of an array of SPDs having
different deadtimes.
2.3 Simulation Results
The received photon number per pulse follows a Poisson distribution model
with the average photon number per pulse of 𝜇. That distribution gives a probability
of having more than zero photons in a pulse as 𝑝:
𝑝 =𝑃(𝑥 ≥0) =1−𝑃(𝑥 =0) =1−𝑒
$%
(2.1)
where:
𝑃(𝑥 𝑝ℎ𝑜𝑡𝑜𝑛𝑠 𝑖𝑛 𝑎 𝑝𝑢𝑙𝑠𝑒)=𝑒
$%
∙
%
!
&!
,𝑥 =0,1,2,… (2.2)
We assume that for each OAM state, the probability of having more than zero
photons in a single pulse period is 𝑞:
𝑞 =1−L
( $)
(
+
)
(
∙𝑒
$%
N=
*
(
(2.3)
We use a Monte Carlo-based simulation to determine the performance of our
switchable SPD array scheme, which is employed to obtain numerical estimations of
the photon detection events. To describe the ratio of missed photon-containing pulses
to all photon-containing pulses, a deadtime fraction (DTF) is defined as [55]:
𝐷𝑇𝐹 =
(+,,-. *01,-, 23456+4+47 *83534,
93561 *01,-, 23456+4+47 *83534,
(2.4)
Our simulation also assumes that: (i) the detector has 100 % detection
efficiency and no afterpulsing or dark counts; (ii) in a typical faint laser-based single-
photon source, 𝜇 is selected to be 0.1 to reduce the multiple-photon emissions; (iii)
an upper detection limit in some detection applications is 10 % DTF [55].

11

Figure 2.2 Simulation results of DTF versus the incident photon rate of different SPD arrays for
a 4-OAM-encoded quantum link. The dashed black horizontal line shows the 10 % DTF level. The
DTF curve for a non-switchable detection scheme (4 SPDs for 4 OAM states, no optical switch) with
10-ns deadtime is also shown for comparison (red dashed line).

As shown in Fig. 2.2, when 𝑀 = 4 with individual SPD deadtime of 50 ns, to
maintain the 10 % DTF level, a switchable 16-SPD array can work at ≈ 20 times the
incident photon rate of that for a non-switchable SPD array. The achieved gain in
speed is significantly more than the 4 times (where 𝑁 𝑀 ⁄ =16 4 ⁄ ) increase in the
number of SPDs. Comparing with the non-switchable detection scheme whose SPDs’
deadtime is reduced 5-fold to 10 ns, the switchable SPD array still offers higher
performance, as measured by the allowed incident photon rate when the number of
SPDs exceeds 7, while keeping the 10 % DTF upper limit. We note that for a non-
switchable SPD array, if the incident photon rate increases from 10 Mcts/s to 50
Mcts/s, 100 Mcts/s, 500 Mcts/s and 1 Gcts/s, to keep the same DTF performance
with that under a 10 Mcts/s incident photon rate, the SPD deadtime need to be
reduced inversely from 50 ns to 10 ns, 5 ns, 1 ns, and 0.5 ns, respectively. However,
when applying the switchable SPD array with the number of SPDs to be 5, 6, 12, and
16 under the incident photon rate of 50 Mcts/s, 100 Mcts/s, 500 Mcts/s and 1 Gcts/s,

12

respectively, the DTF performance could be comparable with that under an incident
photon rate of 10 Mcts/s, while still using 50-ns-deadtime SPDs.

Figure 2.3 Simulation results of DTF versus SPDs’ deadtimes for different SPD arrays for a 4-
OAM-encoded quantum link operating at a 100 Mcts/s incident photon rate. The dashed black
horizontal line shows the 10 % DTF level.

Figure 2.3 shows the DTF performance with different SPD arrays for various
deadtimes. We could see that when 𝑀 = 4 and under a 100 Mcts/s incident photon
rate, a switchable 16-SPD array can have SPDs with deadtime as large as ≈ 870 ns to
achieve a 10 % DTF. However, for a non-switchable SPD array, SPD deadtime of ≈
50 ns are required to achieve the same level of performance. This increase of allowed
deadtime is more than the 4 times increase in the number of SPDs where 𝑁 / 𝑀 = 16
/ 4. We note that if the incident photon rate is > 100 Mcts/s, the tolerance of SPD
deadtime might be less than that under 100 Mcts/s incident photon rate, and we could
use more SPDs in the switchable SPD array to get a suitable tolerance of SPD
deadtime.

13

Figure 2.4 Simulation results of DTF versus 𝝁 for different SPD arrays in a 4-OAM-encoded
quantum link. The dashed black horizontal line shows the 10 % DTF level. The DTF curve for a
non-switchable detection scheme (4 SPDs for 4 OAM states, no optical switch) with a 10-ns deadtime
is also shown for comparison (red dashed line).

In some applications, 𝜇 >0.1 might be needed for a multiple-photon
quantum system [63, 64]. When 𝜇 >0.1, the probability of detecting an event for
each SPD becomes larger so that SPDs are more likely to become “dead”. In this
case, a switchable SPD array with more SPDs is needed. Figure 2.4 shows that, when
𝑀 = 4, operating at an incident photon rate of 100 Mcts/s with individual SPD
deadtime of 50 ns, and the 10 % DTF limit is applied, the tolerance to 𝜇 could reach
≈ 0.6 or ≈ 0.85 with a switchable SPD array having 6 or 8 SPDs. By implementing a
switchable SPD array with > 12 SPDs, 𝜇 could be increased to >1. In addition,
when working at an incident photon rate of 100 Mcts/s, a non-switchable SPD
scheme with its SPDs’ deadtime reduced to 10 ns has a tolerance of 𝜇 ≈ 0.6, while a
switchable SPD scheme with individual deadtime of 50 ns and containing 6 or more
SPDs could tolerate a larger 𝜇 under the same 10 % DTF limit.

14

Figure 2.5 Simulation results of RDTF=10 % versus the number of detectors for a 4-OAM-
encoded quantum link.

RDTF=10 % is defined as the incident photon rate that results in a DTF of 10 %
[55]. It can be seen from Fig. 2.5 that when M = 4 and with SPDs’ individual
deadtime of 50 ns, increasing the number of SPDs from 4 to 20 improves the
RDTF=10 % from ≈ 90 Mcts/s to ≈ 2250 Mcts/s. This improvement in RDTF=10 % is
significantly more than the 5 times increase in the number of SPDs where N / M =
20 / 4. We could infer from Fig. 2.5 that if the SPD deadtime is limited, we could
still operate at a higher incident photon rate with more number of SPDs in a
switchable SPD array to maintain a DTF upper limitation of 10 %. We note that our
simulation indicates an ≈ 90 Mcts/s incident photon rate is allowed under the 10%
DTF limit when using 4 SPDs for 4 channels (the non-switchable SPD array case).
This allowed incident photon rate is larger than the estimation given in [65]. We
believe this is because under the µ = 0.1 assumption in our simulation model, there
are some “empty” pulses that the amount of incident photons at the receiver will be
less than that in [65] at the same incident photon rate. Thus a larger incident photon
rate could be allowed than that in [65] under the same condition.

15

Figure 2.6 Simulation results of DTF versus switch loss for different SPD arrays for a 4-OAM-
encoded quantum link operating at an incident photon rate of 100 Mcts/s. The dashed black
horizontal line shows the 10 % DTF level.

Clearly, the inevitable optical loss added by the switch needs to be kept to a
minimum, because as the switch loss increasing, more photons would be lost and the
DTF would increase. Figure 2.6 shows the DTF versus the switch loss for a 4-OAM-
encoded quantum link with different switchable SPD arrays. One can see that, with
individual SPD deadtime of 50 ns and an incident photon rate of 100 Mcts/s, in order
to keep within the DTF upper limit of 10 %, a switchable SPD array with 6, 8, 12, 16
SPDs could tolerate a switch loss of ≈ 0.26 dB, ≈ 0.45 dB, ≈ 0.47 dB, and ≈ 0.48
dB, respectively. We could also see from Fig. 2.6 that if the switch loss is > 2 dB, the
loss would be the major factor for the increased DTF, thereby diminishing the
advantage of using switchable SPD arrays. Moreover, there are reports showing
potential methods for low-loss, fast optical switches, like photonic crystal, quantum
dot, and silicon photonic based Mach-Zehnder type optical switches [66, 67]. This
might open the possibility for future applications of the switchable SPD array to
reduce the deadtime effects.
2.4 Conclusion and Discussion

16

In this chapter, we explore the use of an SPD array scheme to reduce the
effect of a detector’s deadtime for a multi-bit/photon quantum link. The case of data
encoding using M possible OAM states is specifically studied in this paper. Our
method uses 𝑁 SPDs with a controllable 𝑀 × 𝑁 optical switch and we use a Monte
Carlo-based method to simulate the quantum detection process. The simulation
results show that with the use of the switchable SPD array, the detection system can
allow a higher incident photon rate than what might otherwise be limited by
detectors’ deadtime. For the case of 𝑀 = 4, 𝑁 = 20, a 50-ns deadtime for the
individual SPDs, an average photon number per pulse of 0.1, and under the limit that
at most 10 % of the photon-containing pulses are missed, the switchable SPD array
will allow an incident photon rate of 2250 million counts/s (Mcts/s). This is 25 times
the 90 Mcts/s incident photon rate that a non-switchable, 4-SPD array will allow.
The increase in incident photon rate is more than the 5 times increase, which is the
simple increase in the number of SPDs and the number of OAM encoding states (e.g.,
𝑁 𝑀 ⁄ =20 4 ⁄ ).
In a quantum information system, the effects of detector dark counts must
also be considered, as it introduces additional errors. While passive beam-splitter tree
detection schemes have also been employed as an approach to reduce the effect of
the SPDs’ deadtime [55], the effects of detector dark counts in this approach have a
larger impact than the switchable SPD array scheme. This is because all SPDs in the
beam-splitter tree scheme are “turned on” for each incident photon pulse, the system
dark count rate is the sum of all the individual SPD dark count rates. However, for an
actively switchable scheme the system dark count rate is just the dark count rate of
the single SPD turned on by the control algorithm.

17

Chapter 3 Adaptive Optics (AO) Compensation in
an OAM-encoded Quantum Link
3.1 Introduction
Quantum optical communications holds the promise for secure transfer of data
over both free-space and fiber links [8, 40, 44, 68]. Commonly, data could be
encoded on two orthogonal quantum states of the photon, e.g., polarization [44, 68].
Orthogonality between the states is important in order to limit any crosstalk from one
state onto the other when encoding, transmitting, and decoding the single photon.
Importantly, there has been interest in quantum systems that utilize a larger
number of orthogonal states by using a larger “alphabet” set of characteristics of
photons. Such a larger alphabet might enable better performance in quantum
communication links, such as: (i) a larger transmission capacity in terms of bits/sec,
since an alphabet of 2N possible values can transmit N bits per symbol period; and (ii)
a higher photon efficiency in terms of bits/photon, since a single photon can now
carry N bits of information instead of 1; this is very similar to the difference between
binary data encoding using {0, 1} and M-ary data encoding using {0, 1, …, M-1} [9,
10].
One possible approach to a larger quantum alphabet could be utilizing a spatial
modal basis set for which a single photon could occupy one of many different
orthogonal spatial modes [7, 47, 51, 53, 69]. One possible basis set is OAM modes,
which is a subset of circularly symmetric LG modes [1, 2, 54, 70]. OAM-carrying
photons have phasefronts that “twist” at different rates and are orthogonal to each
other when propagating coaxially. The OAM-carrying photon also exhibits a vortex,
ring-like accumulated intensity profile with little power in the center [1, 2, 47].
In a uni-directional quantum free-space optical (FSO) communications link
using OAM encoding, the transmitter would encode each photon on one of many
possible OAM states and transmit the photon through free space, the receiver would
detect its OAM state [10]. For higher performance, it is often considered

18

advantageous to enable bi-directional data transmission in a quantum communication
system [11, 71].
In general, a key limitation of both classical and quantum FSO links is the
system performance degradation due to atmospheric turbulence [72-76]. For example,
turbulence affects the wavefront of a photon, such that the unique spatial phase
profile that defines its OAM state would be distorted. Turbulence is perhaps more
challenging for OAM encoding of a single photon than for polarization encoding,
and turbulence can decrease OAM modal purity and thereby increase inter-modal
crosstalk [72, 75, 76]. Adaptive optics (AO) has been shown to help mitigate
turbulence in: (i) single-directional OAM-based quantum links [77, 78] and (ii) bi-
directional OAM-based classical links [79]. To our knowledge, there has been little
reported work on using AO in bi-directional quantum links, especially for OAM-
encoded links.
In this chapter, we demonstrate using single-end AO compensation for
emulated turbulence in an OAM-encoded, bi-directional FSO quantum
communication link at 10 Mbit/s per channel. A rotatable phase screen plate with
pseudo-random phase distributions obeying Kolmogorov spectrum statistics is used
to emulate turbulence effects in the laboratory environment [72, 78]. Specifically,
with emulated turbulence and when the probe is turned on, the mode purity of
photons carrying OAM ℓ=1 is improved by ~ 21 % with AO mitigation. As a
proof-of-concept experiment, data is encoded with OAM values of {ℓ=−1,+2}
and {ℓ=−2,+1} for the forward and backward channels, respectively. For this
case, we found that the AO system could reduce the turbulence effects increased
quantum-symbol-error-rate (QSER) by ~ 76 % and ~ 74 %, for both channels in the
uni-directional and bi-directional cases, respectively.
3.2 Atmospheric Turbulence and AO Compensation to OAM-
Based Links
The inhomogeneity in the temperature and pressure of the atmosphere can lead
to variations of the refractive index in the transmission path of an FSO link. The

19

variations of refractive index can introduce phase distortion to the helical phasefront
of an OAM-carrying beam or photon, thereby increasing modal coupling and inter-
modal crosstalk [72, 75, 76], as presented in Fig. 3.1.

Figure 3.1 Concept of the atmospheric turbulence effects to the OAM-carrying photon. The
OAM photons will be converted from the desired state into other states with some probability due to
the turbulence effect.

An AO system can be used to mitigate the turbulence effects for both non-
OAM and OAM-based FSO links. The concept of utilizing AO system for crosstalk
mitigation is shown in Fig. 3.2. In a typical AO system, the wavefront distortion of a
beam could be measured by a wavefront sensor (WFS). Based on this measurement,
an error correction pattern could be derived and sent to a wavefront corrector (e.g., a
spatial light modulator (SLM) or a deformable mirror) through a feed-back loop [78].
Due to the phase structure of an OAM beam, it would be challenging to directly
measure its phasefront using typical Shack-Hartmann WFSs. One approach could be
using a Gaussian probe beam on a different polarization or wavelength that can be
easily separated out. This Gaussian probe can be measured by a Shack-Hartmann
WFS and be readily for being separated out [72, 78].
Atmospheric turbulence
Probability of the
photon state
!
1
A pure OAM state
!
1
After turbulence
!
4
!
2
!
3
!
5
1
Classical display
Classical display
Probability of the
photon state
1

20

Figure 3.2 Concept of using AO for crosstalk mitigation. The wavefront sensor measures the
phasefront distortion of the beam and the corresponding correction pattern is loaded on the wavefront
corrector to undo the distortion. (a2-a3) The measured OAM beam profiles after being transmitted
through the turbulent medium without and with the AO compensation. With the AO system, the
distorted OAM beams can be efficiently compensated.
3.3 Concept and Experimental Setup

Figure 3.3 Concept diagram of (a) using a single-end AO module for the bi-directional coaxis
OAM mode propagation through atmospheric turbulence and (b) simultaneous pre- and post-
AO compensation for a turbulence-induced, OAM-encoded, bi-directional quantum
communication link. TX: transmitter; RX: receiver; SPD: single photon detector.

Figure 3.3 (a) depicts the concept of counter-propagating OAM modes through
atmospheric turbulence with single-end AO compensation [11]. Two groups of
OAM-carrying photons coaxially propagate through the atmosphere in opposite
directions. The AO module placed at one end of the link (TX-2 side) is used to
compensate the phase distortion of the received OAM photons from TX-1 as the
post-compensation. The wavefront of the OAM-carrying photons coming from TX-2
Beam separator
Feedback
controller
Wavefront
Corrector
Beam
splitter
Wavefront
Corrector
Wavefront
Sensor
Corrected
OAM beams
Corrected
Gaussian beam
Gaussian beam
OAM beams
Turbulence Emulator
Free Space Propagation Adaptive Optics Compensator
@ #
!
@ #
"
Wavelength
demultiplexer
(b2) (b3) (b4) (b5) (b6)
(a1) (a2) (a3) (a4) (a5) (a6)
OAM
+1
OAM
+3
OAM
+5
OAM
+7
OAM
+9
Gaussian Beam
(b1)
(a1)
(a2)
Without AO system
(b2) (b3) (b4) (b5) (b6)
(a1) (a2) (a3) (a4) (a5) (a6)
OAM
+1
OAM
+3
OAM
+5
OAM
+7
OAM
+9
Gaussian Beam
(b1)
With AO system
(a3)
Time T1 T2 T3
…
OAM Converter
…
Free space bi-directional
photon propagation
OAM Converter
TX-1
OAM ℓ
"
OAM ℓ
#
Time T1 T2 T3
…
…
TX-2 OAM ℓ
$
OAM ℓ
%
RX-1 RX-2
AO
module
Atmospheric
turbulence
0 1 0 …
Data 1
0 1 1 …
Data 2
SPDs
0 1 1 …
Data 2
SPDs 0 1 0 …
Data 1
…
Forward propagation Backward propagation
T1 T2 T3
T1 T2 T3
Single-end
AO module
TX-1
OAM mode
Distorted OAM mode
Mitigated OAM
mode at RX-1
TX-2
OAM mode
Pre-distorted OAM mode
Mitigated OAM
mode at RX-2
Atmospheric
turbulence
(b)
(a)

21

are modulated by the wavefront corrector, with the same correction pattern used in
the post-compensation, in the AO module as the pre-compensation. These photons
then propagate backward through the same turbulent atmosphere. Fig. 3.3(b) shows
the concept diagram of simultaneous pre- and post-AO turbulence mitigation for an
OAM-encoded, bi-directional quantum communication link transmitting through the
atmosphere. The forward and backward data-carrying quantum channels are each
encoded with two different sets of OAM modes, generated at TX-1 and TX-2,
respectively. The phasefronts of the transmitted OAM photons will be distorted by
the turbulence effects, and the AO module could potentially reduce the distortion-
induced degradation for both the forward and backward channels simultaneously [79,
80].

Figure 3.4 Experimental setup of the AO-compensated, bi-directional, OAM-encoded quantum
communication link. AWG: arbitrary waveform generator; Attn.: attenuator; PBS: polarizing beam
splitter; Col.: collimator; PC: polarization controller; HWP: half-wave plate; SLM: spatial light
modulator; WFS: wavefront sensor; SPD: single photon detector; M.: mirror. *The OAM intensity
profiles are collected by using charge coupled device (CCD)-based camera in the classical domain.

Figure 3.4 presents the experimental setup. Two quantum channels are
generated at TX-1 and TX-2 by directly modulated lasers at 𝜆
)
=850 nm. Fiber-
based attenuators are used to attenuate the power of data channels to a single-photon
level. After the attenuation, custom-designed, fiber-input, free-space-output multi-
plane light conversion (MPLC)-based OAM converters transform Gaussian photons
into different OAM photons. Each converter has 7 single-mode fiber (SMF) inputs
corresponding to OAM {ℓ=−3,−2,−1,0,+1,+2,+3}. In the converter, the SMFs
are connected to a fiber array followed by a micro-lens array, collimating the
Gaussian photons to propagate in free space. The free-space Gaussian photons are
Turbulence
emulating
plate
Feedback
controller
Laser (λ
2
=785 nm)
Lasers (λ
1
=850 nm)
SLM
SPD 4
PBS
Col.
4-f system
λ
1
filter
HWP
Port (T1)
Port (T2)
Port (R3)
Port (R4)
SPD 3
Port (R2)
Port (R1)
Port (T3)
Port (T4)
AWG
Lasers (λ
1
=850 nm)
PC
Beam
reducer
Beam
expander
SPD 2
SPD 1
TX 1
RX 2
TX 2
RX 1
OAM photon (TX1-RX1)
OAM photon (TX2-RX2)
Classical Gaussian probe
Fiber
Electrical signal
M.
M.
M.
Beam
expander
Attn.
Attn.
λ
1
filter
OAM converter
AWG
ℓ=# ℓ=$ ℓ=% ℓ=&
Generated OAM intensity profiles*
OAM converter
AO module

22

sent to a multi-pass cavity where the photons are reflected 15 times at different
locations on a reflective phase plate. In each reflection, the wavefront of the photons
are shaped by different transverse phase profiles. The succession of these transverse
phase profiles forms a spatial unitary transform that converts the Gaussian photons to
coaxially propagating OAM photons with different orders (ℓ) [81].
A classical Gaussian probe beam at 𝜆
!
=785 nm placed at the TX-1 side is
orthogonally polarized with respect to the quantum channels. The probe is expanded
to the same diameter of the generated OAM beam with the largest beam size (i.e.,
ℓ=−3 beam in this experiment), which is 5.2 mm. The expanded Gaussian beam is
then combined with the quantum channels by using a polarizing beam splitter (PBS).
A 1.5:1 beam reducer is used to adjust the combined beam size such that the beam
could be fully captured by the SLM and the WFS. The reduced probe beam diameter
(D) is 3.24 mm. The combined probe beam and quantum channels coaxially
propagate through the turbulence emulator and the AO module. The turbulence
emulator is characterized by its Fried parameter, 𝑟
:
=1 mm [72]. The ratio 𝐷 𝑟
:
⁄ can
be used to describe the turbulence strength (𝐷 𝑟
:
⁄ =3.24 in this experiment) [72].
The AO module is placed at the TX-2 side, to mitigate distorted OAM photons from
TX-1 as the post-compensation. In the AO module, the probe beam serves for
wavefront distortion estimations and correction pattern retrieval [77-79]. The SLM
serves as a wavefront corrector. Two half-wave plates (HWPs) are used to align the
linear polarizations of the coming beams to the orientation of the SLM. The WFS
detects the wavefront distortion of the probe and the SLM is imaged with the WFS
using a 4-𝑓 lens system. A feedback loop is used to send the correction pattern
derived from the WFS to the SLM. The total length of the free-space optical path is
~1.5 m.
The mitigated quantum channel from TX-1 passes through another PBS and a
free-space bandpass filter centered at 𝜆
)
to filter out the probe beam. The OAM
photons are enlarged by a 1:1.5 beam expander and then counter-propagate through
another MPLC-based OAM converter. By using the OAM converter reversely, OAM
photons could be transformed back to Gaussian photons which are then sorted to

23

corresponding SMF outputs. The demultiplexed photons are then detected at RX-1
using silicon avalanche photodiode (APD)-based single-photon detectors (SPDs).
The SPDs have 50 ns deadtimes, 0.5 % after-pulsing probabilities, 500 count/sec
dark count rates, and ~ 40 % quantum efficiencies at the wavelength of 850 nm. The
detected events are recorded for offline digital signal processing [72]. The quantum
channel transmitted from TX-2 is first sent to the AO module and then propagated
through the turbulence emulator. Consequently, this quantum channel is pre-distorted
by the correction patterns on the SLM in the AO module as the pre-compensation,
before experiencing the turbulence distortion. Finally, this quantum channel is
received by RX-2 for demultiplexing and detection.
3.4 Experimental Results
A. AO Compensation for OAM-carrying Photons in Quantum
Communication Systems

Figure 3.5 (a1-e1) Channel transfer matrices when sending OAM modes {𝓵=−𝟑,…,+𝟑}
respectively for different cases. The numbers in (a1-e1) are measured in the quantum domain as
the ratio of the measured photon counts to the maximum photon counts in this matrix in a unit
of dB. (a2-e2) The photon counts ratio on received OAM modes {𝓵=−𝟑,…,+𝟑} when sending
only OAM 𝓵=𝟏 photons for different cases. TX: transmitter; RX: receiver.

Figures 3.5(a1-e1) show the quantum channel transfer matrices: (i) in the back-
to-back link (without the turbulence emulator in the optical path) with the probe
0.65
0.57
0.31
0.36
0.52
Photon counts ratio
Received OAM state Received OAM state Received OAM state Received OAM state Received OAM state
(a2) (b2) (c2) (d2) (e2)
RX OAM
(a1) (b1) (d1) (e1)
-3 -2 -1 0 1 2 3
-5.2 -6.2 -12.9 -9.6 -18.1 -19 -10.8
-3
-2
-1
0
1
2
3
TX OAM
-6.5 -3.6 -5.4 -10.7 -12.7 -9.9 -15.3
-8.6 -6.9 -3.2 -4.5 -7.2 12.6 -11.4
-10.8 -10.3 -3.8 0 -5.8 -7.5 -9.2
-9.1 -10.6 -5.7 -4.1 -2.7 -5.9 -9.6
-10.4 -16.9 -15.8 -7.3 -4.3 -4.4 -7.6
-13.5 -10.1 -7.3 -12.8 -12.4 -4.5 -4.5
(c1)
B2B w/o probe B2B w/ probe W/Tur. w/o AO w/o probe W/Tur. w/o AO w/ probe W/Tur. w/ AO w/ probe

24

being turned off (Fig. 3.5(a1)) and on (Fig. 3.5(b1)), (ii) under a random turbulence
realization with the probe off (Fig. 3.5(c1)) and on (Fig. 3.5(d1)) without AO
mitigation, and (iii) with AO mitigation while the probe is on (Fig. 3.5(e1)). Only the
forward quantum channel is transmitted in the link and the power of the classical
probe is ~ 72 dB higher than that of the quantum channel. In the back-to-back link
(Fig. 3.5(a1)), when sending OAM ℓ photons, most of the received photons remain
in the ℓ-th OAM order because of the orthogonality between OAM modes. The
influence of the classical probe on the quantum channel is shown in Fig. 3.5(b1).
Turbulence effects could induce the distortion to the wavefront of OAM-carrying
photons and increases the probability of the OAM photons existing in the undesired
orders (Fig. 3.5(c1)). The influence of the probe on the disturbed quantum channel is
shown in Fig. 3.5(d1). With AO mitigation, photons are better confined to their
desired OAM orders, as shown in Fig. 3.5(e1). Figs. 3.5(a2-e2) show the photon
leakage from the OAM ℓ=1 mode to the other modes when only OAM ℓ=1
photons are sent. In the back-to-back link with the probe off (Fig. 3.5(a2)), 65 % of
the received photons would stay in the desired mode. The received OAM ℓ=1
photon count ratio reduces to 57 % because of the power leakage of the probe (Fig.
3.5(b2)). With turbulence effects, this percentage decreases to 36 % with the probe
off (Fig. 3.5(c2)) and 31 % with the probe on (Fig. 3.5(d2)). This is improved by the
AO mitigation: 52 % of the received photons remain in the desired mode with the
AO mitigation (Fig. 3.5(e2)). The mode purity of OAM ℓ=1 photons is improved
by ~ 21 % with the AO mitigation when the probe is on.

QSER
Average photon number per pulse
(a)
0.106
0.102
0.071
0.060
0.053
∆=#
10 Mbit/s
$ %
&
⁄ =3.24
OAM mode spacing
QSER
(b)
(=1
10 Mbit/s
$ %
&
⁄ =3.24
*Ref. 6

25

Figure 3.6 QSER for (a) the OAM {𝓵=−𝟐,+𝟏}-encoded quantum link as a function of the
average photon number per pulse (𝛍) and (b) the two-OAM-encoded link as a function of OAM
mode spacing when 𝝁=𝟏. The transmitted rate of the link is 10 Mbit/s. *The dash-dot line are
experimental results from Ref. [6], in which the encoding OAM modes are {ℓ=+1,+4} generated
and received by SLMs.

Figure 3.6(a) shows the QSER curves as functions of the average photon
number per pulse (µ) under the five different situations in Fig. 3.5. The QSER is
defined as the ratio of error symbols to the total registered symbols. Only the forward
channel is transmitted at 10 Mbit/s and the channel is encoded with OAM {ℓ=
−2,+1}. When µ=1, the back-to-back QSER increases from 0.053 to 0.06 under
the influence of the power leakage of probe beam. Under the influence of turbulence
effects, the QSER increases to 0.102 with the probe off and 0.106 with the probe on.
This QSER is reduced to 0.071 with AO mitigation while the probe is on. The AO
mitigation reduces ~ 76 % (
:.):<$:.:=)
:.):<$:.:<:
×100 %) of the additional QSER increased
by the turbulence effects. We note that in reference [6], the QSER for the back-to-
back link is < 0.02 when µ=1, this might because in reference [6] the SLMs is used
to generate and receive encoding OAM-carrying photons of {ℓ=+1,+4}, which
have < -28 dB inter-modal crosstalk. Fig. 3.6(b) shows the AO compensation for the
quantum channel encoded with OAM modes with different mode spacings. The
channel is transmitted at 10 Mbit/s when µ=1. We use OAM mode groups {ℓ=
−1,−2}, {ℓ=−1,+1}, {ℓ=−2,+1}, and {ℓ=−2,+2} for the OAM mode
spacing ∆=1,2,3,4, respectively. The maximum back-to-back intermodal quantum
channel crosstalk values for these mode spacings are -9.3 dB, -14.9 dB, -19.9 dB and
-23.9 dB with the probe off, respectively. We can see from Fig. 3.6(b) that for a fixed
µ, smaller OAM mode spacing tends to result in larger back-to-back QSERs due to
the crosstalk effects. The AO mitigation tends to provide a better QSER
improvement when the back-to-back QSER is smaller, which correspond to a larger
OAM mode spacing. When ∆ >2 the channel crosstalk is <−15 dB, and the
QSERs tends to decrease slower with the increase of the OAM mode spacing.

26

B. AO Compensation for a Two-OAM Encoded, Bi-directional
Quantum Communication Link

Figure 3.7 The crosstalk matrices between encoded OAM states measured in the quantum
domain under different situations in a bi-directional quantum communication link. The numbers
in the matrices are normalized and in a unit of dB. The forward and backward channels are encoded
by OAM {ℓ=−1,+2} and OAM {ℓ=−2,+1}, respectively.

Figure 3.7 shows the crosstalk matrices between encoded OAM modes in the
bi-directional quantum link under the following situations (left to right): the back-to-
back link with the probe turned off and on; under a random turbulence realization
without AO compensation when the probe is turned off and on; and under the same
turbulence realization with the AO compensation when the probe is on. The forward
and backward channels are encoded with OAM {ℓ=−1,+2} and OAM {ℓ=
−2,+1}, respectively. The power of the classical probe is ~ 72 dB higher than that
of each quantum channel. In the back-to-back link, the orthogonality between
different OAM modes provides a ~ -14 dB crosstalk between encoding OAM modes.
The crosstalk of the bi-directional case is slightly higher than that of the single-
directional case for the same encoding OAM modes. This is perhaps majorly due to
the power reflection in the OAM converters. In the bi-directional case, the turbulence
effects added ~ 5 dB of crosstalk, which could be reduced by ~ 4 dB with AO
mitigation.
-1 +2
-2 +1
-1
+2
-2
+1
0 -14.9
-14.5 -1.4
0 -15.6
-14.9 -1.2
-1
+2
-1 +2
-2 +1
-2
+1
0 -14.1
-13.3 -1.9
0 -14.3
-13.8 -1.2
-1 +2
-1
+2
-2 +1
-2
+1
0 -10.3
-9 -2.2
0 -10.7
-9 -1.1
-1 +2
-1
+2
-2 +1
-2
+1
0 -9.7
-8.4 -0.8
0 -10.9
-8.8 -1.7
-1 +2
-1
+2
-2 +1
-2
+1
0 -13
-12.1 -1.6
0 -14.1
-13 -0.8
TX OAM TX OAM TX OAM TX OAM TX OAM
RX OAM
RX OAM
Fwd Ch. Bcwd Ch.
B2B w/o
probe
B2B w/
probe
W/Tur.
w/o AO
w/o probe
W/Tur.
w/o AO
w/ probe
W/Tur.
w/ AO w/
probe

27

Figure 3.8 (a) The QSER and (b) the registered photon rate in single-directional and bi-
directional quantum communication links for one random turbulence realization and (c)
QSERs under four different turbulence realizations, all at the strength of 𝐃 𝐫
𝟎
⁄ =𝟑.𝟐𝟒. (d) The
improvements of the AO mitigation in (a-c).

Figure 3.8 shows the QSER (Fig. 3.8(a)) and the registered photon rate (Fig.
3.8(b)) of the single-directional and bi-directional quantum communication links at
10 Mbit/s for each direction under one random turbulence realization. Fig. 3.8(c)
presents the QSERs under four different turbulence realizations. Fig. 3.8(d) shows
the AO mitigation improvements for Figs. 3.8(a-c). The quantum link is encoded by
OAM mode groups {ℓ=−1,+2} and {ℓ=−2,+1} for the forward and the
backward quantum channels, respectively. It could be seen from Fig.3.8(a) that the
AO system could help to reduce the turbulence-induced QSER by ~76 % and ~74 %
and improve the registered photon rates by ~64 % and ~62 %, for the single-
directional and the bi-directional link, respectively. Photon’s wavefront is distorted
because of the turbulence effect, and this increases the probability of the OAM
photons to be detected in the undesired orders, causing a larger QSER measurement.
The higher error rate could be mitigated by the AO system. The turbulence effects
also cause less photon registration, perhaps because the photons are distorted and
cannot be demultiplexed to ℓ=0 photons and recorded by the SPDs. This reduction
could also be mitigated by the AO system. We also notice that the improvement in
the forward and backward channels are similar (the difference is < 1 %) for the same
case. This similar improvement might due to the similar crosstalk in the opposite
directions. Fig. 3.8(c) shows that, under the four random-chose turbulence
realizations, QSERs all improved by >50 % with the AO mitigation. The QSERs of
B2B w/o
probe
B2B w/
probe
W/Tur.
w/o AO
w/o probe
W/Tur.
w/o AO
w/ probe
W/Tur.
w/ AO w/
probe
(b)
(Mbit/s)
B2B w/o
probe
B2B w/
probe
W/Tur.
w/o AO
w/o probe
W/Tur.
w/o AO
w/ probe
W/Tur.
w/ AO w/
probe
(a)
10 Mbit/s Rate; ! "
#
=%.'( ⁄ ; Forward channel: OAM -1 & +2; Backward channel: OAM -2 & +1; , = %; - =.
Realiza
-tion
Improvement
1 ~74 %
2 ~75 %
3 ~55 %
4 ~60 %
(c)
Improvements
Cases QSER Photon
counts
Single
-d
~76 % ~64 %
Bi-d ~74 % ~62 %
(d)

28

the forward and backward channels for these four turbulence realizations are all
similar, which also indicates the reciprocity of atmospheric turbulence and the
symmetry of the AO system [82].
3.5 Conclusion and Discussion
In this chapter, we presented that a single-end AO module is experimentally
demonstrated to mitigate the emulated atmospheric turbulence effects in a bi-
directional quantum communication link, which employs OAM for data encoding. A
classical Gaussian beam is used as a probe to detect the turbulence-induced
wavefront distortion in the forward direction of the link. Based on the detected
wavefront distortion, an AO system located on one end of the link is used to
simultaneously compensate for the forward and backward channels. Specifically,
with emulated turbulence and when the probe is turned on, the mode purity of
photons carrying OAM ℓ=1 is improved by ~ 21 % with AO mitigation. We also
measured the performance when encoding data using OAM {ℓ=−1,+2} and {ℓ=
−2,+1} in the forward and backward channels, respectively, at 10 Mbit/s per
channel with one photon per pulse on average. For this case, we found that the AO
system could reduce the turbulence effects increased quantum-symbol-error-rate
(QSER) by ~ 76 % and ~ 74 %, for both channels in the uni-directional and bi-
directional cases, respectively. Similar QSER improvement is observed for the
opposite direction channels in the bi-directional case.

29

Chapter 4 Photon Acceleration using a Time-
varying Epsilon-near-zero (ENZ) Metasurface
4.1 Introduction
An ENZ material exhibit a near-zero real permittivity — and consequently, a
small linear refractive index — over a certain spectral range. They exhibit intriguing
linear effects such as energy squeezing through narrow channels and arbitrary bends
[14, 15, 83], geometry-invariant resonance [21, 84, 85], quantum optical properties
[20], and unprecedentedly large nonlinear optical responses [17, 18]. It has recently
been demonstrated that large spectral translations of a probe beam can be induced by
pumping an ITO-based thin ENZ film through adiabatic frequency conversion (AFC)
process [29, 31, 86]. Prior work by Zhou et al. explains the AFC process by time-
refraction – that is a pump-induced, time- dependent change in the refractive index
(∆n) of an ITO film leads to a frequency blueshift or a redshift depending on the sign
of ∆n. In this chapter we investigate a complementary pathway for frequency
translation: a frequency blueshift of a beam through self-action effect where a carrier
frequency of the pump beam changes due to the time-varying effect induced by the
same beam. This effect was first experimentally observed in the optical domain using
gaseous plasma and is known as photon acceleration (PA) [87-89]. PA is a specific
case of the time- refraction process that results in only frequency blueshift. We note
that our experimental observation can also be explained as delayed-time self-phase
modulation effect [12].
A high-intensity laser pulse propagating through an ionization front
experiences a rapidly decreasing refractive index, leading to a spectral blueshift of
the light beam. While propagating through such medium, the leading edge of the
pulse experiences a higher index than its trailing part. As a result, the local phase
velocity increases over the duration of the pulse. For a sufficiently long propagation
distance, the trailing edge of the pulse accelerates to catch up to the leading edge,
resulting in temporal compression, as well as spectral broadening and blueshifting of

30

the pulse. If the change in the refractive index occurs at a timescale that is slower
than the characteristic oscillation time of the carrier frequency, this process leads to
AFC through self-action effect (Fig. 4.1).

Figure 4.1 Conceptual illustration of photon acceleration. When a laser pulse propagates in a
medium exhibiting a time-dependent refractive index (n), a decrease in n results in a blueshift of the
pulse and a broadening of the spectrum.
laser pulse
blueshift &
broadened spectrum
!
!
!
!
"
!
!
time-varying medium
Δn
t
t
0
pulse
0

31

Figure 4.2 (a) A schematic of the metasurface structure: An ENZ-based metasurface can be
optically induced as a time-varying medium, where (b) a dynamic redshift of the resonance
wavelength (λ0) leads to (c) a decrease in the effective refractive index of the metasurface at λ0.
This results in a frequency blueshift of a sufficiently intense pump pulse. (d) The measured
linear permittivity of the ITO layer using ellipsometry. (e) The numerically obtained field
enhancement in the vicinity of an antenna at the λ0 of the metasurface when pumped with an
electric field polarized along the horizontal axis as indicated by the horizontal arrow in the
figure. The vertical view of the field enhancement in ln(|E|
2
) is plotted from the center of one antenna
unit.

To demonstrate the self-action-induced PA effect, we consider a plasmonic
ENZ-based metasurface. Such an engineered metasurface exhibits a nonlinear
response that is orders of magnitude larger than the nonlinear response of the ENZ
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-8
-6
-4
-2
0
2
4
6
8
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-10
-8
-6
-4
-2
0
2
4
6
8
10
nanoantenna
ITO
glass substrate
high intensity
pump pulse
output blueshift
Re(n )
eff
Δn
eff
<0
λ
λ
0
high pump
intensity
low pump intensity
low pump
intensity
high pump intensity
Transmission
λ
λ0
b. c.
a.
1200 1000 1400 1600
Permittivity
0
imaginary
Wavelength (nm)
-1
1
real
d.
e.
ln(|E|
2
)
air
antenna
ITO
glass
field enhancement

32

medium itself [13, 30, 90-93]. The operation power requirement in such a
metasurface is reduced compared to that of a bare ENZ film due to a) the plasmonic-
antenna-enhanced near- field interactions with the ENZ layer, b) increased coupling
efficiency of the electromagnetic energy into the ENZ layer, and c) dynamic tuning
of the antenna resonance due to the change in the refractive index of the ENZ layer
(Fig. 4.2(a-c)). Consequently, the metasurface also exhibits an effective change in
the refractive index ∆n that is as large as |2.5| [90]. We note that there have been
several other demonstrations of AFC using solid-state systems, such as high-Q
optical cavity and photonic crystal waveguides [94-96]. In all of those cases a beam
needs to propagate through many wavelength long materials for frequency shift of
less than 200 GHz.
In this chapter, we report that nonlinear interactions of a near-IR pump beam
with a 92-nm thick ENZ metasurface leads to a frequency blueshift of ∼1.6 with
incident intensity of ∼4 GW/cm
2
due to PA effect. That incident intensity is up to
200 times lower than the previous demonstrations using pure ENZ thin films [31, 86].
We define the performance of such an interaction as the achievable frequency shift
per unit required in- tensity per unit nonlinear propagation distance, which is
4.35×10
−3
GHz·(GW/cm
2
)
−1
· μm
−1
of this ENZ metasurface. We note that in our
metasurface the thick glass substrate is for structural integrity and does not induce
any nonlinear response. Therefore, the nonlinear propagation distance for our
metasurface is the total thickness of the ITO film and the antenna. Furthermore, we
only use this performance metric for the ease of comparison with the reported
demonstrations of the effect using different nonlinear media. This performance
metric for the metasurface reported in this work is up to seven orders of magnitude
larger than previous demonstrations of PA in gaseous plasmas [88, 89]. We also
demonstrate that the observed blueshift is accompanied by a spectral compression of
the pump beam when operated near the metasurface resonance, which is due to the
anomalous dispersion.
4.2 ENZ Metasurface Device and Its Linear Characterization

33

The metasurface investigated in this work comprises an array of 27-nm-thick
gold plasmonic antenna on top of a 65-nm-thick ITO layer on a 1-mm-thick float
glass substrate. The ITO film exhibits a zero-real permittivity at ∼1390 nm
wavelength as measured using spectroscopic ellipsometry (Fig. 4.2(d)). A thin ITO-
ENZ film exhibits a number of leaky and surface modes [97]. Due to the near-field
interactions between the ITO and the antenna array, the metasurface exhibits a large
field enhancement inside the ITO layer (Fig. 4.2(e)). We present numerically
calculated dispersion curves in the wavelength-wavevector space in Fig. 4.3. Close
to the zero-permittivity frequency, the thin ITO film supports an ENZ mode that
resides outside the light line cone. The polarization-insensitive plasmonic antenna
array is fabricated using e-beam lithography on top of the ITO film. We choose the
dimensions of the plasmonic antenna array (inset of Fig. 4.4) such that the resonance
wavelength, in the absence of the ITO layer, is ∼1300 nm. Figure 4.4 shows the
simulated (using FDTD) and the experimentally obtained linear responses of the
metasurface measured using a thermal light source. The antenna array geometry is
chosen to be cross-shaped such that there is no polarization dependence in the linear
or nonlinear response. We note that the measurements shown in Fig. 4.4 is
insensitive to the input light linear polarization. In the presence of the ITO layer, the
localized plasmonic mode of the antenna array interacts with the ENZ mode of the
ITO layer. This near-field mediated interaction leads to a strong coupling-induced
resonance splitting of ∼500 nm. This splitting is larger than the linewidths of both
the plasmonic resonance and the ENZ mode. The strong coupling-induced resonance
splitting results in two distinct dips in the linear transmittance response of the
metasurface [13, 90, 91, 98]. We observe a dominant resonance at ∼1240 nm and a
weaker resonance at ∼1720 nm. As presented in Fig. 4.4, the two resonances are
clearly visible in the numerical simulation (red line). The main dip is observed in the
measured linear transmission (black line) of the metasurface. We note that i) the
simulation and experimental results of the linear transmission are close, and we
attribute the minor disagreements to various fabrication imperfections; and ii) the
weaker resonance of the metasurface at ∼1720 nm is out of the measurement range

34

of our optical spectrum analyzer (OSA), and thus we could not measure it in the
laboratory.

Figure 4.3: The calculated dispersion relations of the ITO layer in the metasurface using FDTD
method. LR-SPP: Long-range surface plasmon polariton, which is also referred to as the ENZ mode;
SR-SPP: Short-range surface plasmon polariton.

Figure 4.4 The normalized linear transmittance of the ENZ metasurface (Black dots:
experimental measurement; Red line: FDTD simulation). The blue dashed line shows the
simulated transmission resonance of the antenna array in the absence of the ITO layer. The inset
shows an SEM image of the fabricated metasurface. Each antenna unit has a dimension of 125 × 450
nm with a periodicity of 600 nm.
Wavelength (micron)
Re[k
x
] (10
7
m
-1
)
1.5 2.0 2.5 3.0
glass lightline
air lightline
b.
1.00
Berreman
1.15
1.36
1.66
2.14
3.00
0.5 1.0
SR-SPP
LR-SPP / ENZ
zero permittivity
c.
1
antenna array
without the ITO layer
1400 1600 1000 1200 1800 2000
Normalized transmittance
0.2
0
0.4
0.6
0.8
0.5μm
Wavelength (nm)
metasurface
(antenna on the ITO layer)

35

4.3 Nonlinear Characterizations of the ENZ Metasurface
We measure the nonlinear response using a single pump configuration [22].
The pump pulse, obtained from the output of a Ti:Sapph laser pumped optical
parametric amplifier, has a pulse duration of ∼60 fs and a repetition rate of 1 kHz.
We set the central wavelength of the pump pulse to be at ∼1240 nm which is nearly
resonant with the main dip of the metasurface. An adjustable free-space attenuator is
used to vary the intensity of the pump light. The average power is measured using a
calibrated photodiode. We use a 200-mm-long focal length lens to focus the beam
onto the metasurface with a measured focal spot size of 250 μm. The transmitted
light from the metasurface is collected by a multi-mode fiber that has a core diameter
of 50 μm with the help of another 100-mm focal length lens. The collected light is
then sent to an OSA to record the spectral information as a function of incident
intensity. Four representative normalized spectra of the measurements are presented
in Fig. 4.5(a). In Fig. 4.5(b), we show the central frequency of the pump light, as
collected after the metasurface, vs. the incident intensity. We observe that the central
frequency of the pump blueshifts with an in- crease in pump intensity and that the
maximum achievable blueshift of ∼1.6 THz occurs with a pump intensity of ∼4
GW/cm
2
. For an incident pump intensity larger than ∼4 GW/cm
2
, the frequency shift
saturates.
To verify the model of AFC, we perform a set of FDTD simulations to
numerically obtain the nonlinear frequency shift. We model the ITO layer with a
delayed, normalized χ
(3)
response while setting the intrinsic nonlinearity of the gold
layer to zero. We note that in our simulation, χ
(3)
·|E|
2
leads to the effective non-
linear change in the refractive index (∆neff) as observed in our experiment. The
results of the numerical simulation are shown in Fig. 4.5(b). The simulation results
are in excellent agreement with the experiment, confirming our hypothesis that the
large nonlinearity of the ITO layer is primarily responsible for the overall nonlinear
response of the system.
Next, we estimate the total intensity-dependent change in the ∆neff of the
material as experienced by the pump from the experimental and the simulation data.

36

To estimate the ∆neff, we can express the change in the frequency as ∆𝑓 =−L
>?
! @
N∗
(∆𝑛
-AA
(𝑡)/∆𝑡) [18]. Here, 𝑘 is the free space wavevector and L is the thickness of
the metasurface. Since the timescale of the nonlinear dynamics is set by the pump
pulse duration, we can set ∆𝑡 to be equivalent to the pump pulse duration. We
present these results in Fig. 4.5(c). We find that under pulsed excitation the
metasurface exhibits an absolute ∆neff that is as large as ∼1.45 which is equivalent to
the linear refractive index of most common optical materials (e.g., glass). We note
that although the ∆n of the ITO layer is positive due to the intraband dynamics [18],
the ∆neff of the coupled structure is negative [90]. This is because a positive ∆n of the
ITO layer leads to a beam that is resonant with the structure to become nonresonant
due to the time-varying change of the resonant condition.
We observe the frequency blueshift in experiment is accompanied by spectral
compression (Fig. 4.5(d)). This observation is in contrast to previous reports of
adiabatic frequency blueshift [31] and theoretical predictions [99] showing that in a
normally dispersive medium, the frequency blueshift is accompanied by spectral
broadening. We attribute our observation due to near-resonant excitation of the
coupled system. We inherently operate in the anomalous dispersion regime. Due to
the large ∆n, the pulse also experiences a large time-varying change in the dispersion
condition. We posit that a time-dependent change of anomalous dispersion
compresses the spectra in a dual fashion to temporal compression obtained using a
time- invariant anomalously dispersive medium. Our findings indicate the possibility
of spectral and, by extension, temporal manipulation of ultrafast pulse using
dispersion engineering in the time domain.

37

Figure 4.5 (a) Four representative intensity-dependent measured output spectra of the
metasurface. The spectral amplitudes are normalized to their respective peak values recorded
by the spectrum analyzer. (b) The pump frequency shifts as functions of the pump intensity. (c)
The intensity- dependent ∆neff induced by the pump pulse. The blue curves are simulation
results while the orange curves are experiment results in (b) and (c). (d) The measured full
width at half maximum (FWHM) of the output pulses as a function of incident intensity.
4.4 Conclusion and Discussion
In conclusion, we have demonstrated that a time-varying ENZ-based
metasurface can be used for frequency blueshifting. We emphasize that the nonlinear
effect we observed in a ENZ matasurface has a significantly reduced propagation
distance and an energy requirement that is many orders of magnitude smaller
compared with the implementation using gaseous plasma. Furthermore, due to the
extraordinarily large and ultrafast effective decrease in the refractive index, a time-
varying change in the dispersion condition can be exploited for the spectral
manipulation of an ultrafast pulse in the time domain. The findings may find
practical applications in designing on-chip or fiber-based frequency translators and
in investigating light-matter interactions at the nanoscale using a time-varying
medium.
1150 1200 1250 1300 1350
Wavelength (nm)
Normalized spectra (a.u.)
a.
1.6 THz
4.69 GW/cm
2
3.26 GW/cm
2
0.95 GW/cm
2
incident
0 1 2 3 4 5
Intensity (GW/cm
2
)
-1.5
-1
-0.5
0
n
eff
b. c.
measurements
simulation
0 1 2 3 4 5
Intensity (GW/cm
2
)
0
0.5
1
1.5
2
Shift in frequency (THz)
simulation
measurements
b.
0 1 2 3 4 5
Intensity (GW/cm
2
)
50
55
60
65
70
75
80
FWHM (nm)
d.

38

Chapter 5 Tunable Doppler Shift Using a Time-
varying Epsilon-near-zero (ENZ) Thin Film near
1550 nm
5.1 Introduction
Materials containing free charges, such as highly doped semiconductors, can
exhibit zero real part of permittivity at their bulk plasmon wavelength (zero-
permittivity wavelength, λzero) [14]. These materials are known as ENZ materials,
which have a near-zero linear refractive index near λzero due to the vanishingly small
real permittivity value. This region near λzero is referred to as the ENZ region of the
material. Such ENZ materials are reported to have the ability to exhibit unique linear
and strong nonlinear properties [13, 14, 16-19, 31, 33, 100]. Based on their strong
nonlinear optical responses, ENZ materials can be suitable candidates for exploiting
various reconfigurable telecom applications, such as high-speed optical switching,
optical signal processing, dynamic routing, and broadband frequency shifting [23, 29,
83, 101-103].
A subwavelength-thick ITO material, as one example of ENZ materials, has
been reported to possess an ultrafast, large, non-instantaneous, and intensity-
dependent time-varying change in the refractive index [13, 18]. Due to this time-
varying refractive index of ITO induced by a pump beam, the carrier frequency of a
sub-picosecond pulsed excitation beam can be shifted by up-to a terahertz (i.e., tens
of nanometers in wavelength) in a sub-μm thick ENZ material [31, 33]. This
frequency shift is analogous to the Doppler shift of light arising from a moving
boundary [33, 104, 105].
The nonlinear frequency shift utilizing time-varying ENZ materials has been
previous demonstrated: i) an up-to ∼2.8 THz frequency shift was induced in a 900-
nm thick aluminum-doped zinc oxide film when pumped at its λzero of 1250 nm [33],
and ii) an up to 14.9 THz frequency shift was observed in a 620-nm thick ITO film
when pumped near its λzero of 1240 nm [31]. However, there have been few reports

39

on an ENZ material-based, telecom C band nonlinear frequency shift. Therefore, it
could be of interest to explore the nonlinear optical effects, such as a Doppler shift in
light using ENZ materials in the telecom wavelength region.
In this chapter, we experimentally demonstrate tunable Doppler shift in the
reflected light of an ITO-ENZ film with a thickness of 80 nm. The ITO film is
pumped with pulsed light centered near the ENZ region of the ITO film (i.e., ∼1550
nm). We observe tunable frequency redshift in the spectra of light reflected from the
ITO film with a maximum value of 1.8 THz when the pump light has a ∼140
GW/cm
2
peak intensity, a ∼580 fs pulse duration, and a 40° incident angle. The
frequency shift saturates at a pump intensity of ∼140 GW/cm
2
. The maximum
attainable frequency shift decreases from 1.8 THz to 0.7 THz when the pump pulse
duration increases from ∼580 fs to ∼1380 fs. Moreover, for a pulse duration of ≲1
ps, the saturation energy of frequency shift for the ITO film decreases with the
increase of the pump pulse duration. This saturation energy remains almost stable for
≳1 ps pulse durations. The pulse intensity, incident angle and duration could be used
as “knobs” for controlling the magnitude of frequency shift introduced by the time-
varying ITO-ENZ film.
5.2 Concept and ENZ Material Design
A Doppler shift ∆f can arise from light reflected by i) a medium with moving
boundary and fixed refractive index n0 (Fig. 5.1(a)) or ii) a stationary medium with a
time-varying refractive index n = n(t) (Fig. 5.1(b)), which are identical to each other.
In ii), the plane of constant phase experiences a phase shift φ [104, 105]:
𝜑 =𝑘
:
𝑛(𝑡)𝐿, (5.1)
where 𝑘
:
=2𝜋𝑓
:
/𝑐 is the free-space wavenumber of the pump light, 𝑛(𝑡) is the time-
varying refractive index of the medium, and 𝐿 is the thickness of the medium. For a thin
(sub-μm) time-varying medium, the frequency shift induced to the wavefront can be
expressed by [33]:
∆𝑓 =
∆C
! @
=−
)
! @
DE
D5
=−
>
#
?
! @
.4 (5)
.5
=−𝐿
.4 (5)
.5
∙
A
#
2
(5.2)

40

with the time-dependent change of refractive index (i.e., ∆𝑛) inside the material, a
Doppler shift could be induced in the reflected light, as presented in Fig. 5.1(c) [33,
106].
We design and deposit an 80-nm ITO film by using direct current (DC)-
magnetron sputtering at an elevated temperature of 500°C, in an oxygen partial
pressure on a z-cut sapphire substrate (Fig. 5.2(a)). The λzero of the ITO can be
engineered by tuning the doping density [18, 25, 107, 108]. We design the λzero of
this ITO film to be ∼1550 nm, which is verified by the linear permittivity
measurement using ellipsometry, as shown in Fig. 5.2(b). We define the ENZ region
to be the wavelength range where |Re(ε)| < 0.2, thus the ENZ region of this ITO
material sample is ∼1520 nm to ∼1580 nm.

Figure 5.1 Concept of Doppler shift. A Doppler shift in frequency can be induced when the light is
reflected by (a) a moving medium with a fixed refractive index n0 or (b) a stationary medium with a
time-varying refractive index n(t). (c) In the latter case, the change in refractive index (∆n) of the
medium results in a frequency shift in light. f0: the central frequency of the pump light; ∆f: the
frequency shift in the reflected light; L: the medium thickness.

Pump light
Redshifted
light
!(#)
%
stationary medium
t
!
∆!
"
'
!
'
!
−∆'
∆'
(b)
Pump light Redshifted light
(c)
moving medium
Pump light
Redshifted
light
!
!
%
(a)

41

Figure 5.2 (a) The sample: 80 nm thick ITO film deposited on a sapphire substrate. (b) Linear
relative permittivity of the ITO material measured by spectroscopic ellipsometry, showing λzero
∼1550 nm.
5.3 Experimental Setup and Results

Figure 5.3 (a) The experimental setup for the nonlinear frequency Doppler shift
characterization shown in Fig. 5.4(b). Examples of (b1) the input and (b2) output spectra of the
ITO film. The output spectrum shows a maximum attained frequency shift of 1.8 THz at a pump
intensity of ∼140 GW/cm
2
and a 40° incident angle. HWP: half-wave plate.

We characterize the Doppler shift and the experimental setup is shown in Fig.
5.3(a) [32]. A pulsed laser source with a 606 kHz repetition rate and a ∼580 fs pulse
duration provides the pump light. The laser output light has a spectral wavelength
Permittivity (!) measurement
!
!"#$
~1550 '(
(b)
Sapphire
ITO
80 nm
ITO-ENZ material (a)
ENZ region
1
0.5
0
1500 1550 1600 1500 1550 1600
Normalized Intensity (a.u.)
Wavelength (nm) Wavelength (nm)
Input peak:
1545 nm
(194.0 THz)
Shifted peak:
1560 nm
(192.2 THz)
Wavelength
shift: 15 nm
(1.8 THz)
Input spectrum Output spectrum
(a)
(b1) (b2)
Short pulsed laser
Power meter
HWP
Spectrum analyzer
ITO-ENZ film
Collimator
Polarizer Flip mirror
!

42

center at ∼1550 nm and is parallel polarized with respect to the plane of incidence.
The incident power is tuned by using a polarizer and a half-wave plate. We focus the
light onto the ITO film as a spot with a ∼13 μm diameter using an aspheric lens
which has an effective focal length of 11 mm. The reflected light from the ITO film
is collected by using another aspheric lens of same focal length and a 1-m multi-
mode fiber with a core diameter of 50 μm. An optical spectrum analyzer is used to
measure the spectrum.
We observe a 1.8 THz maximum frequency shift value in the reflected light at
a pump intensity of ∼140 GW/cm
2
and an incident angle of 40°. Figure 5.3(b1-b2)
presents the normalized spectra of the incident and reflected light, respectively,
showing the maximum frequency shift of 1.8 THz. The reflected spectrum has two
peaks: the reflected pump light with a center of 1545 nm (∼194.0 THz), and the
redshifted light with a center at 1560 nm (∼192.2 THz). The reasons for the two
observed peaks in the reflected light might be a) the ITO thickness is smaller than the
longitudinal length of the pulse, therefore not all of the pulse reside inside the layer
at the same instance and the spectrometer measures the time-averaged spectra of the
reflected pulse; b) some of the pump light may be reflected directly from the top
surface of the ITO and may not pass through the time-varying ITO medium, and c)
the ∆n in the ITO medium induced by the pump light might be delayed in time
domain compared to the pump pulse itself so that some of the pump light does not
experience this ∆n and cannot be shifted [18].

Figure 5.4 (a) Illustration of pump pulse intensity influence to the frequency shift amount: (a1)
a lower pump power leads to a smaller ∆n in the ITO material, thus resulting in smaller ∆f,
while (a2) a larger pump power leads to a larger ∆f. (a3) The amount of ∆n has a limitation due
(b)
t
I
pump
(t)
!n(t)
SmallerΔ#/Δt
(a1) Lower power
Smaller Δ%
t
I
pump
(t)
!n(t)
(a2) Higher power
Larger Δ#/Δt
Larger Δ%
(a3) Even higher power
I
pump
(t)
!n(t)
t
Δ#/Δt saturates
Δ% saturates
Pump power increasing

43

to free-electron density limitation that the ∆f saturates with the increase of pump power. (b)
Measured Doppler shifts as functions of pump intensity under various pump incident angles (θ).

A pulsed pump with a central wavelength in the ENZ region of ITO induces a
time-dependent ∆n of the ITO film over sub-ps time [18, 31]. This ∆n is caught by
the pump light, which induces the frequency shift. According to Eq. 5.2, the light
beam’s frequency shift is proportional to 𝑑𝑛 𝑑𝑡 ⁄ . When the light experiences a
positive ∆𝑛 during the rising side of the pulse, a redshift in the frequency can be
observed. The amount and sign of 𝑑𝑛 𝑑𝑡 ⁄ depend on the pump intensity, pump
temporal envelope, and the intrinsic nonlinear properties of the ITO material [18, 31,
32]. For pump pulses with a fixed duration, the ∆𝑛 of the ITO is over a fixed time
period (∆𝑡), a higher pump intensity leads to a larger ∆𝑛 over the same ∆𝑡 compared
with the case of a lower pump intensity (Fig. 5.4(a1-a2)). In addition, the amount of
the ∆𝑛 in the ITO has a limitation due to the limitation of free-electron density inside
the ITO medium [109], thus 𝑑𝑛 𝑑𝑡 ⁄ saturates as the ∆𝑛 reaches the limitation at a
certain pump intensity, leading to the saturation of frequency shift (Fig. 5.4(a3)).
We characterize the frequency shift amount as functions of pump intensity for
various pump incident angles (θ) as shown in Fig. 5.4(b) and frequency redshifts are
observed. When θ is fixed, the frequency shift magnitude increases with the increase
of pump intensity until reaching a saturation (i.e., the frequency shift amount does
not continue to change with the increase of the pump intensity). This agrees with the
time-dependent ∆𝑛 explained in Fig. 5.4(a). We note that in Fig. 5.4(b), for small
incident angles (0°∼10°) we add a pellicle beam splitter (BS) to collect the ITO
reflected light. This nearly halves the pump intensity shining on the ITO film thus
the maximum pump intensity is smaller than other angles.
5.4 Influence of Pump Pulse Duration on the Doppler Shift
Effect of ITO-ENZ Material

44

Figure 5.5 Experimental setup for modifying the pump pulse duration for measurements in Fig.
6(b-d). Inset (i-ii): FROG measurement of the pulse temporal shape of (i) the initial pulse and (ii)
one example of the stretched pulse. HWP: half-wave plate; M.: mirror; FROG: frequency-resolved
optical gating.

To investigate the influence of the pump pulse duration on the Doppler shift
effect of the ITO material, we stretch the duration of the pump pulses. The
experimental setup is presented in Fig. 5.5. A pair of diffraction gratings (Richardson
Gratings, 53-*-660R) are used to stretch the pulse duration. Between the gratings,
different wavelength components in the pulsed light travel with different distances,
which leads to stretching of the pulses due to the chromatic dispersion of light. This
dispersion is measured to be positive and can be tuned by varying the distance
between the two gratings using a moving stage to parallelly move one of the gratings.
A frequency-resolved optical gating (FROG) is used to measure the stretched pulses
in the temporal domain. Fig. 5.5 inset (i) shows the FROG measurement of the
original pulse with 584 fs duration, and Fig. 5.5 inset (ii) shows an example of
modifying the pulse to 1020 fs duration. The pulsed light is then focused onto the
ITO film using the same aspheric lens as in the setup of Fig. 5.3(a) to achieve the
same spot diameter of ∼13 μm. With the same reflected light collection method as in
Fig. 5.3(a), the output light is collected for spectrum analysis.
Short pulsed laser
Power meter
HWP
Spectrum analyzer
ITO-ENZ film
Collimator
FROG measurement
Grating 1
Grating 2 M.
D-shape M.
Flip M.
M.
Flip M.
Moving stage
HWP
-1000 -500 0 500 1000
1
0.5
0
Normalized amplitude (a.u.)
584 fs
-1000 -500 0 500 1000
(i)
1020 fs
(ii)
Time (fs)
1
0.5
0

45

Figure 5.6 (a) Illustration of the pump pulse duration influence on the n(t) of ITO. (b) Measured
frequency shift as functions of the pump pulse energy under different pulse durations. (c) The
maximum attainable frequency shifts and (d) the energy at which the frequency shifts saturate
as functions of pump pulse duration.

As presented in Fig. 6(a), pump pulse with a shorter duration has a larger pulse
amplitude changing slope, leading to a larger 𝑑𝑛 𝑑𝑡 ⁄ in the ITO material compared to
the case of a longer pump pulse duration. Moreover, the saturation of 𝑑𝑛 𝑑𝑡 ⁄ would
also be reached at a higher pulse energy when the pulses are narrower in time
domain. The Doppler shift amount is relatively proportional to the 𝑑𝑛 𝑑𝑡 ⁄ in the ITO
material. Fig. 5.6(b) presents the measured Doppler shifts under different pump pulse
durations. The measurements are taken at an incident angle of 40°, under which the
maximum frequency shift is achieved for the original pulse case with 584 fs pulse
duration. We find that under a given pump pulse duration, the frequency shift firstly
increases with the increase of pulse energy then saturates, which is similar to the case
with the original, unstretched pulse. We note that adding the grating-pair introduces
extra loss in the setup, thus the stretched pulse case has lower maximum energy than
the original pulse case in Fig. 5.6(b). The maximum attainable frequency shifts for
different pump pulse durations are summarized in Fig. 6(c). When the frequency
shift saturates with pump energy, the maximum attainable frequency shift is
achieved. This maximum attainable frequency shift decreases almost linearly from
1.8 THz to 0.7 THz when the pump pulse duration increases from ∼580 fs to ∼1380
fs. This may be due to the smaller 𝑑𝑛 𝑑𝑡 ⁄ induced by the longer pulse duration. Fig.
5.6(d) shows that the saturation energy of frequency shift decreases with the increase
(d)
(b)
(c)
(a)
t
I
pump
(t)
∆"($)
t
I
pump
(t)
Ø Larger
!"($)
!$
Ø
!"($)
!$
saturates at
higher energy
Ø Smaller
!"($)
!$
Ø
!"($)
!$
saturates at
lower energy
Narrower pump pulse
Wider pump pulse
Slope
!"($)
!$
Slope
!"($)
!$
∆"($)
580 fs
full curve

46

of the pulse duration and remains almost unchanged for pulses longer than 1 ps. This
is likely because that the 𝑑𝑛 𝑑𝑡 ⁄ saturates at a lower pump pulse energy under a
wider pulse and the saturation of 𝑑𝑛 𝑑𝑡 ⁄ leads to the saturation of frequency shift
amount with the pulse energy.
5.5 Conclusion and Discussion
In this chapter, we experimentally investigate tunable Doppler shift in an 80
nm thick indium-tin-oxide (ITO) film at its epsilon-near-zero region. Under strong
and pulsed excitation, ITO exhibits a time-varying change in the refractive index. A
maximum frequency redshift of 1.8 THz is observed in the reflected light when the
pump light has a peak intensity of ∼140 GW/cm
2
and a pulse duration of ∼580 fs, at
an incident angle of 40°. The frequency shift increases with the increase of the pump
intensity and saturates at the intensity of ∼140 GW/cm
2
. When the pump pulse
duration increases from ∼580 fs to ∼1380 fs, the maximum attainable frequency
shift decreases from 1.8 THz to 0.7 THz. In addition, the pump energy required to
saturate the frequency shift decreases with the increase of pump pulse duration for
≲1 ps and remains unchanged for ≳1 ps durations. Tunability exists among the
pump pulse energy, duration, and incident angle for the Doppler shift of the ITO-
ENZ material, which can be employed for designing efficient frequency shifter for
telecom applications.

47

Chapter 6 Nonlinear Response of Epsilon-Near-
Zero (ENZ) Plasmon Modes in Indium-Tin-Oxide
(ITO) Thin Films near 1550 nm
6.1 Introduction
Materials with near-zero permittivity (i.e., ENZ materials) can perform unit-
order, pumping intensity dependent nonlinear refractive index change, which is
significantly larger compared to the conventional materials whose nonlinear
refractive index change are mostly on the order of 10
−3
[12]. This nonlinear
refractive index change has been shown to be a few times larger than the linear
refractive index in ENZ materials and leads to strong nonlinear optical properties [13,
17, 18, 25, 26, 31].
ITO, as a common transparent conductive oxide, is one example of ENZ
material and has been demonstrated to exhibit nonlinear effects such as large
nonlinear refractive index change [13, 18, 31]. Third harmonic generation (THG), as
another nonlinear optical effect, has been demonstrated in sub-μm ITO film in the
near-infrared region [25, 26] and has been shown to perform an efficiency of ∼600
times larger than that in the crystalline silicon [25]. Specifically, nonlinear optical
phenomena in the ∼1550 nm band enables broad range of telecommunication and
optical data processing applications [12, 101]. Due to their large nonlinear optical
responses, ENZ materials has been considered as a suitable candidate for these
applications particularly on chip for the sub-μm light matter interaction length [23,
29, 83, 102, 103]. Previous work has reported an intensity-dependent nonlinear
frequency shift using ITO-ENZ material in the ∼1550 nm band [32].
By excitation of ENZ mode in sub-μm ITO film using Kretschmann geometry
coupling method under total reflection condition, the THG efficiency has been
shown to be enhanced by two orders of magnitude compared with the case using air-
coupling method under the normal incident angle due to the field enhancement inside
the ITO film [26]. It might be beneficial to explore the mode coupling conditions

48

inside the ITO thin film to enhance the ITO-ENZ material nonlinearity and to reduce
the intensity requirement for the nonlinear responses, especially in the ∼1550 nm
band for potential applications.
In this chapter, we show in simulation that the nonlinear phase change
(NLPC)– one of the nonlinear refractive index change effects–of sub-μm ITO-ENZ
film can be enhanced by efficient light coupling to the ENZ mode of ITO. The ITO-
ENZ film we study in this paper has an ENZ wavelength (λENZ) of ∼1550 nm. We
observe that the efficient ENZ mode coupling can be achieved by utilizing the
Kretschmann geometry coupling method at the total reflection angle. Under this
efficient ENZ mode coupling condition, the required pumping energy can be
decreased by around two orders of magnitude to achieve similar amount of NLPC
compared with the case of bulk nonlinear response of the same film. This reduction
of required energy is majorly due to the electrical field enhancement inside the ITO
film. It was also indicated in simulation that the NLPC decreases with the increase of
ITO loss and reaches a maximum amount at an optimal thickness of ITO (this
optimized thickness in our simulation is ∼100 nm). We believe this is related to the
combined effects of the electrical field and the light-matter interaction length inside
the ITO film.
6.2 Concept of ENZ Mode Coupling and Dispersion Relation in
ITO Thin Film
The ITO material, as one example of ENZ materials, perform zero-value real
part permittivity at a certain frequency (zero-permittivity frequency/wavelength, also
referred to as ENZ frequency/wavelength, fENZ or λENZ). The ITO layer supports a
Berreman mode at λENZ and the surface plasmon-polariton (SPP). In a thin (sub-μm)
ITO layer, the SPP splits into short- range SPP and long-range SPP, the long-range
SPP is referred to as ENZ mode which is also close to λENZ [97]. By efficient light
coupling to the ENZ mode of the ITO material, the electrical field inside the ITO
film would be concentrated and thus the ITO nonlinear response would be enhanced.
Fig. 6.1 shows the excitation geometries we investigate [110]. Fig. 6.1(a1) shows the

49

air-coupling geometry in which the pump incident at an angle of θ to the ITO film
from the air (n=1). The lightline in the air does not cross the ENZ mode thus it is
hard to couple the light from air, as presented in Fig. 6.1(a2). In the Kretschmann
geometry (Fig. 6.1(b1)), a prism is index-matched to the sapphire substrate (n=1.45)
of the ITO sample and is put at the substrate side, the pump light incidents an angle θ
from the prism side. The Kretschmann geometry provide the lightline in sapphire
substrate which crosses the ENZ mode of ITO, thus providing required light
momentum for pump light and ENZ mode coupling (Fig. 6.1(b2)).

Figure 6.1 Concept of the ENZ mode coupling. (a) Air coupling: the pump incidents from air
(a1) and the ENZ mode line does not cross the lightline in the air thus it is hard to couple from
air (a2). (b) Kretschmann geometry coupling: the pump incidents from the prism which is
index-matched to the substrate of ITO (b1) and the ENZ mode crosses the lightline in the prism,
provides required momentum for light coupling (b2).
Pump
R
T
ITO
Substrate
(a1) Air coupling
!
air lightline
k
!
(a2) ITO dispersion relation
Pump
R
T
ITO
Substrate
(b1) Kretschmann geometry
!
Prism
Light coupled to
the ENZ mode
k
!
(b2) ITO dispersion relation
Berreman
LR-SPP/ENZ
air lightline
sapphire lightline
LR-SPP/ENZ
Berreman

50

Figure 6.2 Calculated dispersion relations of (a) 100-nm ITO film and (b) 20-nm ITO film by
using FDTD method.

Figure 6.2 presents the calculated dispersion relations of the ITO films with
different thicknesses [110]. A Berreman mode at fENZ is supported and surface
plasmon-polariton (SPP) exists in both thicker (100 nm, Fig. 6.2(a)) and thinner (20
nm, Fig. 6.2(b)) ITO films. Compared with a thicker 100-nm ITO film as shown in
Fig. 6.2(a), a thinner 20-nm ITO, the dispersion diagram of which is shown in Fig.
6.2(b), has a long-range SPP closer to and almost at the same frequency with the
Berreman mode of ITO. In addition, a lightline which has a crossing with a mode of
the ITO material can provide required light momentum to couple to this mode. The
lightlines in sapphire shown in Fig. 6.2 have crossings with the ENZ mode for both
of the 20-nm and 100-nm thick ITO films, but the lightline in air does not cross with
the ENZ mode. Thus, we can infer from the dispersion relation that if pump light can
be coupled from sapphire (ITO sample substrate material in this paper) to the ITO
film, it might be more efficiently coupled to the ENZ mode.
6.3 Simulation Results
(a) (b)
air lightline
sapphire
lightline
air lightline
sapphire lightline
SR-SPP
SR-SPP
LR-SPP/ENZ
Berreman & LR-SPP/ENZ
Berreman

51

Figure 6.3 Simulation results of: (a) the |E|
2
enhancement factor for various incident angle for
air coupling and Kretschmann geometry coupling; and the nonlinear phase change (NLPC) (b)
at an incident angle of 35° for air-coupling and Kretschmann geometry cases and (c) at
Kretschmann geometry coupling case with 0° and 35° incident angles. All the |E|
2
enhancements
are compared with the |E|
2
of 0°, air-coupling case. All the NLPC simulations are for 100-fs short-
pulsed pump light with a 1550 nm central wavelength.

FDTD simulations are performed for the investigation of ENZ mode coupling
conditions. The field intensity (|E|
2
) distribution and nonlinear response of the ITO
material are numerically studied. Figure 6.3 (a) presents the |E|
2
enhancement factor
under various light incident angles θ for the two coupling conditions in Fig. 6.2. The
enhancement factors are calculated compared to the case of air-coupling geometry at
normal incident angle (θ=0°). Up-to ∼5.7 times of |E|
2
enhancement is observed in
Kretschmann coupling geometry at θ=35° which is the sapphire/air critical angle (i.e.,
total reflection angle). In the meantime, up-to ∼2.7 times of |E|
2
enhancement is
observed for the air-coupling condition at around θ=45°. These may be due to that: a)
the index-matching between the prism and the sapphire substrate of ITO film
provides required momentum of light for ENZ mode coupling, thus the Kretschmann
geometry could achieve larger maximum |E|
2
enhancement than the air-coupling case;
and b) the critical angle of incidence helps with a better light absorption of ITO film
therefore leads to larger |E|
2
. We also calculate the NLPC of the output light to
characterize the ITO nonlinear response under different coupling conditions. The
NLPC is calculated by solving Maxwell’s equations using FDTD method [111]. In
the simulation, we consider the time-dependent Kerr interaction to the 3rd order [22,
111] and set the pump to be pulsed light with a 100-fs pulse duration and a 193.4
THz center frequency (i.e., 1550 nm in wavelength). The simulation results of NLPC
for the two coupling conditions are shown in Fig. 6.3(b). We note that for fair
0.8!
0.6!
0.4!
0.2!
0
Nonlinear phase change
Nonlinear phase change
0.8!
0.6!
0.4!
0.2!
0
~100X ~350X
(a)
(b) (c)
~5.7X
~2.7X

52

comparison, we present the two coupling conditions at θ=35°, because the
Kretschmann geometry reaches maximum |E|
2
enhancement at θ=35°, while air-
coupling condition reaches maximum |E|
2
enhancement at θ=45° and the |E|
2
does
not change much between θ=35°∼50°. We observe that in both cases the NLPC
saturates with the in- crease of pump intensity. The Kretschmann geometry coupling
case reaches a) same NLPC value with an up-to ∼350 times reduction in pump light
intensity, and b) ∼1.6 times maximum attainable NLPC value compared to the air-
coupling case. Fig. 6.3(c) presents the NLPC of Kretschmann geometry coupling for
different angles. The θ=35° case provides improved NLPC than the θ=0° case by i)
reducing the required pump intensity of up-to 100 times to reach the same NLPC
value and ii) improving the maximum attainable NLPC of ∼1.3 times. We believe
the above NLPC enhancements are related to the |E|
2
enhancement inside the ITO
film: the Kretschmann geometry provide more efficient ENZ mode coupling, leading
to a more enhanced |E|
2
inside the ITO film, and a good incident angle (e.g., the
critical angle in Kretschmann geometry) provide better light absorption.

Figure 6.4 Simulation results with Kretschmann geometry coupling condition at 35° incident
angle of: (a) the |E|
2
enhancement factor, (b) transmission dip, and (c) NLPC for different ITO
thickness.

The |E|
2
enhancement, linear transmission, and the nonlinear response
dependence on the ITO-thickness are numerically explored as shown in Fig. 6.4 in
which the incident angle is kept at θ=35° and Kretschmann geometry coupling is
employed. We observe from Fig. 6.4(a) that a thinner ITO film results in larger |E|
2

enhancement for ITO thickness of 1-200 nm. When the ITO film is thicker than 200
nm, the |E|
2
enhancement becomes negligible. This maybe because the ENZ mode
becomes weaker for thicker ITO film [97], thus the ENZ mode coupling is also
Nonlinear phase change
0.8!
0.6!
0.4!
0.2!
0
(a) (b) (c)
Dip
T
!
Transmission dip
!
!"#

53

weaker that provide less |E|
2
enhancement. If light can efficiently couple to the ENZ
mode, there might be a dip in the transmission curve of the ITO at the wavelength of
this ENZ mode due to efficient light absorption. Fig. 6.4(b) presents the transmission
dip for different ITO thicknesses. The transmission dip is defined as the depth of the
linear transmission curve for a specific ITO film, which indicates the light absorption
of the ITO film at λENZ. The transmission dip increases with the increase of ITO
thickness for thickness range of 1-50 nm, stays almost the same value for thickness
range of 50-100 nm and decrease with the increase of ITO thickness for 100-500 nm
thickness range. When the ITO is thicker than 500 nm, there’s almost no
transmission dip. We believe this is because the total light absorption at λENZ
depends on the ENZ mode coupling efficiency and the thickness of ITO: a more
efficient ENZ mode coupling leads to a larger absorption and the absorption
accumulates with ITO thickness. For thinner ITO, the accumulated absorption
dominates so the transmission dip increases with the thickness increase. When the
ITO becomes thicker, the ENZ mode coupling efficiency and the accumulation with
thickness plays together. Moreover, for ITO thicker than 500 nm, the ENZ mode
becomes very weak thus very small amount of light can be coupled, thereby having
an almost zero transmission dip. The NLPC curves for different ITO thickness are
shown in Fig. 6.4(c). The NLPC achieves a maximum attainable value at ∼100 nm
ITO thickness and becomes smaller either for thinner ITO (e.g., <50 nm) or for
thicker ITO (e.g., >1000 nm). This may be due to that, the ENZ mode may be
weaker for thinker ITO [97] while the light-material interaction length is longer for
thicker ITO, therefore there’s an optimal ITO thickness for achieving large NLPC.

Nonlinear phase change
0.8!
0.6!
0.4!
0.2!
0
(a) (b)

54

Figure 6.5 Simulation results of (a) the |E|
2
enhancement factor and (b) the NLPC curves under
different imaginary permittivity values with Kretschmann geometry coupling case when θ=35°.

The ITO-ENZ material nonlinear response dependence on material loss is also
investigated. The ITO material loss is varied in our simulation by scaling the
imaginary part of the ITO permittivity obtained from ellipsometry measurement.
Different scaling factors are artificially multipled to the imaginary permittivity to
change the absorption loss of the ITO film. The |E|
2
enhancement factor dependence
on the ITO loss are shown in Fig. 6.5(a). The |E|
2
enhancement factor decreases
almost exponentially with the increase of ITO imaginary permittivity scaling factor
(i.e., the ITO loss). This decrease of |E|
2
inside the ITO film with loss leads to the
decrease of NLPC of the ITO, which is presented in Fig. 6.5(b). For the same pump
intensity, a larger ITO loss factor leads to a smaller NLPC amount. In addition, the
NLPC tends to increase with the increase of pump intensity under the same ITO loss
factor then saturates. A smaller ITO loss factor results in a saturation at lower
pumping intensity. We can infer a general rule that if the ITO loss could be reduced
without changing other properties during the fabrication process, the nonlinear
response of the ITO material has the potential to be enhanced.
6.4 Conclusion and Discussion
In this chapter, we numerically investigate the nonlinear response of ITO based,
sub-μm thick ENZ film with an ENZ wavelength of ∼1550 nm. We find that the
nonlinear response of ITO-ENZ material depends on the coupling condition, the
pump incident angle, the thickness and loss of the material. By efficiently coupling
to the ENZ mode of the ITO film using Kretschmann geometry coupling method at
total reflection angle, the required pumping energy can be reduced for around two
orders of magnitude to acquire similar amount of nonlinear phase change in the
pump light compared to the case of bulk nonlinear response by employing air-
coupling method. This reduction of required energy is majorly due to the electrical
field enhancement inside the ITO film. The maximum achievable nonlinear phase
change decreases when the ITO material loss increases. In addition, this nonlinear

55

response reaches the maximum value when the ITO film has a thickness of 100 nm,
which might due to the trade-off between the electrical field strength and the light-
matter interaction length inside the ITO film for different ITO thicknesses.

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Abstract (if available)

Abstract The first part of this dissertation will study orbital-angular-momentum (OAM) modes for high-dimensional quantum communications. In the case of a quantum communication system, an individual photon can carry one of the many different OAM values, similar to digital data taking on one of many values. A binary signal has 2 values of “0” and “1” data bits, whereas an M-ary signal may have many more possibilities ranging from “0” to “M-1” values. The number of data bits per unit time would be log₂M. If each photon can be encoded with a specific OAM value from M possibilities, the photon efficiency in bit/photon can be increased. This has the potential to be useful for quantum communication systems which are typically photon “starved” and of which qubits commonly can be encoded on one of only two orthogonal polarization states. Therefore, a larger alphabet for each qubit is, in general, highly desirable for enhancing system performance. In this dissertation, research issues about high-dimensional, OAM-encoded quantum communication systems, such as: (i) developing quantum detection methods for high-dimensional quantum system and (ii) mitigating coupling among multiple orthogonal states due to distortions (e.g., atmospheric turbulence effects) will be addressed and discussed. ❧ The second part of this dissertation is the investigation of epsilon-near-zero (ENZ) material and metasurface. ENZ materials can exhibit ultra-fast (sub-ps) and unit-order time-dependent refractive index change, therefore perform strong nonlinear effects in a relatively short (sub-µm) light-matter interaction length. Firstly, we experimentally demonstrate photon acceleration effect which is one example of nonlinear effect induced by the time-varying refractive index in an ENZ metasurface. Then, we characterize the Doppler shift in light utilizing an indium tin oxide (ITO) film with a zero-permittivity wavelength of 1550 nm for potential benefits in telecom applications. We also numerically investigate the nonlinear response of ENZ plasmon modes in ITO thin films near 1550 nm, which might be helpful to further enhance the nonlinearity of ENZ materials.

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Asset Metadata

Creator Liu, Cong (author)

Core Title Applications in optical communications: quantum communication systems and optical nonlinear device

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Physics

Publication Date 04/01/2021

Defense Date 03/10/2021

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

Tag adaptive optics,epsilon-near-zero (ENZ) material,nonlinear optics,OAI-PMH Harvest,orbital angular momentum,quantum communication

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Haas, Stephan (committee chair), Brun, Todd (committee member), Nakano, Aiichiro (committee member), Shakeshaft, Robin (committee member), Willner, Alan (committee member)

Creator Email liucong@usc.edu,liucong20140527@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-435585

Unique identifier UC11667429

Identifier etd-LiuCong-9389.pdf (filename),usctheses-c89-435585 (legacy record id)

Legacy Identifier etd-LiuCong-9389.pdf

Dmrecord 435585

Document Type Dissertation

Rights Liu, Cong

Type texts

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

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

Repository Name University of Southern California Digital Library

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