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Reconfigurable high speed optical signal processing for optical communication and modulation format manipulation

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Reconfigurable high speed optical signal processing for optical communication and modulation format manipulation

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RECONFIGURABLE HIGH SPEED OPTICAL SIGNAL PROCESSING FOR
OPTICAL COMMUNICATION AND MODULATION FORMAT
MANIPULATION

by

Ahmad Fallahpour

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

August 2021

Copyright 2021 Ahmad Fallahpour
ii

Dedication

To my parents, Ghorbanali Fallahpour and Kobra Ahangari,

and to my siblings, Khadijeh and Abouzar,

for their unconditional love and endless support.

iii

Acknowledgements
First and foremost, I would like to express my deepest appreciation to my advisor,
Prof. Alan E. Willner, for the support, ideas, and guidance he has provided during my
PhD. I would also like to thank my defense committee Prof. Stephan Wolfgang Haas
and Prof. Jonathan Habif and also my qualification exam committee Prof. Hossein
Hashemi, Prof. Keith Jenkins, and Prof. Todd Andrew Brun. I would also like to thank
Prof. Moshe Tur for his guidance and support during his visits to USC.
My warmest thanks goes to my wonderful seniors, Dr. Morteza Ziyadi, Dr.
Amirhossein Mohajerin-Ariaei, Dr. Ahmed Almaiman, Dr. Yinwen Cao, at Optical
Communications Lab (OCLab) who were very kind and helpful mentors for me from
the very first moment I joined the lab. I would also thank my colleagues, Fatemeh
Alishahi, Amir Minoofar, Dr. Peicheng Liao, Dr. Changjin Bao, Kaiheng Zou, Dr.
Cong Liu, Dr. Yan Yan, Dr. Nisar Ahmed, Dr. Bishara Shamee, Dr. Guodong Xie, Dr.
Long Li, Dr. Zhe Zhao, Runzhou Zhang, Haoqian Song, Hao Song, Huibin Zhou,
Karapet Manukyan, Nanzhe Hu, and Xinzhou Su for their support and help in our
OClab. Thank you all! I enjoyed all the days and sleepless nights we spent in the lab
and I wish you all the best in your careers.
The journey of PhD is long and very hard by itself. Being an international
student far away from your family and not having the chance to visit them for more
than five years (almost the whole PhD!) makes it much harder. In such a circumstance,
having intimate, faithful, and loyal friends is a privilege that words cannot express
how grateful I am for having that. A wonderful circle of friends who were with me in
happy and sad moments of my life during this journey and make me feel like I have a
family here with me. My sincerest thanks to my wonderful friends here at USC: Ali
Zarei, Mehrdad Kiamari, Ghasem Pasandi, Mohammad Asghari, Mehdi Jafarnia,
Seyed Mohammadreza Mousavi, Pezhman Mamdouh. You guys are tied with my life
during PhD and made me lovely memories including the Lunch Time in front of RTH,
Tea Time at our offices, Persian restaurants, Friday nights, fruitful spiritual discussions,
attending events at mosques all around LA, road trips, birthday parties, and many more.
iv

Finally, but very importantly, I would like to express my deepest love and
sincere appreciation to my parents Ghorbanali Fallahpour and Kobra Ahangari, and
my siblings Khadijeh and Abouzar, for their unconditional support during my whole
life. Although they had many difficulties in their own life, they never let me feel that
with their sacrifices. I could never be where I am without their continuous support in
my life. It was the biggest misfortune that I could not see them in person during these
years, but they are always close to my heart.

v

Table of Contents
Dedication ................................................................................................................... ii
Acknowledgements .................................................................................................... iii
Chapter 1 Introduction .............................................................................................. 1
1.1 Modulation Formats and Coherent Detection ................................................ 1
1.2 Nonlinear Processes ........................................................................................ 3
1.3 Nonlinear Materials and Frequency Comb ..................................................... 5
Chapter 2 Tunable Optical De-aggregation of Each of Multiple Wavelength 16-
QAM Channels into Two 4-PAM Channels .......................................... 7
2.1 Introduction .................................................................................................... 7
2.2 Concept of Optical Deaggregation ................................................................. 8
2.3 Experimental Setup....................................................................................... 14
2.4 Experimental Results .................................................................................... 16
Chapter 3 Generation of a 64-QAM by Optically Aggregating Three
Independent QPSK Channels ............................................................... 20
3.1 Introduction .................................................................................................. 20
3.2 Concept of Optical Aggregation ................................................................... 21
3.3 Experimental Setup....................................................................................... 22
3.4 Experimental Results .................................................................................... 23
Chapter 4 Tunable and Reconfigurable Optical Nyquist Channel Aggregation
of QPSK-to-16QAM and BPSK-to-4PAM ........................................... 25
4.1 Introduction .................................................................................................. 25
4.2 Concept of Optical Nyquist Generation and Aggregation ............................ 26
4.3 Experimental Setup....................................................................................... 30
4.4 Experimental Results .................................................................................... 32
Chapter 5 QPSK-to-PAM4 Data-Format and Wavelength Conversion to Enable
All-Optical Gateway from Long-haul to Datacenter .......................... 37
5.1 Introduction .................................................................................................. 37
5.2 Concept of QPSK to PAM4 Format Conversion.......................................... 38
5.3 Experimental Setup....................................................................................... 41
5.4 Experimental Results .................................................................................... 42
Chapter 6 Probabilistic Constellation Shaping by Adaptively Modifying the
Distribution of Transmitted Symbols Based on Errors at the
Receiver ................................................................................................... 47
6.1 Introduction .................................................................................................. 47
6.2 Concept of Feedback-based Probabilistic Constellation Shaping ................ 48
6.3 Simulation Setup and Results ....................................................................... 50
6.4 Experimental Setup and Results ................................................................... 54
vi

Chapter 7 Remotely Powered and Controlled Optical Switching and
Monitoring Based on Laser-Delivered Power and Control Signals .. 57
7.1 Introduction .................................................................................................. 57
7.2 Concept ......................................................................................................... 58
7.3 Characterization ............................................................................................ 59
7.4 Experimental Setup and Results ................................................................... 61
References ................................................................................................................. 68
vii

Abstract

One of the key functions that can be implemented using optical signal
processing is modulation format conversion. Flexible networks should be able to
manage heterogeneous channels and various subnetworks with different properties
such as different modulation formats, resource allocation, quality of service, etc.,
depending on their applications. Consequently, future flexible all-optical networks
will contain various subnetworks that can speak different languages. In this context,
language translators can be used to connect these subnetworks together. In other words,
using optical gateways at network access points could be beneficial to perform
modulation format conversion in an all-optical fashion, which brings the benefits of
avoiding inefficient OEO conversion and enhancing network flexibility, tunability,
and spectral efficiency. In this dissertation, we employ optical signal processing to
implement some of these modulation format conversions including aggregation
(combination of multiple lower order modulation formats to a single higher order one),
de-aggregation (reverse function of aggregation), and phase modulation to amplitude
modulation format conversion. Furthermore, manipulation of a specific modulation
format is demonstrated by optimizing the probability distribution of the transmitting
symbols. Finally, the feasibility of remote optical signal processing without using local
electrical power supply is investigated by demonstrating a remotely controlled and
powered optical switching and monitoring.

1

Chapter 1 Introduction
In this chapter, we review some basic enabling technologies for optical signal
processing (OSP) functions that would be discussed in later chapters. First, different
modulation formats are explained for data transmission and detection at the receiver.
Then, some basic high-speed nonlinear processes are studied as the building blocks
for the following OSP functions. Finally, some of the nonlinear devices including a
micro-ring resonator for Kerr frequency comb generation are reviewed.
1.1 Modulation Formats and Coherent Detection
Information can be encoded on the amplitude and/or phase of an optical wave
[1-3]. Coherent detection can be used to extract the phase and/or amplitude
information from the received optical wave. Generally, each symbol has M finite states
and represents n=log2M bits of information. Different symbols can be chosen with
distinct amplitudes, distinct phases, or a combination of both. Amplitude modulations
are beneficial in the case of using simple and low-cost direct detection at the receiver.
Phase information would be discarded in this case where only the intensity levels
should be decoded. For example, in on-off-keying (OOK) modulation, there is either
optical power or no power, which represents one and zero symbols. Similarly, 4-level
pulse amplitude modulation (PAM4), which has attracted a fair amount of attention
recently for applications in data center networks, encodes two bits of information on
four distinct intensity levels. On the other hand, phase information has the same optical
power for all symbols, and could not be directly detected by a single photodetector.
For example, in binary phase shift keying (BPSK), the same optical power is sent
during both zero and one, but there is a phase difference between the two cases. For
quadrature phase shift keying (QPSK), there are four different possibilities in phase
while they all have the same amplitude. Quadrature amplitude modulation (QAM) is
the combination of amplitude and phase modulation. As an example, 16-QAM has
sixteen possibilities for encoding four bits of information. Constellation diagrams of
PAM4, QPSK and 16-QAM are depicted in Figure 1.1. The constellation diagram
2

indicates the amplitude and relative phase of each symbol on the X and Y axes known
as the in-phase (I) and quadrature (Q) component, respectively.

Figure 1.1 Data can be encoded over the amplitude or/and phase of an optical wave, e.g. four-level pulse
amplitude modulation (PAM4), quadrature phase shift keying (QPSK), or 16-quadrature amplitude
modulation (16-QAM).

The phase and amplitude information can be recovered in a coherent receiver
with the aid of a local oscillator (LO), which is a continuous-wave (CW) laser [4]. The
received signal ES(t) and the LO are sent to a 900 hybrid and then detected by two
balanced-photodetectors, which are square law devices, to recover I and Q. The
recovered signals are proportional to

𝐼 (𝑡 )∝|𝐸 𝑆 (𝑡 )+𝐸 𝐿𝑂
|
2
−|𝐸 𝑆 (𝑡 )−𝐸 𝐿𝑂
|
2
∝𝐸 𝑆 (𝑡 )𝐸 𝐿𝑂
cos([𝜔 𝑆 −𝜔 𝐿𝑂
]𝑡 +[𝜑 𝑆 (𝑡 )−𝜑 𝐿𝑂
])
(1.1)
𝑄 (𝑡 )∝|𝐸 𝑆 (𝑡 )−𝑗 𝐸 𝐿𝑂
|
2
−|𝐸 𝑆 (𝑡 )+𝑗 𝐸 𝐿𝑂
|
2
∝𝐸 𝑆 (𝑡 )𝐸 𝐿𝑂
sin([𝜔 𝑆 −𝜔 𝐿𝑂
]𝑡 +[𝜑 𝑆 (𝑡 )−𝜑 𝐿𝑂
])
(1.2)

As the equations show, there is a beating term between the signal and LO after
photodetection. If we assume the signal and LO have almost the same frequency, the
data signal would be shifted from optical carrier frequency to the baseband where the
I and Q information can be recovered. High speed analog to digital converters can be
employed to sample these baseband waveforms. Afterwards, digital signal processing
(DSP) can be employed for linear and nonlinear channel distortion compensation,
clock recovery, and phase recovery and frequency offset compensation [5].
Amplitude Modulation
10
PAM4
11 00 01
Phase Modulation
QPSK
10
11
00 01
Amplitude and Phase Modulation
16QAM
1111 1110 1101 1100
1011 1010 1001 1000
0111 0110 0101 0100
0011 0010 0001 0000
( + )

Q
I
3

1.2 Nonlinear Processes
Nonlinear optical processes are key components of optical signal processing.
Optical waves can be manipulated in a nonlinear element with femtosecond response
time to process the encoded data [6]. Second-order susceptibility χ
(2)
leads to three-
wave mixing such as sum frequency generation (SFG), difference frequency
generation (DFG) and second harmonic generation (SHG). Third-order susceptibility
χ(3) can result in four-wave mixing (FWM), self-phase modulation (SPM), and cross-
phase modulation (XPM). In general, wave mixing is the interaction of multiple waves
on different frequencies and generation of an idler signal in a new frequency. During
these processes, energy conservation and phase matching conditions should be
satisfied [7-9]. In this section, we overview some of these nonlinear interactions that
are used for optical signal processing functions explained in next sections.

1) FWM: In this type of interaction, the waves in the input are mixed together
in a χ(3) material and generate another wave at the output. As shown in Figure 1.2(a),
if a CW pump at fpump along with the data signal at fsignal are sent to a χ(3) nonlinear
medium like highly nonlinear fibers (HNLFs) and the pump is located near zero-
dispersion-wavelength (ZDW) of the HNLF, an idler signal will be generated with the
following electric field, frequency, and phase:
𝐸 𝑖𝑑𝑙𝑒𝑟 ∝𝐸 𝑝𝑢𝑚𝑝 2
×𝐸 𝑠𝑖𝑔𝑛𝑎𝑙 ∗
(1.3)
𝑓 𝑖𝑑𝑙𝑒𝑟 2𝑓 𝑝𝑢𝑚𝑝 −𝑓 𝑠𝑖𝑔𝑛𝑎𝑙 (1.4)
𝜑 𝑖𝑑𝑙𝑒𝑟 2𝜑 𝑝𝑢𝑚𝑝 −𝜑 𝑠𝑖𝑔𝑛𝑎𝑙 (1.5)

These equations are derived from the energy conservation rule and phase
matching conditions in nonlinear material. Note that “*” indicates the complex
conjugate of the field. Therefore, the idler is a conjugate copy of the original signal,
and its central frequency is symmetric to the signal with respect to the pump frequency.

4

2) cSFG-DFG: A χ
(2)
nonlinear medium such as periodically poled lithium
niobate (PPLN) waveguides [10] can be designed to produce cascading of SFG and
DFG wave mixing. In each of these processes, two waves are mixed together and
generate a third wave. As Figure 1.3(b) illustrates, if we put the pump and signal
symmetric with respect to the quasi-phase-matching (QPM) wavelength of the PPLN,
they will interact and generate the SFG signal at fSFG = fpump + fsignal = 2fQPM. If another
dummy pump at fdummy is also sent to the PPLN, it could interact with the generated
signal at fSFG and generate the DFG signal at fDFG = fSFG – fdummy. The resulting idler
electric field, frequency, and phase are as follows:
𝐸 𝑖𝑑𝑙𝑒𝑟 ∝𝐸 𝑖𝑑𝑙𝑒𝑟 ×𝐸 𝑝𝑢𝑚𝑝 ×𝐸 𝑑𝑢𝑚𝑚𝑦 ∗
(1.6)
𝑓 𝑖𝑑𝑙𝑒𝑟 𝑓 𝐷𝐹𝐺 2𝑓 𝑄𝑃𝑀 −𝑓 𝑑𝑢𝑚𝑚𝑦 (1.7)
𝜑 𝑖𝑑𝑙𝑒𝑟 𝜑 𝑠𝑖𝑔𝑛𝑎𝑙 +𝜑 𝑝𝑢𝑚𝑝 −𝜑 𝑑𝑢𝑚𝑚𝑦 (1.8)
In this interaction, the resultant idler is the copy of the signal itself (not the
conjugate copy), and the output frequency can be engineered by the injected dummy
pump (it is not dictated by the signal). Furthermore, if we inject more than one dummy
pump, multiple copies of the signal will be generated, which is basically a multicasting
function [11].

3) cSHG-DFG: Similar to cSFG-DFG, this interaction is the result of
cascading two χ
(2)
interactions, i.e., SHG and DFG. Instead of locating two waves
symmetrically around the QPM, one can locate the pump on the QPM frequency. In
this case, the pump would interact with itself and generate the SHG signal at fSHG =
2fQPM. Then, the SHG signal would interact with the input data signal and generate the
idler with the following electric field, frequency and phase:
𝐸 𝑖𝑑𝑙𝑒𝑟 ∝𝐸 𝑝𝑢𝑚𝑝 2
×𝐸 𝑠𝑖𝑔𝑛𝑎𝑙 ∗
(1.9)
𝑓 𝑖𝑑𝑙𝑒𝑟 2𝑓 𝑝𝑢𝑚𝑝 −𝑓 𝑠𝑖𝑔𝑛𝑎𝑙 (1.10)
𝜑 𝑖𝑑𝑙𝑒𝑟 2𝜑 𝑝𝑢𝑚𝑝 −𝜑 𝑠𝑖𝑔𝑛𝑎𝑙 (1.11)
5

These equations show that the idler resulting from cSHG-DFG is similar to the
FWM when a pump is next to ZDW. In this subsection, we just mentioned the simplest
nonlinear processes which are used as the most basic building blocks of the optical
signal processing functions in the following sections.

Figure 1.2 Nonlinear wave mixing (a) four wave mixing (FWM) schemes in χ(3) material, (b) cascaded
sum and difference frequency generations (cSFG-DFG), and (c) second harmonic generation and DFG
(cSHF-DFG) in χ(2) material. ZDW: zero dispersion wavelength, QPM: quasi-phase matching.
1.3 Nonlinear Materials and Frequency Comb
Optical signal processing can be done using different nonlinear material and
devices including HNLF, PPLN, semiconductor optical amplifiers (SOAs),
chalcogenide waveguides, silicon waveguides, photonic crystals, and epsilon-near-
zero (ENZ) materials [12-14]. The choice of material depends on many parameters
such as nonlinear efficiency, bandwidth, loss, data format transparency, dispersion,
and so on. In general, the nonlinear optical response of most materials is weak, which
requires high optical power and/or long interaction length. However, some preliminary
work shows that ENZ materials, in which the dielectric permittivity is extremely small,
exhibit relatively high nonlinearities in a small footprint.
Optical frequency combs are another enabler of OSP. A frequency comb can
provide multiple equidistant spectral lines (comb fingers), which are mutually
coherent with low linewidth. These features allow one to coherently manipulate the
phase and amplitude of multiple fingers and then process them together [15-18].
Mode-locked-laser-based frequency combs have resulted in many advanced
technologies such as microwave photonic filters, optical correlators, optical tapped
delay lines, etc. Moreover, microresonator-based Kerr frequency combs have recently
6

attracted enormous attention due to their broadband operation and chip-scale
integration [19-21]. These combs can be generated by cascaded FWM via coupling a
CW pump into a high quality (Q) factor resonator. Depending on the pump power and
wavelength, the formation of Kerr combs consists of several dynamic regimes,
including Turing patterns, chaos, low-phase-noise (non-soliton) combs, and soliton
combs.

7

Chapter 2 Tunable Optical De-aggregation of Each
of Multiple Wavelength 16-QAM Channels into
Two 4-PAM Channels
2.1 Introduction
Future flexible optical networks that are heterogeneous and reconfigurable may
contain various subnetworks that can have different modulation formats and spectral
efficiencies. In this context, optical gateways that can convert physical layer properties
from one subnetwork and make it suitable for another one might be useful. One
potentially important function of such an interface would be all-optical modulation-
format conversion that can avoid inefficient optical-to-electrical-optical conversion,
and might enable enhanced network performance [22].
Potential functions at network access points include data-channel aggregation
and de-aggregation in order to optimize spectral usage. By aggregating multiple data-
channels of lower-order modulation formats into a single higher order one, spectral
efficiency in terms of bit/s/Hz would increase. Such optical aggregation has been
demonstrated to generate 16-quadrature-amplitude-modulation (QAM) by
aggregating four on-off keying (OOK) signals [23].
De-aggregation, the inverse function of aggregation, is the decomposition of a
single higher-order modulation format to multiple lower-order channels which has also
attracted attention. The de-aggregation of the following modulation formats have been
experimentally demonstrated: (a) QPSK to binary-phase-shift-keying (BPSK) [24-27],
(b) 8-PSK to 4-level pulse amplitude modulation (PAM) [28]. Most of these
approaches have employed a feedback loop to stabilize phase in the de-aggregator.
Furthermore, there have been simulations that have shown the optical de-aggregation
of higher-order modulation formats: (a) 8-PSK to three BPSK signals [29], (b) 8-QAM
to QPSK and amplitude-shift-keying (ASK) [30], (c) 16-QAM to two QPSK signals
[31], and (d) 64-QAM to 8-PAM [32]. The previous reports have shown the de-
aggregation of a single higher-order data channel into lower-order channels. However,
8

it might be valuable to experimentally de-aggregate multiple higher-order wavelength-
division-multiplexed (WDM) channels simultaneously in a single nonlinear stage
without the need for feedback-based phase stabilization.
In this chapter, we experimentally demonstrate tunable optical de-aggregation
from 16-QAM to 4-PAM for two wavelength multiplexed channels in a single
nonlinear element to map constellation onto axes without the need for feedback. In
order to implement constellation mapping, the signal conjugate is generated and added
to the signal itself. In this way, an in-phase (I) component will be produced. To
generate the quadrature-phase (Q) component, we apply a 180-degree phase shift to
the conjugate copy of the signal. This process can be performed concurrently for two
channels on different wavelengths in a single χ
(3)
nonlinear element. Each of two 10
and 15 Gbaud 16-QAM channels are de-aggregated to their I and Q components.
Modulation format tunability is also investigated by de-aggregation of two 10 and 15
Gbaud QPSK channels into BPSK signals.
2.2 Concept of Optical Deaggregation
The concept of mapping a complex data constellation to its I and Q component
is shown in Figure 2.1. The I-component of the signal S is generated by adding the
signal to its conjugate, i.e., I S+S
∗
, which achieves the mapping of the
constellation onto the real axis. As shown in Figure 2.1, the 16-QAM signal can be de-
aggregated into a 4-PAM signal on the real axis; although this signal has zero mean,
it can still be called 4-PAM [33-34]. The Q-component can be derived by subtracting
the signal’s conjugate from itself, i.e., Q S−S
∗
, which maps the constellation onto
the imaginary axis.
9

Figure 2.1 Mapping 16-QAM to its I and Q components. By adding the signal with its conjugate, the
I-component can be achieved. Similarly, Q-component can be generated by subtracting conjugate
from the signal.

The conceptual block diagram demonstrating how the mapping can be
implemented in the optical domain is illustrated in Figure 2.2. The first channel, 𝑆 1
(𝑡 ),
along with the two coherent pumps, 𝑃 11
(𝑡 ) and 𝑃 12
(𝑡 ), are coupled with another
dummy pump, 𝑃 1
(𝑡 ) into a fiber. The electric fields of the signal and the
corresponding pumps can be written as follow:

𝑆 1
(𝑡 ) 𝐴 𝑆 1
(𝑡 )𝑒 𝑗 (𝜔 𝑆 1
𝑡 +𝜑 𝑆 1
(𝑡 ))
𝐴 𝑆 1
(𝑡 )𝑒 𝑗 (𝜔 𝑆 1
𝑡 +𝜑 𝑆 1
𝐷 (𝑡 )+𝜑 𝑆 1
𝑁 (𝑡 ))

(2.1)
𝑃 11
(𝑡 ) 𝐴 𝑃 11
𝑒 𝑗 (𝜔 𝑃 11
𝑡 +𝜑 𝑃 11
(𝑡 ))
𝐴 𝑃 11
𝑒 𝑗 (𝜔 𝑃 11
𝑡 +𝜑 𝑃 11
𝑁 (𝑡 ))

(2.2)
𝑃 12
(𝑡 ) 𝐴 𝑃 12
𝑒 𝑗 (𝜔 𝑃 12
𝑡 +𝜑 𝑃 12
(𝑡 ))
𝐴 𝑃 12
𝑒 𝑗 (𝜔 𝑃 12
𝑡 +𝜑 𝑃 12
𝑁 (𝑡 ))

(2.3)
𝑃 1
(𝑡 ) 𝐴 𝑃 1
𝑒 𝑗 (𝜔 𝑃 1
𝑡 +𝜑 𝑃 1
(𝑡 ))
𝐴 𝑃 1
𝑒 𝑗 (𝜔 𝑃 1
𝑡 +𝜑 𝑃 1
𝑁 (𝑡 ))

(2.4)

where 𝐴 𝑆 1
(𝑡 ), 𝐴 𝑃 11
, 𝐴 𝑃 12
, and 𝐴 𝑃 1
are the amplitudes, 𝜔 𝑆 1
, 𝜔 𝑃 11
, 𝜔 𝑃 12
, and
𝜔 𝑃 1
are the wavelengths and 𝜑 𝑆 1
(𝑡 ), 𝜑 𝑃 11
(𝑡 ), 𝜑 𝑃 12
(𝑡 ), and 𝜑 𝑃 1
(𝑡 ) are the phases of
𝑆 1
(𝑡 ), 𝑃 11
(𝑡 ), 𝑃 12
(𝑡 ), and 𝑃 1
(𝑡 ), respectively. Phase of the signal include both data
and noise, 𝜑 𝑆 1
𝐷 (𝑡 ) and 𝜑 𝑆 1
𝑁 (𝑡 ); however, pumps only carry the phase noises. 𝑃 11
(𝑡 ) and
16-QAM
𝐼 𝑆 +𝑆 ∗
𝑄 𝑆 −𝑆 ∗
Optical Channel
De-aggregator
Generating I:
Generating Q:
Re
Im
Re
Im
𝑆 : Signal
: Conjugate of signal
: In-phase component
: Quadrature-phase component
𝑆 𝑆 ∗
𝐼 𝑄 Re
Im
Re
Im
Re
Im
INPUT OUTPUT
4-PAM
In-phase signal
4-PAM
Quadrature signal
10

𝑃 12
(𝑡 ) are placed in symmetry with respect to 𝑆 1
(𝑡 ), and if the pumps and the signal
are coherent, following equations can be used:
𝜔 𝑃 12
−𝜔 𝑆 1
𝜔 𝑆 1
−𝜔 𝑃 11
∆𝜔 (2.5)
𝜑 𝑆 1
𝑁 (𝑡 ) 𝜑 𝑃 11
𝑁 (𝑡 ) 𝜑 𝑃 12
𝑁 (𝑡 ) (2.6)

where ∆𝜔 is the wavelength difference between signal and its coherent pumps.
A second channel, 𝑆 2
(𝑡 ), along with two coherent pumps, 𝑃 21
(𝑡 ) and 𝑃 22
(𝑡 ), and a
dummy pump, 𝑃 2
(𝑡 ) , can be multiplexed into the same fiber with a similar
configuration to the first channel and its corresponding pumps. All signals and pumps
are transmitted into a programmable filter that can adjust the amplitude and the phase
of signals and pumps independently. In this filter, the complex coefficients of 𝛼 and 𝛽
are applied to 𝑃 12
(𝑡 ) and 𝑃 11
(𝑡 ), respectively. Subsequently, these signals are sent
into a χ
(3)
nonlinear material, e.g., highly nonlinear fiber (HNLF), to generate the
mixing terms. In the HNLF, each three waves can mix though four-wave mixing
(FWM) process under the phase-matching conditions to produce a fourth wave. Here,
we focus on the generated terms that are on our wavelength of interest. Mixing of
𝑆 1
(𝑡 ), 𝑃 12
(𝑡 ), and 𝑃 1
(𝑡 ) can generate nine new waves [35-36] including two idlers
which are symmetrical with respect to 𝑃 1
(𝑡 ). We denote the electric field of these two
idlers as 𝑋 11
(𝑡 ) and 𝑋 12
(𝑡 ) which are shown as follows:

𝑋 11
(𝑡 ) 𝑃 1
(𝑡 )×𝑆 1
(𝑡 )×𝛼 𝑃 12
∗
(𝑡 )
𝛼 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 12
𝑒 𝑗 ((𝜔 𝑃 1
+𝜔 𝑆 1
−𝜔 𝑃 12
)𝑡 +𝜑 𝑃 1
𝑁 (𝑡 )+𝜑 𝑆 1
𝐷 (𝑡 )+𝜑 𝑆 1
𝑁 (𝑡 )−𝜑 𝑃 12
𝑁 (𝑡 ))

(2.7)
𝑋 12
(𝑡 ) 𝑃 1
(𝑡 )×𝑆 1
∗
(𝑡 )×𝛼 𝑃 12

(𝑡 )
𝛼 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 12
𝑒 𝑗 ((𝜔 𝑃 1
−𝜔 𝑆 1
+𝜔 𝑃 12
)𝑡 +𝜑 𝑃 1
𝑁 (𝑡 )−𝜑 𝑆 1
𝐷 (𝑡 )−𝜑 𝑆 1
𝑁 (𝑡 )+𝜑 𝑃 12
𝑁 (𝑡 ))

(2.8)

By plugging eq.(2.5) and eq.(2.6) into eq.(2.7) and eq.(2.8), the latter equations
can be simplified to:
11

𝑋 11
(𝑡 ) 𝛼 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 12
𝑒 𝑗 ((𝜔 𝑃 1
−∆𝜔 )𝑡 +𝜑 𝑃 1
𝑁 (𝑡 )+𝜑 𝑆 1
𝐷 (𝑡 ))

(2.9)
𝑋 12
(𝑡 ) 𝛼 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 12
𝑒 𝑗 ((𝜔 𝑃 1
+∆𝜔 )𝑡 +𝜑 𝑃 1
𝑁 (𝑡 )−𝜑 𝑆 1
𝐷 (𝑡 ))

(2.10)

Based on eq.(2.9) and eq.(2.10) and due to the coherence between 𝑆 1
(𝑡 ), and
𝑃 12
(𝑡 ), the phase noises of the signal, 𝑆 1
(𝑡 ), and the pump, 𝑃 12
(𝑡 ), cancel each other.
As a result, the phase noises of the generated idlers, 𝑋 11
(𝑡 ) and 𝑋 12
(𝑡 ), only depend
on the phase noise of 𝑃 1
(𝑡 ), which does not need to be phase locked to the signal.
Furthermore, 𝑆 1
(𝑡 ), 𝑃 11
(𝑡 ), and 𝑃 1
(𝑡 ) can mix through FWM and generate following
electric fields:

𝑋 13
(𝑡 ) 𝑃 1
(𝑡 )×𝑆 1
(𝑡 )×𝛽 𝑃 11
∗
(𝑡 )
𝛽 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 11
𝑒 𝑗 ((𝜔 𝑃 1
+𝜔 𝑆 1
−𝜔 𝑃 11
)𝑡 +𝜑 𝑃 1
𝑁 (𝑡 )+𝜑 𝑆 1
𝐷 (𝑡 )+𝜑 𝑆 1
𝑁 (𝑡 )−𝜑 𝑃 11
𝑁 (𝑡 ))

(2.11)
𝑋 14
(𝑡 ) 𝑃 1
(𝑡 )×𝑆 1
∗
(𝑡 )×𝛽 𝑃 11

(𝑡 )
𝛽 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 11
𝑒 𝑗 ((𝜔 𝑃 1
−𝜔 𝑆 1
+𝜔 𝑃 11
)𝑡 +𝜑 𝑃 1
𝑁 (𝑡 )−𝜑 𝑆 1
𝐷 (𝑡 )−𝜑 𝑆 1
𝑁 (𝑡 )+𝜑 𝑃 11
𝑁 (𝑡 ))

(2.12)

By plugging eq.(2.5) and eq.(2.6) into eq.(2.11) and eq.(2.12), they are
simplified as follow:

𝑋 13
(𝑡 ) 𝛽 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 11
𝑒 𝑗 ((𝜔 𝑃 1
+∆𝜔 )𝑡 +𝜑 𝑃 1
𝑁 (𝑡 )+𝜑 𝑆 1
𝐷 (𝑡 ))

(2.13)
𝑋 14
(𝑡 ) 𝛽 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 11
𝑒 𝑗 ((𝜔 𝑃 1
−∆𝜔 )𝑡 +𝜑 𝑃 1
𝑁 (𝑡 )−𝜑 𝑆 1
𝐷 (𝑡 ))

(2.14)

Similarly, 𝑋 13
(𝑡 ) and 𝑋 14
(𝑡 ) are symmetrical with respect to 𝑃 1
(𝑡 ) and their
phase noises only depend on the phase noise of the pump 𝑃 1
(𝑡 ) due to the fact that
𝑆 1
(𝑡 ) and 𝑃 11
(𝑡 ) are coherent and their phase noises cancel each other.

12

Figure 2.2 The block diagram of the proposed two channel de-aggregator using mapping and wave
mixing in single nonlinear stage. Signal copy and its conjugate copy are generated at the same
frequency through four-wave mixing. The amplitude and phase of the signal and pumps can be
adjusted in the programmable filter.

According to eq.(2.9) and eq.(2.14), 𝑋 11
(𝑡 ) and 𝑋 14
(𝑡 ) are phase and
frequency locked; therefore, they can be coherently added as follows:

𝑋 11
(𝑡 )+𝑋 14
(𝑡 )
(𝛼 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 12
+𝛽 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 11
) 𝑒 𝑗 ((𝜔 𝑃 1
−∆𝜔 )𝑡 +𝜑 𝑃 1
𝑁 (𝑡 ))
(𝑒 𝑗 𝜑 𝑆 1
𝐷 (𝑡 )
+𝑒 −𝑗 𝜑 𝑆 1
𝐷 (𝑡 )
)
(𝛼 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 12
+𝛽 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 11
) 𝑒 𝑗 ((𝜔 𝑃 1
−∆𝜔 )𝑡 +𝜑 𝑃 1
𝑁 (𝑡 ))
(2cos𝜑 𝑆 1
𝐷 (𝑡 ))
(2.15)

Note that the coefficients 𝛼 and 𝛽 are adjusted such that the amplitudes of
𝑋 11
(𝑡 ) and 𝑋 14
(𝑡 ) to be equal. Eq. (2.15) indicates the constellation points that are
symmetric with respect to the real axis are mapped to the same value on real axis. For

+

∝(

+

∗
)
( )
Nonlinear Element
(HNLF)
Programmable
Phase and
Amplitude filter
λ

∆ ∆

∆ ∆

=

∗

=

∗

=

∗

=

∗
Mixing Terms Phase Frequency
Channel 1

∗

−

+

=

−(

−

) =

−∆

=

∗

+

−

=

+(

−

) =

+∆

=

∗

−

+

=

+(

−

) =

+∆

=

∗

+

−

=

−(

−

) =

−∆

+

∝(

+

∗
)

∆ ∆

∆ ∆

=

∗

=

∗

=

∗

=

∗
λ

∆ ∆

∆ ∆

INPUT
OUTPUT
+ +
13

example, for both 𝜑 𝑆 1
𝐷 (𝑡 ) 𝜋 /4 and 𝜑 𝑆 1
𝐷 (𝑡 ) −𝜋 /4, the output is proportional to
cos𝜑 𝑆 1
𝐷 (𝑡 ) √2/2. This fact confirms the concept of mapping constellation to real
axis which generates the I component.
By adjusting the phase of the complex coefficient 𝛽 , the quadrature selection
can be performed. Eq.(2.15) indicates that the I component can be recovered if the
phase of 𝛽 is equal to zero. In order to generate the Q component, we only need to
apply a 180-degree phase shift to 𝑃 11
(𝑡 ) by changing the phase of 𝛽 in the
programmable filter. In this manner, eq.(2.15) is modified to:

𝑋 11
(𝑡 )+𝑋 14
(𝑡 )
(𝛼 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 12
+𝛽 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 11
) 𝑒 𝑗 ((𝜔 𝑃 1
−∆𝜔 )𝑡 +𝜑 𝑃 1
𝑁 (𝑡 ))
(𝑒 𝑗 𝜑 𝑆 1
𝐷 (𝑡 )
+𝑒 𝑗𝜋
𝑒 −𝑗 𝜑 𝑆 1
𝐷 (𝑡 )
)
(𝛼 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 12
+𝛽 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 11
) 𝑒 𝑗 ((𝜔 𝑃 1
−∆𝜔 )𝑡 +𝜑 𝑃 1
𝑁 (𝑡 ))
(𝑒 𝑗 𝜑 𝑆 1
𝐷 (𝑡 )
−𝑒 −𝑗 𝜑 𝑆 1
𝐷 (𝑡 )
)
(𝛼 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 12
+𝛽 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 11
) 𝑒 𝑗 ((𝜔 𝑃 1
−∆𝜔 )𝑡 +𝜑 𝑃 1
𝑁 (𝑡 ))
(2𝑗 sin𝜑 𝑆 1
𝐷 (𝑡 ))
(𝛼 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 12
+𝛽 𝐴 𝑃 1
𝐴 𝑆 1
(𝑡 )𝐴 𝑃 11
) 𝑒 𝑗 ((𝜔 𝑃 1
−∆𝜔 )𝑡 +𝜑 𝑃 1
𝑁 (𝑡 ))
𝑒 𝑗 𝜋 2
(2sin𝜑 𝑆 1
𝐷 (𝑡 ))
(2.16)

Eq. (2.16) shows the constellation points that are symmetric with respect to the
imaginary axis are mapped to the same value on the imaginary axis. For example, for
both 𝜑 𝑆 1
𝐷 (𝑡 ) 𝜋 /4 and 𝜑 𝑆 1
𝐷 (𝑡 ) 3𝜋 /4, the output is proportional to sin𝜑 𝑆 1
𝐷 (𝑡 )
√2/2. Accordingly, de-aggregation of a complex constellation into the I and Q
component is realized by phase adjustment of 𝑃 11
(𝑡 ) and combining 𝑋 11
(𝑡 ) and
𝑋 14
(𝑡 ). Similarly, 𝑋 12
(𝑡 ) and 𝑋 13
(𝑡 ) are phase and frequency locked which can
generate the de-aggregated signal at 𝜔 𝑃 1
+∆𝜔 . These equations can also be derived
for the second channel and its corresponding pumps that lead to de-aggregation of the
second channel at the HNLF output.
14

2.3 Experimental Setup
The experimental setup of the proposed de-aggregator system is shown in
Figure 2.3(a). At the transmitter, two lasers at wavelengths of λ
S
1
1546.9 nm and
λ
S
2
1556.9 nm are coupled into a fiber to be modulated as the first and the second
channel signals. Data is generated in a high-speed arbitrary waveform generator
(AWG). In order to generate the coherent pumps which are symmetric with respect to
the signal, the I component of the signal is mixed with a sinusoidal tone that is
generated by a 20GHz clock synthesizer. The clock in the AWG is synchronized with
the synthesizer by a 10MHz reference. The spectrum of the modulated signal and its
coherent pumps can be seen in Figure 2.3(b1). The 20GHz is the frequency difference
between the signal and the coherent pumps (∆𝜔 in eq.(2.5)). By reducing the
frequency difference, the spectral efficiency will be improved; however, the baud rate
of the signal will be limited. In addition, by reducing the frequency of the synthesizer,
the signal may experience more severe crosstalk. The amplitude of the AWG output
is set ~250 mV peak-to-peak to keep the electrical signal at the linear region of the
modulator. Moreover, the amplitude of the sinusoidal tone is tuned such that the signal
and the coherent pumps have almost equal peak power (see Figure 2.3(b1)).
The same data is encoded onto both channels using a nested Mach–Zehnder
modulator with 10/15 Gbaud QPSK/16-QAM data generated by a 2
15
−1 pseudo
random bit sequence (PRBS). The output of the modulator is amplified in a low-noise
erbium-doped fiber amplifier (EDFA) and sent into the optical de-aggregator. First,
the signal and the pumps’ amplitudes and phases are adjusted on both channels in a
programmable filter based on Liquid Crystal on Silicon (LCoS) technology. Adjusting
the phase of P
11
and P
21
in the LCoS filter can determine which quadrature will be
selected at the output of de-aggregator. At the output of the filter, the two channels are
decorrelated by applying delay to the second channel. Consequently, each channel is
amplified to 18dB in a high-power EDFA. Each of the laser pumps of P
1
and P
2
at
wavelengths of λ
P
1
1547.9 nm and λ
P
2
1558.9 nm are also amplified in high-
power EDFAs to 21dB and coupled in to the fiber with their corresponding channels.
After amplification, both channels and their corresponding pumps are combined in a
15

polarization beam splitter (PBS) and sent into a 450 m HNLF with a zero-dispersion
wavelength (ZDW) of ~1551 nm and a nonlinear coefficient of 20 W-1 km-1. The
PBS could help to put two sets of waves on two orthogonal polarization before sending
them into the HNLF. In this way, the nonlinear interaction between channel 1 and
channel 2 could be decreased and each channel will suffer less from the mutual
crosstalk. Figure 2.3(b2) shows the spectrum of the first channel signal along with
pumps that are arranged in the same fashion as shown in Figure 2.2. The spectrum at
the output of the HNLF for first channel is depicted in Figure 2.3(b3). As indicated in
the figure, the de-aggregated signal, which is either the I or Q component (BPSK/4-
PAM) of the original signal (QPSK/16-QAM), is generated through the wave mixing
described earlier. The de-aggregated signal at the output of the HNLF is filtered out
by using an optical band-pass filter (BPF) and sent into an 80Gsample/s coherent
receiver to be analyzed.
Figure 2.3(b4) illustrates the spectrum at the output of the HNLF, including the
first and the second channels, the pumps, and the de-aggregated signals for both
channels. The spectrum also shows other mixing terms generated in the HNLF that are
not desirable. Although these mixing terms do not impact the de-aggregated signal,
they limit the number of channels that can be multiplexed for de-aggregation. This is
the reason why we limit our study to two wavelength multiplexed channels.
Some of the additional undesirable mixing terms depend on the spacing
between the signal and the dummy pump. In other words, if this spacing is equal for
both channels, some of the generated mixing terms will overlap and they cannot be
separated in the spectrum domain. In order to show all the additional mixing terms in
the spectrum of Figure 2.3(b4), we choose to have different frequency spacing between
the signal and the dummy pump for two channels. We note that this different frequency
spacing should not impact the performance of the de-aggregated signal because the
additional mixing terms lie on different wavelengths.
The current setup only allows recovering one quadrature, i.e. I or Q, at a time.
In order to adapt the scheme to recover two quadratures simultaneously, additional
HNLF and LCoS filter should be utilized. The output of the isolator in Figure 2.3(a)
16

can be split by a 50/50 coupler into two arms to generate I and Q components
simultaneously. The first arm is connected to the first HNLF to generate one of the
quadratures, i.e. I or Q. The second arm can be connected to the additional LCoS filter
followed by the second HNLF. In this way, the orthogonal quadrature, i.e. Q or I, can
be obtained by adjusting the relative phase in the second arm using the additional
LCoS filter.

Figure 2.3 (a) The experimental setup for the proposed optical channel de-aggregator; (b) the
corresponding spectra measured at each node. AWG: Arbitrary Waveform Generator, EDFA: Erbium-
Doped Fiber Amplifier, LCoS: Liquid Crystal on Silicon, BPF: Band Pass Filter, PC: Polarization
Controller, PBS: Polarization Beam Splitter, HNLF: Highly Non-Linear Fiber, ATT: attenuator.

2.4 Experimental Results
Figure 2.4 shows the constellations of the QPSK and 16-QAM signals at the
input of the optical de-aggregator and their corresponding I and Q de-multiplexed
outputs for both channels simultaneously. Two 10 Gbaud QPSK signals with error
vector magnitudes (EVMs) of 11.3% and 11.8% are sent as channel 1 and 2
(respectively) and mapped onto the in-phase and quadrature-phase axes as BPSK
signals with EVMs of 14.3% and 14.6% for channel 1 and 13.9% and 14.7% for
channel 2. To demonstrate bitrate tunability of the proposed system, de-aggregation of
a 15 Gbaud QPSK signal is also shown. Here, the EVMs of QPSK signals in channel
1 and 2 are 13.1% and 13.5%, respectively. These signals are de-aggregated into BPSK
signals with EVMs of 16.7% and 16.9% for I and Q of the first channel and EVMs of
17.1% for both I and Q of the second channel. In addition, the tunability of the
1549.8 1550
-50
-40
-30
-20
1549.5 1550 1550.5 1551
-60
-40
-20
0
1549.5 1550 1550.5 1551
-40
-20
0
1546.8 1547
Wavelength (nm)
Power (10 dB/div)
1548 1550 1552 1554 1556 1558
-60
-40
-20
0
Power (20 dB/div)
Power (20 dB/div)
Power (20 dB/div)
1548 1550 1552 1554 1556 1558
Wavelength (nm)
1546.5 1547 1547.5 1548 1546.5 1547 1547.5 1548
Wavelength (nm) Wavelength (nm)
2
S2 P2
P22 P21
P1
S1
P11
P12
S1
P11
P12
Ch1 De-aggregation
P1
S1
P11 P12
1
4
3
(b) Transmitter
Modulator
AWG
+ ~
20GHz
LCoS
Filter
λ
S2
~1556.9nm
10MHz
Reference
10G/15G
PRBS 2
15
-1
λ
S1
~1546.9nm
1
HNLF~450m
λ
P1
~1547.9nm
λ
P2
~1558.9nm
Delay
Q
I
BPF
PC
EDFA
ATT
Coherent
Rx
BPF
EDFA
1 nm
1 nm
1 nm
1 nm
PBS
De-aggregator
Detection
2 3 4
(a)
Isolator
20GHz 20GHz
17

proposed system over the constellation is verified by changing the input constellation
to 16-QAM. In channel 1, a 10 Gbaud 16-QAM signal with an EVM of 10.2% is de-
multiplexed into a 4-PAM signal with an EVM of 11.4% for the I component and an
EVM of 11.7% for the Q component. Similarly, for channel 2, a 16-QAM signal with
an EVM of 10.3% is de-aggregated into 4-PAM signals with I and Q components with
EVMs of 11.2% and 11.4%, respectively. Furthermore, 15 Gbaud 16-QAM signal in
channel 1 and 2 with an EVMs of 11.5% are de-aggregated to the 4-PAM signals.
EVMs of I and Q components are 12.5% and 13.9% for channel 1 and they are 12.4%
and 13.5% for channel 2.

Figure 2.4 Constellation of the input and output of the optical channel de-aggregator. Two 10/15 Gbaud
16-QAM signals on channel 1 and 2 are de-aggregated into 4-PAM. Similarly, two 10/15 Gbaud QPSK
signals are de-aggregated to BPSK for both channels.

The BER measurement of the optical de-aggregator is shown in Figure 2.5. The
BER of the 10 Gbaud QPSK signals at both channels and the de-aggregated BPSK I
and Q signals at the output of two channels is plotted against the resulting optical
signal-to-noise ratio (OSNR) in Figure 2.5(a). At a BER of 10-4, the OSNR difference
between the input QPSK signal and the output BPSK signal is ~2.3 dB and ~2.4 dB
for channels 1 and 2, respectively. Although the theoretical OSNR difference between
INPUT OUTPUT
In-phase Quadrature
QPSK (10 Gbaud)
Channel 1
EVM=11.3% EVM=14.3%
EVM=14.6%
Channel 2
EVM=11.8% EVM=13.9%
EVM=14.7%
QPSK (15 Gbaud)
Channel 1
EVM=13.1% EVM=16.7%
EVM=16.9%
Channel 2
EVM=13.5% EVM=17.1%
EVM=17.1%
INPUT OUTPUT
In-phase Quadrature
16-QAM (10 Gbaud)
Channel 1
EVM=10.2% EVM=11.4%
EVM=11.7%
Channel 2
EVM=10.3% EVM=11.2%
EVM=11.4%
16-QAM (15 Gbaud)
Channel 1
EVM=11.5% EVM=12.5%
EVM=13.9%
Channel 2
EVM=11.5% EVM=12.4%
EVM=13.5%
(a) (b)
18

QPSK and BPSK is 3 dB [37], the system performance is still good, incurring a penalty
of only ~0.7 dB. The system performance is also investigated for 15 Gbaud QPSK
signals as the input of both channels. In this case, the OSNR differences are ~2.3 dB
and ~2.6 dB between input and output for channels 1 and 2 at a BER of 10-3. Similarly,
Figure 2.5(c) and (d) illustrates BER measurement for 10 and 15 Gbaud 16-QAM data
channels de-aggregation into 4-PAM signals. In channel 1 the OSNR difference
between 10 Gbaud 16-QAM and 4-PAM is ~2.3 dB and it is ~2.5 dB for channel 2. In
15 Gbaud case, the OSNR differences are ~2.5 dB and ~2.7 dB for channel 1 and 2,
respectively, at BER of 10-3. By comparing the BER of TX-QPSK and TX-16QAM
with the theoretical values [38], around 6dB penalty is observed in the experiment.
This is mainly because of unoptimized DSP calculation in the coherent receiver. We
did not use any equalizer at the receiver which could have improved the experimental
BER performance. However, the BER of the input and the output of the experimental
setup is measured under the same condition.

Figure 2.5 BER performance of the optical de-aggregator for the input (a) 10 Gbaud QPSK, (b) 15
Gbaud QPSK, (c) 10 Gbaud 16-QAM , and (d) 15 Gbaud 16-QAM and their de-aggregated signals in
both channels.
-5.5
-5
-4.5
-4
-3.5
-3
-2.5
9 11 13 15 17
-Log(BER)
OSNR (dB)
10 Gbaud
TX-QPSK-Ch1
RX-BPSK(I)-Ch1
RX-BPSK(Q)-Ch1
TX-QPSK-Ch2
RX-BPSK(I)-Ch2
RX-BPSK(Q)-Ch2
(a) (b)
-5
-4.5
-4
-3.5
-3
-2.5
-2
7 9 11 13 15 17
-Log(BER)
OSNR (dB)
15 Gbaud
TX-QPSK-Ch1
RX-BPSK(I)-Ch1
RX-BPSK(Q)-Ch1
TX-QPSK-Ch2
RX-BPSK(I)-Ch2
RX-BPSK(Q)-Ch2
(c) (d)
-4
-3.5
-3
-2.5
-2
-1.5
-1
12 14 16 18 20 22
-Log(BER)
OSNR (dB)
10 Gbaud
TX-16QAM-Ch1
RX-4PAM(I)-Ch1
RX-4PAM(Q)-Ch1
TX-16QAM-Ch2
RX-4PAM(I)-Ch2
RX-4PAM(Q)-Ch2
-4
-3.5
-3
-2.5
-2
-1.5
-1
14 16 18 20 22
-Log(BER)
OSNR (dB)
15 Gbaud
TX-16QAM-Ch1
RX-4PAM(I)-Ch1
RX-4PAM(Q)-Ch1
TX-16QAM-Ch2
RX-4PAM(I)-Ch2
RX-4PAM(Q)-Ch2
19

We note that the de-aggregated signals, i.e., BPSK and 4-PAM, are “zero mean”
data streams that are similar to their original complex constellations of QPSK and 16-
QAM, respectively. This means that coherent detection might be required to recover
data from these signals. However, there might be interest in direct detection of the de-
aggregated signals due to its simpler and less-costly implementation. One method
would be to include another nonlinear stage to add a fixed amount of power to the
BPSK or 4-PAM signals [39]. This enables either two-level or four-level intensity
signals to be detected by direct detection. A second option is to use a delay line
interferometer (DLI), which can convert multiple channels simultaneously [40]. In that
case, phase information is converted into intensity by applying a one-bit delay between
the two arms of interferometer. Furthermore, such formats can also be detected in two
parallel direct-detection and interferometric receivers [41]. In order to optimize the
performance of such a receiver, the extinction ratio of the received 4-PAM should be
adjusted. However, in our scheme, the extinction ratio is dictated by the 16-QAM
constellation at the transmitter.

20

Chapter 3 Generation of a 64-QAM by Optically
Aggregating Three Independent QPSK Channels
3.1 Introduction
There is interest in high-capacity optical communication systems to increase the
spectral efficiency (i.e., bits/sec/Hz) of the generated data channels. One common
approach is to have multi-level data encoding on both the amplitude and phase of the
optical carrier wave, such as by quadrature-amplitude-modulation (QAM) [42-43].
Typically, QAM can be generated today by driving two Mach-Zehnder interferometers
with multi-level voltage signals [44-45]. As the number of QAM levels and baud rate
increase, the technical challenges in generating the data in this fashion can become
more difficult, including: (i) generating a linear transfer function using Mach Zehnders
for many input voltage levels, and (ii) generating a high-quality drive signal for high
baud rates. Approaches that use optical nonlinear wave mixing may have a larger
linear transfer function and a higher bandwidth capability [46].
In this work, we experimentally demonstrate the generation of a 64-QAM 20-
Gbaud data channel by optically aggregating three independent QPSK channels using
nonlinear wave mixing of multiple Kerr comb lines. There have been a few reports
using Kerr frequency comb for optical signal processing applications. Here, we use
the coherency of the Kerr comb lines to generate higher order QAM signals. In order
to generate 64-QAM, instead of copying three signals into fourth wavelength, we keep
one signal and generate the copy of two others to the same frequency as the first signal.
In this way we can save conversion efficiency power loss in compare with previous
approach. Also, we do not need to add fourth pump to generate copy which in turn
save power. Using this method 120 Gbit/s 64-QAM and 80 Gbit/s 16-QAM with EVM
of 6.5% and 5.5% are generated.

21

3.2 Concept of Optical Aggregation
The concept of principle operation of our proposed optical higher-order QAM
generation is shown in Figure 3.1. As illustrated in Figure 3.1(a), in order to generate
a 64-QAM signal, we can add coherently three QPSK signals with different complex
coefficient which enables vector addition. Figure 3.1(b) depicts conceptual block
diagram in which wave mixing in nonlinear element is illustrated for both old approach
(approach 1) and the new proposed approach (approach 2). First, Kerr frequency comb
is used to generate multiple frequency comb fingers at different wavelength which are
coherent with each other. A liquid crystal on silicon (LCoS) programmable filter is
used to select suitable fingers as pumps and signals and apply complex weights on the
comb lines. At the output, there are two separate path for signals and pumps. In signal
path, an optical modulator is used to modulate QPSK signal of the selected comb
fingers. Then, signals and pumps merge together and send into periodically poled
lithium niobate (PPLN) waveguide for nonlinear mixing in order to generate higher
order QAM. In approach 1, we generate the copy of three signals in the fourth
wavelength by exploiting sum frequency generation (SFG) and difference frequency
generation (DFG) processes and adding fourth pump in PPLN. In approach 2, we keep
one of the signals at the output as it is and generate the copy of the two other signals
on the same frequency as the first signal. In this way, not only we avoid power loss
due to conversion of one signal, but also the fourth pump is eliminated which leads to
power saving for the rest of them.
22

Figure 3.1 Concept of optical modulation format multiplexing, (a) concept of generating 64-QAM using
three QPSK signals through vector addition (b) conceptual block diagram of higher order modulation
format generation with two approaches.

3.3 Experimental Setup
The experimental setup is depicted in Figure 3.2. The frequency comb is generated in
the silicon nitride microring resonator through parametric frequency conversion. An external
cavity tunable diode laser (ECDL) is amplified by a high power C-band erbium doped fiber
laser (EDFA). Then, the amplified continuous wave passes through filter, isolator and
polarization controller to be coupled into the chip through a lensed fiber. Optical spectrum of
the generated Kerr frequency comb is shown on Figure 3.2(a). The frequency spectrum range
(FSR) of the generated comb is 191.8 GHz. We used six fingers around 1550 nm, Figure
3.2(b). In order to boost their power, they are amplified using a low-noise EDFA and then sent
to the LCoS filter. In order to generate 16-QAM from two QPSK signal, we choose six fingers
in LCoS, three lines for signals and three lines as pumps. 20-Gbaud QPSK signals are
modulated on the selected lines and the amplified in a low noise EDFA. The spectrum of it is
illustrated in Figure 3.2(c). Afterward, signals and pumps passes through high power EDFAs
and merge together to be sent into PPLN. A 400 m DCF is used to induce one symbol delay
between signals. A Band-pass filter (BPF) is used to select the generated higher order signal
and the output is sent into an 80Gsample/s coherent receiver for analysis.
+ + =
1
st
QPSK 2
nd
QPSK 3
rd
QPSK
64-QAM
LCoS
Filter
(Comb
fingers
selected
and
weighted )
QPSK
modulation
PPLN
(Phase
Coherent
Addition)
Kerr Frequency
Comb
Si
3
N
4
Pump
Fingers
P
3
P
2
P
1
S S
Modulated
Fingers
S
Output=S
1
+a*S
2
+b*S
3
SFG
+DFG

+
P
3
P
2 Output
P
1

SFG
+DFG

+
P
3
P
2 Output
P
1

S
1
S
2
S
3
Pump
P
e.g.,
64-QAM
Approach 1
Approach 2
h
1
h
2
h
3
Amplitude Weights: [ 1 , 0.5 , 0.25 ]
Relative
Delay
S(t) S(t-2T)
S(t-T)
(a)
(b)
23

Figure 3.2 Experimental setup and spectrum of (a) generated Kerr frequency comb, (b) zoom in target
comb lines, (c) modulated signals.

3.4 Experimental Results
Figure 3.3 shows spectrums of PPLN output and constellation of the received
signal in both approaches. In Figure 3.3(a-b) generation of 64-QAM is illustrated.
Figure 3.3(a) shows the constellation of 64-QAM generated with approach 2, along
with its corresponding spectrum. Its EVM is 5.5% which is better than the result for
approach 1, Figure 3.3(b). By turning off one channel we can achieve 16-QAM as its
results depicted in Figure 3.3(c-d). EVM of generated 16-QAM in approach 1 is 8.7%,
Figure 3.3(d), whereas EVM of approach 2 is 6.5%, Figure 3.3(c). Similarly, better
result is achieved in approach 2 in compare with approach 1 because, as it can be seen
from spectrums, we save more than 10 dB power in this approach.
9 nm
DCF
400m
EDFA
LCoS
Filter
Kerr Comb Generation
20 Gbaud
PPLN
1 nm
EDFA
9 nm
EDFA
5 nm
1 nm
BPF
BPF
BPF
Coherent
Rx
EDFA
a
b
c

1500 1550 1600
Wavelength (nm)
Power (10 dB/div)
a

Power (10 dB/div)
1546 154 1550 155 155 Wavelength (nm)
c
6 -QAM
ECDL
Isolator
ATT
1 nm

9 nm
Power (10 dB/div)
1546 1547 1548 1549
Wavelength (nm)
b
QPSK
QPSK
QPSK
24

Figure 3.3 Spectrums of PPLN output and constellations of received signal in both approaches. in both
approaches.
1544 1546 1548 1550 1552 1554 1556
-50
0
1544 1546 1548 1550 1552 1554 1556
-50
0

154 154 15 155 1552 1554 1556
Power (10 dB/div)
Wavelength (nm)
6 -QAM
64-QAM - EVM= 5.5 %
64-QAM - EVM= 6.4 %
16-QAM - EVM= 6.5 %
16-QAM - EVM= 8.7 %
154 154 15 155 1552 1554 1556

Power (10 dB/div)
Wavelength (nm)
6 -QAM
154 154 15 155 1552 1554 1556
Power (10 dB/div)
Wavelength (nm)
16-QAM
154 154 15 155 1552 1554 1556
Power (10 dB/div)
Wavelength (nm)
16-QAM
(c)
(d)
(a)
(b)
25

Chapter 4 Tunable and Reconfigurable Optical
Nyquist Channel Aggregation of QPSK-to-16QAM
and BPSK-to-4PAM
4.1 Introduction
Optical signal processing functions may enable efficient optical networking. One
potential scenario is the enabling of flexible optical networks, and these networks may
benefit from the ability to aggregate multiple low-bit-rate data channels into a single
high-bit-rate data channel within the same spectral bandwidth [47-53]. Specifically,
multiple lower-rate data channels at an access point from a local network entering a
larger network may be efficiently combined into a higher-rate and spectrally efficient
single channel [54]. For example, two quadrature-phase-shift-keying (QPSK) data
channels may benefit from being able to fit into a single 16-quadrature amplitude
modulation (16-QAM) signal and efficiently share the same bandwidth.
There might be advantages to performing such data channel aggregation in the
optical domain. For example, optical data aggregation could potentially enable high-
speed operation and reduce the need for optical-to-electrical-to-optical conversion.
Optical data aggregation may benefit from the characteristics data modulation
transparency, data-rate tunability, and data format reconfigurability.
Some approaches for optical data channel aggregation include the wave-mixing
of the lower-rate data channels in a nonlinear element [50-53]. If the two channels are
coherent, then wave mixing should produce a vector addition of the two waves.
Consequently, the output would be an aggregated version of the two data channels in
both amplitude and phase. Moreover, the use of the lines of a Kerr frequency comb as
the carrier waves of the data channels could ensure that the channels are mutually
coherent and could be wave-mixed efficiently in a nonlinear element [55-59]. As
mentioned above, optical channel aggregation could benefit from the ability to
combine data channels of different formats. In this spirit, channel aggregation of
26

Nyquist channels could be of interest since Nyquist data channels are highly spectrally
efficiency and have minimal intersymbol interference (ISI) [60-66].
In this work, we demonstrate a tunable and reconfigurable optical Nyquist
channel aggregation using nonlinear wave mixing and a Kerr frequency comb. The
optical Nyquist pulse trains are generated by a Mach-Zehnder modulator (MZM) that
modulates a sinusoidal tone on a Kerr frequency comb. Afterwards, a lower-order data
format is encoded over the Nyquist pulse trains. Finally, a single higher-order
modulation format Nyquist channel is generated by wave mixing of the lower-order
Nyquist channels in a periodically poled lithium niobate (PPLN) waveguide. We
demonstrate that 10 and 16 Gbaud QPSK Nyquist channels are aggregated to 10 and
16 Gbaud 16-QAM Nyquist channels, respectively. Moreover, two binary-phase-shift-
keying (BPSK) Nyquist channels are flexibly aggregated to either a 4-level pulse
amplitude modulation (4-PAM) or QPSK signal, depending on the relative phase and
amplitude of the inputs. Furthermore, the quality of the generated signal is compared
when two different wave mixing approaches are employed for aggregation.
4.2 Concept of Optical Nyquist Generation and Aggregation
The concept of vector addition for aggregation is shown in Figure 4.1. Two
QPSK channels can be aggregated into a single 16-QAM channel as depicted in Figure
4.1(a). Each constellation point, i.e., symbol, can be represented as a vector that has
both amplitude and phase. In this context, at any symbol time, the addition of two
channels can be considered as the addition of two vectors that may have different
amplitudes and phases. If we want to aggregate two QPSK channels, there are four
vectors for the first channel and four vectors for the second channel. As a result, there
will be 16 different possibilities by combining these two channels, which result in a
16-QAM channel.
Similarly, the vector addition of two BPSK channels can lead to four different
possibilities, which might be interpreted as a 4-PAM or QPSK channel, depending on
the input configuration. If two BPSK constellations have the same phase but different
amplitude, they can be aggregated as a four-level signal such as 4-PAM (see Figure
27

4.1(b)). On the other hand, if there is a 90-degree phase shift between two BPSK
constellations that have the same amplitude, the QPSK constellation can be realized at
the output (see Figure 4.1(c)). Therefore, the optical aggregator can be reconfigured
to generate 4-PAM or QPSK at the output by tuning the phase and amplitude of the
input BPSK signals.

Figure 4.1 Concept of vector addition for aggregation. (a) aggregating two QPSK channels into a 16-
QAM channel, (b) aggregating two BPSK channels into a 4-PAM, (c) aggregating two BPSK channels
into a QPSK.

The concept of the optical generation of multiple Nyquist pulse trains using a
Kerr frequency comb is shown in Figure 4.2. The Kerr frequency comb is generated
by injecting continuous-wave (CW) light into a silicon nitride (Si3N4) microresonator.
Consequently, the comb is sent into an MZM, which is driven by a sinusoidal radio
frequency (RF) clock source at Δf. In this way, equal-intensity, phase-locked, and
symmetrical sidebands with respect to each comb line will be inserted with the spacing
of Δf [67].
16-QAM
+ =
1
st
QPSK
2
nd
QPSK
Phase=45º
Amplitude=1
Phase=135º
Amplitude=0.5
4-PAM
+ =
1
st
BPSK
2
nd
BPSK
Phase=0º
Amplitude=1
Phase=0º
Amplitude=0.5
+ =
2
nd
BPSK
phase=90º
Amplitude=1
1
st
BPSK
Phase=0º
Amplitude=1
QPSK
(a)
(b)
(c)
28

By adjusting the bias voltage of the MZM and the RF signal amplitude, the
modulator can create three equal power spectral lines (the original comb line and two
first-order sidebands) [68]. N equal power spectral lines with a spacing of Δf can be
represented in the frequency domain as follows:
∑ 𝛿 (𝑓 −𝑛 ∆𝑓 )
𝑁 −1
2
𝑛 =−
𝑁 −1
2
∑ 𝑒 𝑗 2𝜋𝑛 ∆𝑓 𝑁 −1
2
𝑛 =−
𝑁 −1
2

(4.1)
The time domain waveform of eq.(4.1) can be obtained by taking its inverse
Fourier transform, which is as follows:
𝐹 −1
{

∑ 𝑒 𝑗 2𝜋𝑛 ∆𝑓 𝑁 −1
2
𝑛 =−
𝑁 −1
2 }

sin(𝜋𝑁 ∆𝑓𝑡 )
sin(𝜋 ∆𝑓𝑡 )

(4.2)
Eq. (4.2) represents a periodic sinc-shaped function with a temporal period of 1/
Δf [68]. Therefore, since there are three flat lines (i.e. equal power) after MZM for
each channel, sinc-shaped Nyquist pulse trains are generated. The intensity of the
optical field in (2) for N=3 is depicted in Figure 4.2.

Figure 4.2 Multiple optical Nyquist pulse trains generation using frequency comb and a Mach-Zehnder
modulator (MZM) with driving frequency Δf.

Si
3
N
4
MZM
MZM
l
…
l
…
t t t
Bias
Laser
∆

∆
∆ ∆ ∆ ∆ ∆

∆

∆
∆
29

Figure 4.3 shows the conceptual block diagram of the optical aggregation of data
channels modulated over Nyquist pulse trains using nonlinear wave mixing. A Kerr frequency
comb is generated in a microresonator that has multiple equidistant coherent frequency tones.
The comb is sent into a programmable filter that can adjust the phase and amplitude of each
comb line independently. In this filter, two comb lines are selected to be sent directly to a
nonlinear element, which act as pumps, i.e., P 1 and P 2. Two other comb lines with equal
frequency spacing as pumps are selected and sent to the other port to generate Nyquist pulse
trains and modulate data over them. Nyquist pulse trains can be generated using an MZM
driven by a sinusoidal RF tone and a bias control for the insertion of flat lines. Subsequently,
Nyquist pulse trains are transmitted through an IQ modulator to modulate a lower order format,
e.g., QPSK, over them.
Two data channels, i.e., S 1 and S 2, and two pumps, i.e., P 1 and P 2, along with another
dummy pump, P, are sent into a nonlinear element to perform coherent addition. In our
proposed scheme, a χ
(2)
nonlinear element, e.g., a PPLN waveguide, is used for realizing the
nonlinear wave mixing. Signals and pumps are located symmetrically with respect to the quasi
phase matching (QPM) wavelength of the PPLN. We consider two approaches for the
nonlinear wave mixing of the input signals and pumps.
In the first approach (Approach 1 in Figure 4.3), S 1 and P 1 interact through sum
frequency generation (SFG) and generate the copy of S1 at 2f QPM. Similarly, S2 and P 2 interact
through SFG and generate the copy of S 2 at 2f QPM, which is at the same frequency as the copy
of S 1. As a result, two copies are coherently added together since they are frequency- and
phase-locked. The final dummy pump P can interact with the resultant wave at 2f QPM through
difference frequency generation (DFG) and convert the combined signal to the same
frequency band as the input (e.g., the C-band).
In the second approach (Approach 2 in Figure 4.3), we do not have to use the final
dummy pump P. In this case, S 1 and P 1 interact through SFG and generate the copy of S 1 at
2f QPM. Then, the copy of S 1 interacts with P 2 through SFG and converts back the copy of S 1 to
the symmetrical frequency of P 2. In other words, the copy of S1 is generated at the same
frequency as S 2, which means that they can be coherently added as they are frequency- and
phase-locked. In the second approach, not only the need for an extra pump is obviated, but
30

also the power loss due to the conversion efficiency of S 2 is avoided. On the other hand, the
output wavelength is arbitrarily selected in the first approach by tuning the wavelength of the
final dummy pump P, whereas it is fixed to the same wavelength as S 2 in the second approach.

Figure 4.3 Conceptual block diagram of optical aggregation of data channels that are modulated over
Nyquist pulse trains using nonlinear wave mixing. Two approaches are shown for nonlinear wave
mixing. In first approach (Approach 1) two channels are mixed together on a third wavelength by
utilizing an additional dummy pump. In second approach (Approach 2) the first channel is wavelength-
converted over second channel to perform aggregation.

4.3 Experimental Setup
Figure 4.4 shows the experimental setup of the proposed optical aggregator. An external
cavity diode laser (ECDL) at wavelength of 1558.6 nm is amplified in a high-power erbium-
doped fiber amplifier (EDFA-1). Then, the amplified light is coupled into a silicon nitride
(Si 3N 4) microresonator with the quality (Q) factor of 1.3×10
6
. A Kerr frequency comb in the
single soliton state is generated by tuning the pump wavelength using an arbitrary function
generator (AFG) [69]. The lines of the generated comb in the soliton state have high coherence,
and the spacing between them is ~192 GHz. The spectrum of the generated comb in the soliton
state is shown in Figure 4.4(a). A tunable fiber Bragg grating (FBG) is used after the
microresonator to suppress the residual pump before sending the comb into the rest of the
system.
After the comb generation, a few lines are filtered in a band-pass filter (BPF) and then
amplified in a low-noise EDFA to be sent into a programmable filter based on liquid crystal
on silicon (LCoS-1) technology. In the LCoS-1, we can select the desired comb lines and
direct them to different ports to be modulated or used as pumps for nonlinear processing.
Comb lines are selected such that they are symmetric with respect to the QPM wavelength of
the PPLN, which is ~1550.5 nm. Two comb lines are transmitted from the first output port of

Nyquist
generation
PPLN
(Phase
Coherent
Addition)
QPSK
modulation
S
1
S
2
Pump
Fingers
P
2
[ 0.5 , 1]
P
Approach 2
Output=a*S
1
+S
2
SFG
+DFG

Output S
1
S
2
P
2
P
1
Output=a*S
1
+S
2
SFG

+
Output

Dummy
Pump
P
e.g.,
16-QAM
S
2
P
2
P
1
Approach Kerr Frequency
Comb
Si
3
N
4
31

LCoS-1 to the high-power EDFA (EDFA-2) to be directly sent to the PPLN. The other two
comb lines are sent out from the second port of the LCoS filter.
Consequently, the two comb lines from the second port are transmitted through an
MZM that is driven by a 10 GHz sinusoidal tone. Sideband harmonics are generated next to
each comb line with a 10 GHz frequency spacing. To generate the Nyquist pulse train, the bias
is tuned to have three spectral lines with almost the same peak power [68]. Since we choose
to send two comb lines into the MZM, two Nyquist pulse trains are generated simultaneously.
The resultant Nyquist pulse train for the first channel (S 1) in the spectral and time domains are
shown in Figs. 12(b) and 12(c), respectively.
Afterward, the Nyquist pulse trains are amplified in a low-noise EDFA and then sent
into a nested MZMs driven by 2
15
-1 pseudo-random bit sequence (PRBS) data to generate
10/16 Gbaud BPSK/QPSK data. The spectrum of the first channel (S1) after the modulation
of 10 Gbaud QPSK over the Nyquist pulse train is shown in Figure 4.4(d). The same data are
modulated over both channels. To decorrelate the two channels, relative symbol delays are
applied between the two channels using a dispersion-compensating fiber (DCF) module and
the second LCoS (LCoS-2) filter. The DCF module can induce the relative delay of 195 ps/nm,
and since the comb-line spacing is ~1.55 nm, the relative delay is ~ 302 ps. This can be 3 or 5
symbol delays when the baud rate is 10 or 16 Gbaud, respectively. The residual delay can be
fine-tuned in the LCoS-2 filter. Moreover, the phase and amplitude of two channels can be
adjusted in LCoS-2 to perform aggregation by realizing vector addition.
The signals are also amplified in a high-power EDFA (EDFA-3) and coupled into the
same fiber with the amplified pumps. The third pump, P, at the wavelength of 1558.1 nm can
be amplified in EDFA-4 and added in this stage when implementing Approach 1. Otherwise,
for Approach 2, the dummy pump P is not needed. The results for these two configurations
are compared in the next section. After coupling all the signals and pumps into the same fiber,
they are transmitted through the PPLN waveguide. The wave mixing processes explained in
the previous section happen in this waveguide, and the aggregated signal will be generated at
the output of the PPLN. The QPM wavelength of the PPLN can be fine-tuned by a temperature
controller to maximize the power of the generated output. The output signal is then filtered
32

and sent to the coherent receiver to capture the constellation and perform bit error rate (BER)
measurements.

Figure 4.4 Experimental setup of optical aggregator of Nyquist channels using Kerr frequency comb
and PPLN. AFG: arbitrary function generator, ECDL: external cavity diode laser, EDFA: erbium
doped fiber amplifier, PC: polarization controller, MZM: Mach-Zehnder modulator, FBG: fiber Bragg
grating, BPF: band-pass filter, LCoS: liquid crystal on silicon, DCF: dispersion compensating fiber,
PPLN: periodically-poled lithium niobite; ATT: attenuator. (a) optical spectrum of soliton comb; (b)
Nyquist pulse in frequency domain; (c) Nyquist pulse in time domain; (d) spectrum of the modulated
signal; (e) spectrum of the PPLN output.
4.4 Experimental Results
Figure 4.5 shows the constellations, eye diagram, and BER of the aggregation of
two QPSK channels into a single 16QAM channel using Approach 1. As shown in
Figure 4.5(a), two 10 Gbaud QPSK signals with error vector magnitudes (EVMs) of
11.3% and 11.2% are aggregated into a single 10 Gbaud 16QAM channel with EVM
of 7.9%. The 16QAM has smaller EVM basically because of the definition of EVM
[70]. Note that the amplitude ratio of two QPSK signals should be 2, to generate
16QAM. This may not be clear from the constellation diagram in Figure 4.5(a) owing
to the normalization in the coherent receiver. However, the spectrum of the PPLN
output in Figure 4.4(e) indicates the 6-dB power difference between the two channels,
which is applied in LCoS-2.
Furthermore, the in-phase and quadrature-phase eye diagrams for two input
QPSK channels and the output 16QAM are shown in Figure 4.5(a). The eye diagrams
demonstrate that the data are modulated over the optically generated Nyquist pulse
trains. Since the Nyquist pulse trains are generated in one MZM, there are only three
9 nm
DCF
EDFA-1
LCoS
Filter-1
Kerr Frequency Comb Generation
10 Gbaud
1 nm
EDFA
EDFA-2
5 nm
1 nm
BPF
Coherent
Receiver
a
ECDL
Isolator
ATT
1 nm
5 nm
~
MZM
QPSK
Modulator
EDFA-3
5 nm
LCoS
Filter-2
1500 1550 1600 1650
Wavelength (nm)
a
b d
e
b
Power (10 dB/div)
1553
Power (10 dB/div)
d
1553
Wavelength (nm)
λ P =1558.1 nm
PC
e
Wavelength (nm)
Power (10 dB/div)
S2 S1
P
P2 P1
1 nm
Time (20 ps/div)
c
c
EDFA
PC
S1
FBG
AFG
10GHz
Bias
6dB
33

flat lines for each Nyquist pulse train. This causes two zero-crossing points in each
period. The zero-crossing points theoretically allow for zero ISI transmission by
multiplexing two more Nyquist pulses with their peaks at these points. By adding more
MZMs, more flat lines will be inserted, which can potentially increase the number of
time-multiplexed Nyquist channels.
The BER measurements were performed to quantify the quality of the generated
signal. These measurements were directly performed in the coherent receiver. Figure
4.5(b) shows the BER curves versus the received optical signal-to-noise ratio (OSNR)
for the input QPSK signals and the generated output 16QAM at 10 Gbaud.

Figure 4.5 (a) Constellations and in-phase and quadrature-phase of two 10Gbaud QPSK channels and
the aggregated 16QAM channel, (b) BER measurement for the input QPSK channels and the output
16QAM.
1
st
QPSK
(10Gbaud)
EVM= 11.3 %

16-QAM
EVM= 7.9 %
Inputs Output
Constellation In-phase Quadrature
(a)
(b)
-5
-4
-3
-2
-1
5 10 15 20
OSNR (dB)
QPSK-1
QPSK-2
16QAM
34

The tunability and reconfigurability of the system are investigated by tuning the
input baud rate and modulation format. Figure 4.6 shows the generated aggregated
output by tuning the input in Approach 1. The baud rate of the input is changed to 16
Gbaud in Figure 4.6(a) where two QPSKs with EVMs of 13.7% and 12.9% are
aggregated to a 16QAM with EVM of 8.7%.
Moreover, the modulation format of the inputs is changed to BPSK where two
10 Gbaud BPSK channels with EVMs of 11.8% and 12.1% can be aggregated to either
4-PAM or QPSK depending on the relative phase and amplitude of the inputs. In the
first configuration, 4-PAM with EVM of 12.4% can be generated if we set two input
BPSK signals with zero relative phase difference but with the amplitude ratio of 2. In
the second configuration, a QPSK with EVM of 15.3% is generated when the relative
phase of the inputs is set to 90-degree whereas the amplitude ratio is 1. These results
confirm the reconfigurability of the system in generating different output format by
tuning the phase and amplitude of the inputs.

Figure 4.6 Constellation of two 16 Gbaud QPSK channels and the aggregated 16QAM channel. (b)
Generation of 4-PAM and QPSK channel by aggregating two 10 Gbaud BPSK channels.
Inputs Output
1
st
Configuration 2
nd
Configuration
1
st
BPSK
(10Gbaud)
EVM= 11.8 %
2
nd
BPSK
(10Gbaud)
EVM= 12.1 %
QPSK
EVM= 15.3 %
1
st
BPSK
(10Gbaud)
EVM= 11.8 %
2
nd
QPSK
(10Gbaud)
EVM= 12.1 %
4-PAM
EVM= 12.4 %
Inputs Output
Constellation
1
st
QPSK
(16Gbaud)
EVM= 13.7 %
2
nd
QPSK
(16Gbaud)
EVM= 12.9 %
16-QAM
EVM= 8.7 %
(a)
(b)
35

As explained in Section III.C, two approaches can be implemented to perform
the aggregation of input channels. Figure 4.7 shows the spectrum of the PPLN output
along with the corresponding output constellation for the two approaches in the case
of two QPSK and three BPSK aggregations.
A 16QAM with EVM of 8.5% is generated in Approach 1, whereas the EVM is
6.9% in Approach 2. We believe that the reasons for the better performance in terms
of EVM in Approach 2 are as follows: (i) there is no need for an extra pump, which
can allow higher power for the signals if we limit the total power of the pumps and the
signals to the maximum input power of the PPLN, which is 200 mw, and (ii) an
additional loss due to wavelength conversion is avoided by keeping the first channel
on its wavelength and converting the other channels into the first channel.
Furthermore, three BPSK channels can be aggregated to generate an 8-PAM
channel. The only change in the experimental setup is the addition of one more channel
by selecting six comb lines in LCoS-1 instead of four. Three comb lines are directed
to the first port to be the pumps, and three lines are transmitted to the second port to
be modulated with BPSK data. The 8-PAM with EVMs of 8.6% and 7.4% can be
generated in Approach 1 and Approach 2, respectively. Again, better performance is
observed in Approach 2. However, Approach 1 has the benefit of flexibility in the
output signal wavelength. In other words, by tuning the wavelength of the final dummy
pump P, the wavelength of the output can be flexibly set, whereas in Approach 2, the
wavelength of the output depends on the wavelength of the input.

36

Figure 4.7 Comparing the quality of the aggregated channels using two different approaches for
aggregation of two QPSK channels into a single 16QAM channel and three BPSK channels into a single
8PAM channel.

8-PAM
EVM= 7.4 %
8-PAM
EVM= 8.6 %
16-QAM
EVM= . %
16-QAM
EVM= . %
16QAM
1545 1549 1553 1557
Wavelength (nm)
Power (20 dB/div)
16QAM
1545 1549 1553 1557
Wavelength (nm)
Power (20 dB/div)
8PAM
1545 1549 1553 1557
Wavelength (nm)
Power (20 dB/div)
8PAM
1545 1549 1553 1557
Wavelength (nm)
Power (20 dB/div)
Aggregating two QPSK channels Aggregating three BPSK channels
Approach 1 Approach 2
37

Chapter 5 QPSK-to-PAM4 Data-Format and
Wavelength Conversion to Enable All-Optical
Gateway from Long-haul to Datacenter
5.1 Introduction
High-order modulation formats have been of great importance for optical
communications systems due to their higher system capacity, increased spectral
efficiency, and lower speed requirement of electronics [71-72]. One of the most
common data formats is quadrature-phase-shift-keying (QPSK), which encodes 2 bits
per symbol and typically requires coherent detection at the receiver. The coherent
receivers can substantially compensate many transmission impairments [73-75].
More recently, simple direct-detection approaches have gained much interest,
especially for data centers and short-haul applications. For example, four-level pulse
amplitude modulation (PAM4) can: (a) have higher capacity and spectral efficiency as
compared to conventional on-off keying (OOK), and (b) be received using relatively
simple and cost-effective direct-detection schemes [76-78]. Note that PAM4 is similar
to QPSK in its spectral efficiency as each symbol represents two bits.
A potential challenge is that the preferred modulation format may be different
for data channels in different parts of an optical network. For example, QPSK may be
preferred for a long-haul segment whereas PAM4 may be preferred for a short-distance
link in a local area. Therefore, it may be valuable to have an optical gateway that can
convert a data-channel’s format between QPSK and PAM4 and avoid optical-to-
electrical-to-optical conversion.
The following operations have previously been reported: (a) de-aggregation of a
16-ary quadrature amplitude modulation (16-QAM) channel into two PAM4 channels
using coherent detection and not direct detection [79]. (b) binary-phase-shift-keying
(BPSK) to OOK based on phase-sensitive amplification [80], (c) OOK to BPSK using
cross-phase modulation (XPM) in a highly nonlinear fiber [81]; and (d) PAM4 to
QPSK format conversion [82].
38

In this work, we demonstrate optical format and wavelength conversion of 20
and 30Gbit/s QPSK-to-PAM4 by using two nonlinear wave mixing stages. We
manipulate the input QPSK constellation to generate PAM4 in the output. The QPSK
constellation is firstly rotated and then offset (biased) by adding with a constant power.
The proposed method maps four symbols of QPSK signal to four different amplitude
levels which can be directly detected in a photo-diode (PD). Open eyes are obtained
for the received PAM4 signal and bit error rate (BER) measurements are also shown
for 20 and 30Gbit/s signals. Wavelength tunability of the converted PAM4 is
investigated as well. Furthermore, a distributed feedback laser (DFB) laser with high
phase noise is used as another laser source for QPSK signal. We demonstrate that the
produced delayed signal conjugate and nonlinear wave mixing can reduce the phase
noise of the laser and open eye can be observed.

5.2 Concept of QPSK to PAM4 Format Conversion
The concept of the proposed QPSK to PAM4 modulation format converter is
shown in Figure 5.1. On a constellation diagram, QPSK has four equi-amplitude
symbols with equidistant phases. Therefore, if a QPSK signal is sent into a PD, only
one amplitude level is captured, and the phase information is erased. In order to detect
four amplitude level at the PD, the QPSK constellation should be manipulated such
that every constellation point should have a distinct amplitude. As shown in Figure
5.1(a), if the QPSK constellation is rotated and then added with a constant-amplitude
wave, the four constellation points would have different amplitude levels. Thus, by
sending the resultant signal to the PD, a PAM4 signal would be detected. Here the
phase rotation angle ∆φ is explained in Figure 5.1(a).
39

Figure 5.1 (a) Concept of QPSK to PAM4 format conversion using constellation rotation and bias
addition; (b) the block diagram of the proposed QPSK to PAM4 converter using nonlinear wave mixing.
Phase rotation is applied in LCoS filter and the power bias is added in the second nonlinear element.
PPLN: Periodically-Poled-Lithium-Niobate, QPM: Quasi-Phase Matching, LCoS: Liquid Crystal on
Silicon, SHG: Second-Harmonic Generation, SFG: Sum Frequency Generation, DFG: Difference
Frequency Generation.

The conceptual block diagram for the demonstration of QPSK into PAM4
conversion using nonlinear wave mixing is illustrated in Figure 5.1(b). The input
QPSK signal 𝑆 𝑖𝑛
(𝑡 ) is coupled with a continuous wave (CW) pump laser 𝑃 1
(𝑡 ) and
then injected into first nonlinear stage to generate the phase conjugate copy of the
signal. The electric fields of the signal and the pump can be written as follow:
𝑆 𝑖𝑛
(𝑡 ) 𝐴 𝑖𝑛
𝑒 𝑗 (𝜔 𝑖𝑛
𝑡 +𝜑 𝑖𝑛
(𝑡 ))
𝐴 𝑖𝑛
𝑒 𝑗 (𝜔 𝑖𝑛
𝑡 +𝜑 𝑖𝑛
𝐷 (𝑡 )+𝜑 𝑖𝑛
𝑁 (𝑡 ))

(5.1)
𝑃 1
(𝑡 ) 𝐴 𝑃 1
𝑒 𝑗 (𝜔 𝑃 1
𝑡 +𝜑 𝑃 1
(𝑡 ))
𝐴 𝑃 1
𝑒 𝑗 (𝜔 𝑃 1
𝑡 +𝜑 𝑃 1
𝑁 (𝑡 ))

(5.2)
where 𝐴 𝑖𝑛
and 𝐴 𝑃 1
are the amplitudes, 𝜔 𝑖𝑛
and 𝜔 𝑃 1
are the wavelengths and
𝜑 𝑖𝑛
(𝑡 ) and 𝜑 𝑃 1
(𝑡 ) are the phases of 𝑆 1
(𝑡 ) and 𝑃 1
(𝑡 ), respectively. The phase of the
signal includes both data and noise, 𝜑 𝑆 1
𝐷 (𝑡 ) and 𝜑 𝑆 1
𝑁 (𝑡 ); however, the pump only
carries the phase noise. In our experimental implementation, periodically-poled-
lithium-niobate (PPLN) waveguides are used as nonlinear elements. The conjugate
I
Photo Detector

λ
s
(t)
QPSK
Signal
Conjugate Copy
Generation
λ

- s
(t-T)
λ
s
(t)+
λ

s
(t )+
SHG
QPM PAM4 Signal
λ
P2
λ
(a)
40

copy is generated in the first nonlinear stage, i.e., PPLN-1. The wavelength of the
pump 𝜔 𝑃 1
is set to the PPLN quasi-phase matching (QPM) wavelength. In this way,
pump interacts with itself through second-harmonic generation (SHG) and generate
𝑃 1
2
(𝑡 ) at 2𝜔 𝑃 1
. Then, 𝑃 1
2
(𝑡 ) interacts with the input signal through difference
frequency generation (DFG) to create the conjugate copy where its electric field is
proportional to:
𝑃 1
2
(𝑡 )×𝑆 𝑖𝑛
∗
(𝑡 ) 𝐴 𝑃 1
2
𝐴 𝑖𝑛
𝑒 𝑗 ((2𝜔 𝑃 1
−𝜔 𝑖𝑛
)𝑡 +(2𝜑 𝑃 1
𝑁 (𝑡 )−𝜑 𝑖𝑛
𝐷 (𝑡 )−𝜑 𝑖𝑛
𝑁 (𝑡 )))

(5.3)
The output of PPLN-1 is sent to a programmable filter based on Liquid Crystal
on Silicon (LCoS) technology in order to (i) select the signal, the conjugate copy, and
the pump by filtering them and reducing the out of band amplified spontaneous
emission (ASE) noise, (ii) adjust relative amplitude of these selected waves, (iii) apply
the phase rotation of ∆φ to the signal which is basically the constellation rotation, and
(iv) apply one symbol delay (T) between signal and its conjugate copy to compensate
the relative phase between the pump and the signal. As a result, the electric fields of
the signal, the conjugate copy, and the pump after LCoS filter are 𝑆 𝑖𝑛
(𝑡 )×𝑒 𝑗 ∆𝜑 ,
𝑃 1
2
(𝑡 −𝑇 )×𝑆 𝑖𝑛
∗
(𝑡 −𝑇 ), and 𝑃 1
(𝑡 ), respectively. The output of the LCoS filter is then
sent into second nonlinear stage, i.e., PPLN-2. The QPM wavelength of the second
PPLN is the same as the first one. As a result, the pump 𝑃 1
(𝑡 ) interacts with itself
through SHG and generate the following:
𝐸 (𝑡 ) 𝑃 1
2
(𝑡 )∝ 𝑒 𝑗 (2𝜔 𝑃 1
𝑡 +2𝜑 𝑃 1
𝑁 (𝑡 ))

(5.4)
Furthermore, since the signal and the delayed conjugate copy are located
symmetrically with respect to the QPM wavelength, they interact through sum
frequency generation (SFG) and generate the following:
𝑋 (𝑡 ) 𝑃 1
2
(𝑡 −𝑇 )×𝑆 𝑖𝑛
∗
(𝑡 −𝑇 )×𝑆 𝑖𝑛
(𝑡 )×𝑒 𝑗 ∆𝜑 ∝ 𝑒 𝑗 (2𝜔 𝑃 1
𝑡 +(2𝜑 𝑃 1
𝑁 (𝑡 −𝑇 )−𝜑 𝑖𝑛
𝐷 (𝑡 −𝑇 )−𝜑 𝑖𝑛
𝑁 (𝑡 −𝑇 )+𝜑 𝑖𝑛
𝐷 (𝑡 )+𝜑 𝑖𝑛
𝑁 (𝑡 )+∆𝜑 ))

(5.5)
Both 𝑋 (𝑡 ) and 𝐸 (𝑡 ) are at 2𝜔 𝑃 1
and they are frequency locked. To perform
coherent addition of 𝑋 (𝑡 ) and 𝐸 (𝑡 ) the relative phase between them should be
compensated. Assuming the source of phase noises for both 𝑆 𝑖𝑛
(𝑡 ) and 𝑃 1
(𝑡 ) are from
41

their lasers linewidth, the fluctuation of their phase noise is much slower than the
symbol rate [83]. Therefore, we can assume:
𝜑 𝑖𝑛
𝑁 (𝑡 )≃𝜑 𝑖𝑛
𝑁 (𝑡 −𝑇 ) (5.6)
𝜑 𝑃 1
𝑁 (𝑡 )≃𝜑 𝑃 1
𝑁 (𝑡 −𝑇 ) (5.7)
By making these assumptions equation (5) is simplified as follows:
𝑋 (𝑡 )∝ 𝑒 𝑗 (2𝜔 𝑃 1
𝑡 +(2𝜑 𝑃 1
𝑁 (𝑡 )+𝜑 𝑖𝑛
𝐷 (𝑡 )−𝜑 𝑖𝑛
𝐷 (𝑡 −𝑇 )+∆𝜑 ))

(5.8)
Therefore, although 𝑃 1
(𝑡 ) is generated from an independent laser than 𝑆 𝑖𝑛
(𝑡 ), it
can act as a bias that would offset the constellation after mixing the signal with its
delayed conjugate copy. In order to convert back the generated signal at 2𝜔 𝑃 1
into C-
band, another pump 𝑃 2
(𝑡 ) at 𝜔 𝑃 2
is also injected in PPLN-2. The pump 𝑃 2
(𝑡 ) is
interacted with the resultant wave at 2𝜔 𝑃 1
through DFG and generate the output at
2𝜔 𝑃 1
−𝜔 𝑃 2
as follow:
𝑆 𝑜𝑢𝑡 (𝑡 ) 𝑃 2
∗
(𝑡 )×(𝐸 (𝑡 )+𝛽𝑋 (𝑡 )) (5.9)
where 𝛽 is a weight that can be adjusted in the LCoS filter and 𝑆 𝑜𝑢𝑡 (𝑡 ) is the
generated output signal at 2𝜔 𝑃 1
−𝜔 𝑃 2
. PAM4 eye diagram is expected to be observed
after PD by properly adjusting the weight and the phase rotation angle. Please note
that the received data is the differential data and the original data should be recovered
from it.

5.3 Experimental Setup

The experimental setup of the proposed QPSK to PAM4 modulation format
converter is shown in Figure 5.2. At the transmitter, a laser at wavelength of λ
𝑆
1552.8 nm is modulated in a nested Mach–Zehnder modulator with 10/15 Gbaud
QPSK data generated by a 2
15
−1 pseudo random bit sequence (PRBS). The output
of the modulator is amplified in a low-noise erbium-doped fiber amplifier (EDFA),
sent into high-power EDFA (EDFA1) and injected into PPLN-1. Another CW laser
42

source, P
1
, at the wavelength of λ
P
1
1550.7 nm is amplified in EDFA2 and also
sent into PPLN-1. The conjugate copy of the signal is generated at the PPLN-1 output
as shown at node A in Figure 5.2. Afterwards, a dispersion compensation fiber (DCF)
and LCoS filter are used to apply one symbol delay between signal and its conjugate,
as well as, phase rotation and amplitude adjustments. The output is amplified in
EDFA3 and coupled with the second pump at λ
P
2
1554.6 nm into PPLN-2. The
QPM wavelengths of both PPLNs are temperature tuned to be the same at 1550.7 nm.
The spectrum of PPLN-2 is shown at node B in Figure 5.2. The final output is filtered
at a band pass filter (BPF) and sent into the PD for eye diagrams and BER processing.

Figure 5.2 The experimental setup for the proposed QPSK to PAM4 converter along with the
corresponding spectra measured at each PPLN output. Output spectrum of the first and second PPLN
is shown in A and B, respectively. PC: Polarization Controller, EDFA: Erbium-Doped Fiber Amplifier,
BPF: Band Pass Filter, PPLN: Periodically-Poled-Lithium-Niobate, DCF: Dispersion Compensation
Fiber, LCoS: Liquid Crystal on Silicon, PD: Photo-Diode.

5.4 Experimental Results
Figure 5.3 shows the output eye diagrams for different phase rotation angles
when the input is 20 and 30Gbit/s QPSK. Phase rotation angle ∆φ is shown in Figure
5.1(a). When the phase rotation angle is 90°, the offset and rotated symbols will only
produce two amplitude levels. Similarly, if ∆φ 90°, three amplitude levels are
detected, which means two of the four symbols are distorted and cannot be recovered.
Substantially, equal eye opening for PAM4 is observed when the phase rotation angle
is ∆φ 71°. Open eyes are captured for both 20 and 30 Gbit/s cases.
PPLN-1
1 nm
Photo
Diode
50/50
SLM
Filter

90 10/15 Gbaud
PRBS (2
15
-1)
a
λ
S
~
1552.8nm
λ
P1
~
1550.7nm
λ
P2
~1554.6nm
EDFA1
DCF
100m
1 nm
1 nm
1 nm
Pre-Amp
1 nm
5 nm
EDFA2
EDFA3
EDFA4
29 dBm
30.8 dBm
27.4 dBm
1548 1550 1552
-60
-40
-20
1549 1551 1553
Wavelength (nm)
Power (20 dB/div)

S*(t)
S(t)
1545 1550 1555
-60
-40
-20
1547 1549 1551 1553 1555
Wavelength (nm)
Power (20 dB/div)
b

S(t)
S*(t-T)
output
43

Here, we define a ratio, which measures the dependence of the eye opening
between the middle two levels as x/A, where x is the amplitude of the middle eye and
A is the peak-to-peak amplitude (see Figure 5.3(b)). Figure 5.3(b) shows how this ratio
changes according to changing the phase values from ∆φ 45° to ∆φ 90° in
simulation. Equal eye opening can be achieved when x/A=1/3. As it is pointed earlier
in Figure 5.3(a), this is the case when ∆φ 71°.

Figure 5.3 (a) Eye diagram of the output signal with different rotation angle (∆φ=45°,90° and 71°) for
20 and 30 Gbit/s QPSK input. (b) Simulation of continuous phase rotation from 45° to 90° and its impact
on eye opening.

Wavelength tunability of the proposed system is shown in Figure 5.4. By tuning
the wavelength of the second injected pump P
2
at the second nonlinear stage, the
converted PAM4 wavelength can be tuned. In Figure 5.4, the input QPSK wavelength
is set to 1552.8 nm while the output PAM4 wavelength is tuned to either 1546.8 nm
or 1543.2 nm in Figure 5.4(a) and (b), respectively. Open eyes are observed in both
cases and the quality of the eyes are almost the same. Therefore, our proposed scheme
not only converts the modulation format from QPSK to PAM4, but also can perform
wavelength conversion from the input wavelength to another desired wavelength that
might be useful in some applications. For example, the wavelength of interest of two
networks, connected by this gateway, may not be necessarily the same.
20Gb/s

45 50 55 60 65 70 75 80 85 90

A
(b)

44

Figure 5.4 Wavelength tunability of the proposed QPSK to PAM4 format and wavelength converter.
The input is 20 Gbit/s QPSK at 1552.8 nm while the output PAM4 wavelength is (a) 1546.8 nm and
(b) 1543.2 nm.

The BER measurement of the QPSK to PAM4 converter is shown in Figure 5.5.
The BER of the input QPSK signal and the output PAM4 signal versus optical signal-
to-noise ratio (OSNR) for both 20 and 30 Gbit/s are illustrated. To measure the BER
of QPSK at the transmitter side, we used an optical coherent receiver that can recover
the amplitude and phase of the QPSK signal with the aid of a local oscillator. On the
other hand, a single PD is used to detect the PAM4 signal at the receiver side. The
generated electronic signal’s waveform at PD output, is recorded and then processed
offline to calculate BER for PAM4. In order to validate the quality of the generated
PAM4 signal, the BER curve for a back to back (B2B) PAM4 is also measured.
By comparing the input QPSK and output PAM4 curves at BER of 1e-3, the
OSNR difference of ~22dB can be seen. Although it seems like a huge OSNR penalty
from input to output, it mostly results from the addition of the bias constant power to
generate PAM4. This fact can become clearer when the BER of the generated PAM4
from format conversion is compared with the BER of the B2B scenario where the
PAM4 is generated at the transmitter and directly received at the PD without going
through the system.
In order to evaluate the system’s penalty, we remove the bias addition in the
second stage by blocking P
1
in the LCoS filter. In other words, E 0 in equation (9)
1542 1544 1546 1548 1550 1552 1554 1556 1558
-60
-40
-20
PAM4
1542 1544 1546 1548 1550 1552 1554 1556 1558
-60
-40
-20

S(t)

45

at the output of the PPLN-2. Therefore, the output cannot be detected using the PD
since the amplitude of all four symbols are equal. However, the system output will
become differentially encoded QPSK, which can be recovered by coherent detection.
By measuring the output BER for this case, we can see OSNR difference of ~3dB at
BER of 1e-3 between the final output and the input.

Figure 5.5 BER measurement of the system input and output. Input is the 20 and 30 Gbit/s QPSK signal
(TX-QPSK). Output is PAM4 when the pump for bias is included (RX-PAM4). The output BER curve
without the bias is also illustrated (RX-w\o Bias). PAM4 B2B BER measurement is also reported to
compare with the converted PAM4 at the output (PAM4-B2B).

We also investigate the system performance by varying the phase noise value of
the input signal. In our experiment, we utilized a narrow-linewidth laser which has low
phase noise. In order to show the impact of higher input phase noise, we replace the
original narrow-linewidth signal’s laser with a distributed feedback laser (DFB) laser,
which has larger linewidth. The constellation of the input signal is shown in Figure 5.6
for both lasers. We define the parameter ∆𝜃 to quantify the phase deviation from the
expected value on constellation diagrams. The constellation of the output is also shown
when the bias is not added. By comparing the constellation of the output and the input,
-4.5
-4
-3.5
-3
-2.5
-2
10 15 20 25 30 35 40
-Log(BER)
TX-QPSK-20Gbps
TX-QPSK-30Gbps
RX-PAM4-20Gbps
RX-PAM4-30Gbps
RX-w/o Bias-20Gbps
RX-w/o Bias-30Gbps
PAM4-B2B-20Gbps
PAM4-B2B-30Gbps
46

it can be seen that the ∆𝜃 is reduced from 47
o
to 28
o
when DFB laser is used. This
feature is the result of phase-noise differentiation in the second stage, when
multiplying the signal with its delayed conjugate [83-84]. However, this feature cannot
be observed when the phase noise of the input is small. By comparing the output
PAM4 eye diagram, it can be seen that both eyes provide four distinct amplitude levels.

Figure 5.6 Captured eye diagram at the receiver by imposing two different phase noise levels. Two
different lasers are utilized at the transmitter and they are modulated with 20 Gbit/s QPSK data.

EVM=10.2%
θ = 19
o
EVM=21.6%
θ = 47
o
θ
EVM=14.5%
θ = 28
o
Input Output without
Bias
Output
with Bias
47

Chapter 6 Probabilistic Constellation Shaping by
Adaptively Modifying the Distribution of
Transmitted Symbols Based on Errors at the
Receiver
6.1 Introduction
Constellation shaping is a well-established technique in optical communications
to increase the system throughput [85-87]. Data constellations can be modified by
altering: (i) the geometry in terms of symbol locations and known as geometric
constellation shaping (GCS), or (ii) the probability of symbols in terms of symbol
occurrence and known as probabilistic constellation shaping (PCS) [88]. There is
interest in PCS due to the fixed geometry which may enable simpler receiver
processing [89]. Although PCS has a lower source entropy (i.e., the average amount
of information per symbol) as compared with traditional uniformly shaped
constellations for a given M-ary signal, it can achieve better system performance in
terms of a lower number of total symbol errors [85-89].
For an additive white Gaussian noise (AWGN) channel, it is known that, the
mutual information of the channel (i.e., mutual dependence between the channel input
and output) can be maximized when the constellation follows a Maxwell–Boltzmann
(M-B) type of distribution [90]. Although the AWGN approximation for the optical
communication channel is valid for a wide range of scenarios, there are situations for
which this approximation may not be optimal. These situations could include cases for
which the nonlinearity of the optical fiber is a dominant factor for a given channel [91-
92] or cases in the optical network where the interference from neighboring channels
can lead to constellation distortion. Therefore, it might be desirable to find an optimal
distribution of the transmitted symbols with a technique which does not require a
presumed model for the channel.
48

Recently, end-to-end learning of communication systems that does not make
assumptions of the channel model has been employed for GCS in optical
communications [93-94] and for PCS in wireless communications [95]. In order to
shape the constellation, a training sequence was used to learn the parameters of an
autoencoder that models the end-to-end communication system [93-95]. It might be
desirable to apply a technique for PCS in an optical communication network for which
the channel conditions and degradations may change.
In this chapter, we show a feedback-based PCS (FB-PCS) to shape a 10-Gbaud
16-QAM signal by modifying the transmitted symbols’ distribution based on error
counting at the receiver [96]. In this technique, knowledge of the channel model is not
necessarily required. A known sequence is transmitted with uniformly shaped 16-
QAM constellation and the error at each constellation point is counted at the receiver.
Using this information, an optimization problem can be solved to find the distribution
that maximizes the mutual information between the transmitter and receiver.
Subsequently, the probability distribution at the transmitter is updated without making
any assumption on channel model. We simulate four different scenarios and compare
the results with uniform and M-B distributions. We find that using FB-PCS can lead
to less symbol errors than uniform constellation shaping in all four scenarios.
Moreover, it has either better or equal performance compare with M-B constellation
shaping in terms of symbol error rate (SER). Finally, we experimentally demonstrate
that FB-PCS can reduce the SER by 50%.
6.2 Concept of Feedback-based Probabilistic Constellation
Shaping
The concept of the FB-PCS is shown in Figure 6.1(a). First, data is modulated
using 16-QAM that the probability of selecting each of the 16 symbols is uniform.
Then, the data are transmitted over an optical network where the 16 received
constellation points may suffer different distortions. At the receiver, the number of
errors at each constellation point are counted to create a 4×4 error matrix, where each
element corresponds to a constellation point. The error matrix is used to solve the
49

optimization problem shown in Figure 6.1(b). Here, the objective function is to find
the optimal distribution that maximizes the mutual information between transmitter
and receiver, i.e., 𝐼 (𝑋 ;𝑌 ) . The conditional probability 𝑝 (𝑋 𝑥 /𝑌 𝑦 ) can be
estimated from the transmitted and received sequence. The uppercase letter X and Y
denote the discrete random variables, at transmitter and receiver, respectively.
Whereas, the lower case x and y are the realizations of the random variables X and Y.
The first constraint of the optimization problem states that if a symbol experiences
higher error count, the probability of selecting that symbol should be lower. This
converse relation between error and probability is a sufficient condition that can be
expressed as different forms of equations (e.g. linear, exponential, logarithmic). We
heuristically select equation (1) because entropy has also logarithmic form in terms of
probability. We note that other equations between error and probability might also be
explored as long as they could satisfy the converse relationship between error and
probability. All errors, (𝑒 1
- 𝑒 16
) are normalized by the maximum value of the error
among all symbols (𝑒 𝑚𝑎𝑥
). The optimization hyperparameter 𝛼 can be tuned to adjust
the entropy at the transmitter, 𝐻 (𝑋 ). The second constraint ensures that the sum of all
the probabilities over all symbols is 1.

Figure 6.1 (a) Concept of feedback-based probabilistic constellation shaping (FB-PCS); (b)
Optimization problem to find the probability distribution. 𝑋 & 𝑌 : transmitted & received sequence,
TX RX
Error Count Probability Distribution Optimization
First
Shaping
Optical
Network
Distortion
TX RX
Second
Shaping Error
Counting

m
𝑃 𝑖 𝐼 𝑋 ;𝑌 𝐻 𝑋 −𝐻 (𝑋 /𝑌 ) New
Distribution

(a)
(b)
Optical
Network
Distortion
50

𝐼 (𝑋 ;𝑌 ): mutual channel information, 𝐻 (𝑋 ): transmitter entropy, 𝑒 𝑖 : number of errors at each
constellation point, 𝑒 𝑚𝑎𝑥
: max. number of errors, 𝑃 𝑖 : prob. of each constellation point, 𝛼 : optimization
hyperparameter.

6.3 Simulation Setup and Results
In order to examine the effectiveness of FB-PCS, we simulate a system model using
VPIphotonics Software. A laser with linewidth of 1 kHz is modulated by 10-Gbaud 16-QAM
which is probabilistically shaped to transmit 16384 symbols over single polarization in four
different scenarios. In each scenario, the desired channel is transmitted in multiple spans of
single mode fiber (SMF) with amplification in an erbium doped fiber amplifier (EDFA). The
nonlinear index of SMF is 2.5×10
-20
m
2
W
-1
and the effective core area of it 80 µm
2
. The
number of spans, length of SMF, and EDFA output power are varied in each scenario of
Figure 6.2. A dispersion compensation fiber (DCF) is used before the receiver to compensate
the dispersion caused by SMF. Polarization rotation and polarization-mode dispersion are not
included in our simulation. We change the power of the target channel and add other channels
to the link, which result in different constellation distortion in each scenario. In order to display
the histogram of constellation diagram at the transmitter in Figure 6.2, we intentionally added
Gaussian noise to the symbols. However, this additional noise is not transmitted to the channel
with the original data. The configuration of four scenarios are shown in Figure 6.2. We
emphasize that these four scenarios are chosen to show the concept of constellation shaping
when the distortion is not uniform over all constellation points. Although they may not match
with current commercial systems, our goal is to show that there are potential scenarios for
which the constellation shaping based on error counting at the receiver is more beneficial than
constellation shaping based on a pre-assumed channel model.
For each case, we begin with the uniform shaping and calculate the error matrix at the
receiver. Then, the optimization problem in Figure 6.1(b) is solved using projected gradient
decent algorithm [97]. In Figure 6.2, the value of 𝛼 is set to 100. The outcome of the
optimization problem is the new probability distribution upon which the constellation should
be shaped. The constant composition distribution matching (CCDM) technique [98] is used
to map the input bit stream to the symbols according to their distribution. The shaped
51

constellation is transmitted over the same network configuration, and error matrix is calculated
at the receiver for comparison. As shown in Figure 6.2, in all the scenarios, the entropy at the
transmitter is reduced; since, the uniform distribution maximizes the entropy 𝐻
−∑𝑃 𝑖 log𝑃 𝑖 𝑖 . Therefore, when the probability distribution deviates from uniform, the
entropy decreases. However, the total number of symbol errors decreases by sending less data
on the error-prone constellation points.

Figure 6.2 Simulation results of the error counting with and without constellation shaping to transmit
16384 symbols with 10-Gbaud 16-QAM using FB-PCS in four different scenarios. H: entropy of the
probability distribution, E: total number of symbol errors.

In the first scenario, there is a single channel where a 5 mW data stream is transmitted
over three spans of 30 km SMF and amplified to 5 mW in the EDFA. Here, the outermost
points at the left, right, top, and bottom corners experience more errors due to the nonlinear
phase noise caused by the transmission over the fiber. After optimization and shaping at the
transmitter, these outermost points have been assigned less frequently to transmit data symbols.
This leads to a reduction of entropy from 4 to 3.61; however, it improves the system
performance in terms of the total number of symbol errors, reducing the count from 1264 to
58. In the second scenario, the target channel with a power of 50 mW is wavelength
multiplexed with another 10-Gbaud 16-QAM channel with uniform shaping and power of 50
mW. There is only one span with the length of 10 km in this scenario. The interference caused
by the neighboring channel leads to constellation distortion. Using FB-PCS the error count is
reduced from 581 to 144. In the third scenario, a phase locked pump is transmitted along with
52

the original channel. This causes a non-symmetric channel distortion in the constellation,
leading to a non-symmetric constellation shaping. In the fourth scenario, we wavelength
multiplex three channels that are modulated with 10-Gbaud 16-QAM data and transmit them
through the fiber. The middle channel is the target channel, to which FB-PCS is applied. The
constellation shaping in this case is similar to the second scenario, but the distortion is more
severe.
To further investigate the effectiveness of FB-PCS, we compare the performance with
the uniform and M-B constellation shaping in these four scenarios. For each scenario, we solve
the optimization problem with two different values of hyperparameter 𝛼 : 10 or 1000. For a
specific value of α, solving the optimization problem results in a probability distribution with
an entropy. Therefore, different values of 𝛼 can result in different probability distributions
with the corresponding entropies. Here, we choose two example values of 𝛼 to investigate the
performance by varying 𝛼 . Hence, 𝛼 : 10 and 1000 lead to two different values of the entropy
and total number of errors after shaping. As the value of 𝛼 increases, the probability of
assigning the error-prone constellation points is reduced. As a result, the entropy and total
errors will be decreased by increasing 𝛼 . We also shape the constellation with an M-B
distribution. We set the entropy of the M-B distribution to roughly the same entropy value as
FB-PCS in order to fairly compare the SER versus optical signal to noise ratio (OSNR).

53

Figure 6.3 Simulation results for performance comparison of FB-PCS with uniform and Maxwell–
Boltzmann (M-B) in four scenarios. The entropy (H) of M-B is set close to the entropy of the optimized
distribution in FB-PCS for two different values in all four scenarios.

In the first scenario, the SER cannot decrease lower than a certain value for uniform and
M-B shaping even if the OSNR increases.; because, the outermost constellation points are the
dominant sources of symbol errors. However, in FB-PCS, we fight this source of errors, and
the probabilities of transmitting the outermost symbols are reduced. Hence, the total number
of errors is reduced. The error reduction is more evident when the entropy goes lower. Similar
behavior is observed in the third scenario where there is one constellation point with dominant
contribution to total errors. Changing the entropy of the M-B distribution do not change the
SER significantly. On the contrary, its impact is clear in FB-PCS. Therefore, FB-PCS can lead
to SER reduction by approximately one order of magnitude in higher OSNR compare with
M-B for the first and third scenario. In the second and fourth scenarios, the distortion of the
constellation is more like a Gaussian shaping; namely, the number of errors increases
0.0005
0.005
0.05
0.5
10 12 14 16 18
SER
OSNR (dB)
Scenario-1
FB-PCS (H=3.58 bits/symbol)
FB-PCS (H=3.76 bits/symbol)
M-B (H=3.59 bits/symbol)
M-B (H=3.76 bits/symbol)
Uniform (H=4 bits/symbol)
0.005
0.05
20 22 24 26 28 30
SER
OSNR (dB)
Scenario-2
FB-PCS (H=3.20 bits/symbol)
FB-PCS (H=3.74 bits/symbol)
M-B (H=3.20 bits/symbol)
M-B (H=3.74 bits/symbol)
Uniform (H=4 bits/symbol)
0.0005
0.005
0.05
25 27 29 31
SER
OSNR (dB)
Scenario-3
FB-PCS (H=3.85 bits/symbol)
FB-PCS (H=3.93 bits/symbol)
M-B (H=3.86 bits/symbol)
M-B (H=3.93 bits/symbol)
Uniform (H=4 bits/symbol)
0.005
0.05
25 30 35
SER
OSNR (dB)
Scenario-4
FB-PCS (H=2.75 bits/symbol)
FB-PCS (H=3.73 bits/symbol)
M-B (H=2.74 bits/symbol)
M-B (H=3.73 bits/symbol)
Uniform (H=4 bits/symbol)
54

gradually when the symbol magnitude increases. In these two cases, the M-B shaping shows
an acceptable performance, and it gets better when the entropy is further reduced. However,
FB-PCS is either as good as or slightly better than M-B.
In our work, we choose SER as a performance metric for the following reasons: (a)
probabilistic shaping is used to reduce the SER [99-102], and (b) FB-PCS is based on counting
“symbol errors” at each constellation point; hence, it might be beneficial to report the total
symbol errors with and without using FB-PCS. The SER can also be reduced by using a
simpler modulation format such as quadrature phase shift keying (QPSK), but this change
comes at the expense of reducing the entropy. For instance, using QPSK instead of 16-QAM
decreases the entropy by half. However, FB-PCS aims to reduce the SER while attempting to
limit any decrease in entropy. This is why, at a given entropy, FB-PCS can lead to lower SER
than M-B in some scenarios.
6.4 Experimental Setup and Results
A proof-of-concept experiment is shown in Figure 6.4. A 10 Gbaud 16-QAM signal is
generated as the first channel (Ch1) using a laser at wavelength of λ
1
1555 nm and an
IQ modulator. The desired pattern is loaded in an arbitrary waveform generator (AWG).
Initially the constellation of Ch1 is uniformly shaped while it is shaped using FB-PCS after
solving the optimization problem. The output of the modulator is amplified in EDFA1 to 10
mW. The second channel (Ch2) is modulated with a 10 Gbaud 16-QAM using a laser at
wavelength of λ
2
1555.4 nm and another IQ modulator. Each laser has a linewidth of ~1
kHz. Ch2 is uniformly shaped and FB-PCS is not applied to it. Indeed, Ch2 acts as the
neighboring channel in the second simulation scenario. After modulator, it is amplified in
EDFA2 to either 50 mW or 100 mW to show two different levels of constellation distortion.
Ch1 and Ch2 are wavelength multiplexed using a 50/50 coupler and transmitted over 25 km
SMF. After transmission, Ch1 is selected using a bandpass filter (BPF) and sent to the coherent
receiver. A polarization controller is adjusted to maximize the amplitude of the signal at the
receiver. Digital signal processing is employed to compensate chromatic dispersion and to
recover carrier phase using blind phase search algorithm [103].
55

Figure 6.4 (a) Experimental setup, (b) constellation diagram of the first channel (Ch1) before and after
shaping with FB-PCS. PC: polarization controller, EDFA: erbium-doped fiber amplifier, SMF: single-
mode fiber, BPF: band-pass filter, AWG: arbitrary waveform generator, H: entropy.

We record the received signal to perform the optimization. In Figure 6.4(b), the
constellation at the coherent receiver for Ch1 is demonstrated when Ch2 is (i) off, (ii) amplified
to 50 mW, and (iii) amplified to 100 mW. When Ch2 is off, the distortion in Ch1 is almost
uniform. However, when Ch2 is on, the outer constellation points experience more distortion.
The distortion is more severe when Ch2 has higher power. The error matrix is calculated for
the cases (ii) and (iii). Then, the new probability distributions are calculated corresponding to
each of the error matrices. The entropies of the new distributions are 3.51 and 3.59,
corresponding to the shaping obtained from the cases (ii) and (iii), respectively.
After finding the new probability distributions, we map the input bit stream into a
symbol stream using CCDM and load the pattern on Ch1. The constellation diagrams of Ch1
at the receiver are compared in three different shaping: (a) uniform shapings, (b) shaping with
the distribution obtained in case (ii), and (c) shaping with the distribution obtained in case (iii).
In the first column of Figure 6.4(b), it can be seen that when Ch2 is off, the constellation has
λ 2 ~1555.4 nm
λ 1 ~1555 nm
SMF~25 km
Coherent
Receiver
BPF
1 nm
1 nm
EDFA1
Modulator
PC
Load Desirable Pattern
10-Gbaud
(a)
(b)
Ch2 (off) Ch2 (50 mW) Ch2 (100 mW)
Uniform Shaping
H = 4 bits/symbol
SER = 0.006 SER = 0.0544 SER = 0.1663
FB-PCS
(Ch2 = 50 mW)
H = 3.51 bits/symbol
SER = 0.0045 SER = 0.0335 SER = 0.0825
FB-PCS
(Ch2 = 100 mW)
H = 3.59 bits/symbol
SER = 0.005 SER = 0.0252 SER = 0.0928
Modulator
EDFA2
AWG
AWG
56

been shaped, and the outer constellation points are transmitted less frequently. When Ch2 is
on and amplified to 50 mW (second column of Figure 6.4(b)), the SER is reduced from 0.0544
in uniform shaping to 0.0335 and 0.0252 for the shaping obtained in cases (ii) and (iii),
respectively. Furthermore, when Ch2 is amplified to 100 mW (third column of Figure 6.4(b)),
the SER is reduced from 0.1663 in uniform shaping to 0.0825 and 0.0928 for the shaping
obtained in cases (ii) and (iii), respectively. Thus, FB-PCS can also lead to the SER reduction
in a proof-of-concept experiment.

57

Chapter 7 Remotely Powered and Controlled
Optical Switching and Monitoring Based on
Laser-Delivered Power and Control Signals
7.1 Introduction
Optical routing and networking typically make use of optical switches at sites
located at various places around the network [104]. However, many locations can be
vulnerable to failure due to intentional or unintentional degradations. One key
operational challenge is the potential for power to be interrupted at the switching site
[105]. If there is no local power, the data passing through the switching node could be
degraded, lost, or routed to the wrong output port [106].
One challenge for such switching that lacks local power is that the switch itself
typically requires a bias voltage and a control signal [107]. One example of an
architecture that allows for an optical switching node that has no local power is to
control the switch from a remote location (e.g., a transmitting node). One approach for
remotely controlled and powered switching is the ability to power the electrical pins
of an optical switch from the output of a series of photodiodes (PDs) that are driven
from a remote laser beam [108-110].
However, another key challenge of a switch that lacks local power is monitoring
the state of the switch, especially since changes might occur due to bias drifts that are
common in typical Mach-Zehnder interferometers (MZIs) (e.g., caused by thermal
variations) [111,112]. Although the remote transmitting site that controls the switch
may “think” that the switch is functioning properly, the actual switch may not be at
the optimal bias point for the “cross” or “bar” states. Specifically, a remotely-
controlled switch might benefit from an architecture that enables: (i) the remote site to
monitor the state of the switch and correct for any drifts by varying a laser bias signal
[113], and (ii) the switch itself to have a feedback loop that can locally stabilize the
operation and correct for bias drifts [113].
58

In this chapter, we experimentally demonstrate remotely powered and controlled
optical switching and monitoring based on laser delivered power and control signal
[114]. In this technique, instead of using local electrical power supply, electrical
voltage for the control and bias pins of the MZI-based optical switch is generated at
the remote location by transmitting optical power from the transmitter and using
optical-to-electrical (OE) conversion at the switch location. The optical switch
functioning using optical power supply is characterized and compared with the case
of using local electrical power supply. The switching function using optical power
supply is demonstrated when 1-Gb/s on-off keying (OOK) data transmitted through
the switch and controlled with 1-MHz control signal. Furthermore, two optical carriers
as the pilot tones can be transmitted along with the signal through the switch where
each tone is assigned to each output ports. Subsequently, these tones can be sent back
through the fiber to be monitored at the transmitter. By comparing the monitoring
tones, we can find out the switch state (i.e. bar or cross) and if there is any bias drift it
can be compensated by tuning the transmitted optical power. A 40-Gb/s quadrature
phase-shift keying (QPSK) is transmitted through the switch in bar/cross state to show
the impact of bias drift in each state.
7.2 Concept
The concept of remotely powered and controlled optical switching and
monitoring is shown in Figure 7.1. Data signal at 𝜆 𝑆 , control signal at 𝜆 𝐶 , optical power
at 𝜆 𝐵 , and monitoring tones at 𝜆 𝑀 1
and 𝜆 𝑀 2
are combined using a wavelength
multiplexer into a single mode fiber (SMF) to be transmitted to a remote location. A
wavelength demultiplexer can be used to separate wavelengths at the remote site.
Signal and monitoring tones are coupled into the same fiber and sent into the input
port of the MZI-based optical switch. The input of the switch can be directed to either
of the two output ports depending on the control signal. OE conversion of the control
signal can be done using photodiodes. Subsequently, the electrical signal drives the
control pins of the switch. A MZI-based switch also requires a bias voltage to adjust
transmission characteristics of it. Since the purpose of this work is to not use local
59

electrical supply, the optical power is transmitted at 𝜆 𝐵 and OE converted for the
switch bias pins. The MZI-based switch may experience bias drift which can be
monitored using the transmitted monitoring pilot tones and adjusted by changing the
transmitted optical power. Moreover, by comparing the monitoring tones at the two
output ports of the switch, the switch state (bar/cross) can be observed.

Figure 7.1 Concept of remotely powered and controlled optical switching and monitoring. SMF: single
mode fiber; O/E: optical to electrical conversion; MZI: Mach–Zehnder interferometer.
7.3 Characterization
Figure 7.2 shows characterization of our 1×2 MZI-switch and OE conversion
using series of PDs for control and bias. Continuous wave (CW) laser is amplified and
fed into 1 to 16 optical splitter which is connected to 16 PDs which are connected in
series. By feeding the optical power to the PDs, they operate in photovoltaic mode and
generate photocurrent that can be turned into electrical voltage using a resistor. Figure
7.2(b) shows the generated voltage at the bias port by inserting three different resistor
values (i.e. 3 KΩ, 4.7 KΩ and 7.5 KΩ) in parallel with the switch bias input. As
expected, higher resistor values generate higher voltage. Also, increasing the optical
power increases the generated voltage; however, it cannot be more than ~8 volt
because of the cut off voltage of the PDs which is ~0.5 volt for each of the InGaAs
PDs. In our experiment, we use 7.5 KΩ resistor in parallel with bias input of the switch
which can provide voltage range of ~ 2 – 8 volt with 10 – 60 mW optical power.
60

Similarly, OE conversion can be used for control port, but the control port of our
MZI-switch is terminated with a 50 Ω resistor which means there is not much of
flexibility by adding resistors in parallel with it. However, we change the number of
PDs in series to demonstrate the converted electrical voltage, current and power at
control port in Figure 7.2(c), (d), and (e), respectively. As shown in Figure 7.2(d), PDs
saturated at high incident light power due to the depletion of available electron-hole
pairs [115]. In Figure 7.2(f), we compare the generated voltage and current using PDs
with the voltage and current that can be applied by exploiting a DC power supply. This
comparison shows that by having more PDs in series we can get closer to the case of
using local DC supply.
The transmission characteristic of the two output ports of the MZI-switch is
demonstrated in Figure 7.2(g-h) for different bias voltage that is generated by optical
power and PDs. By comparing Figure 7.2(g) and (h), the impact of the bias voltage on
characteristic of the switch can be observed. Therefore, we can adjust the transmission
characteristic by changing the transmitted optical power for the bias port in case any
bias drift happened.

Figure 7.2 Characterization of optical to electrical (OE) conversion and Mach-Zehnder interferometer
(MZI) based switch. (a) schematic of optical switch connected with photodiodes (PDs), (b) OE
conversion of 16 PDs connected to bias port of the switch with different resistor values connected to it,
electrical (c) voltage, (d) current, and (e) power generated from 8, 12, or 16 PDs connected to control
port of the optical switch, (f) comparison of the current drawn by control port of the switch when DC
power supply used (no current limit) and PDs used. (g) and (h) the switch characterization when optical
power is sent to 16-PDs for bias and control ports.

61

7.4 Experimental Setup and Results
The experimental setup is shown in Figure 7.3. Six lasers are used for optical
bias power transmission, control signal, data signal, and monitoring. Two lasers on
wavelengths of λ
𝐵 1
1547.72 nm and λ
𝐵 2
1548.51 nm are amplified in erbium-
doped fiber amplifiers (EDFAs) to provide optical power supply for the switch bias
and control ports, respectively. The output power can be adjusted to determine the bias
voltage at remote location. Switching control signal is intensity modulated on another
laser with wavelength of λ
𝐶 1550.12 nm. We generate a data channel using either
1 Gb/s OOK or 40 Gb/s QPSK transmitter at the wavelength of λ
𝑆 1551.72 nm. If
we want to monitor the optical switch state, two pilot tones at λ
𝑀 1
1552.52 nm and
λ
𝑀 2
1553.33 nm can be transmitted. In our experiment, we used a 8×1 wavelength
multiplexer that multiplex DWDM ITU channels 30-37 into a 8-km single mode fiber
(SMF). Two optical circulators are used to separate upstream and downstream waves
in the bidirectional link.
At the remote location, a 1×8 wavelength demultiplexer is used to separate six
wavelengths. Data signal and monitoring tones are combined and sent into the input
port of the optical switch. The input will be directed to either port-1 or port-2
depending on the control signal. The control signal at λ
𝐶 is coupled into an InGaAs
PD which operates in photoconductive mode. In order to operate this PD in
photoconductive mode, the optical power at λ
𝐵 2
is fed into an array of 16 PDs to serve
as the voltage supply for reversely biasing the photoconductive PD. The optical power
at λ
𝐵 1
is fed into another array of 16 PDs which generate the voltage for bias port of
the optical switch. The characterization of the switch and array of PDs are given at
Figure 7.2. At the output ports, the data signal is filtered and transmitted to the receiver
while the monitoring tones are filtered and sent back to the transmitter for comparison
and adjustment of the bias power.
62

Figure 7.3 Experimental setup of remotely controlled and powered optical switching and monitoring.
Six lasers are used for bias (B1 and B2), monitoring (M1 and M2), data signal and control signal. The
optical spectrum of the multiplexed channels into a single fiber is shown in inset. PC: polarization
controller, EDFA: erbium-doped fiber amplifier, IM: intensity modulator, PM: phase modulator, Mux:
multiplexer, Demux: de-multiplexer, SMF: single mode fiber, MZI: Mach-Zehnder interferometer.

In order to examine the quality of the converted control signal with optical power
supply, an unmodulated CW laser is sent into the switch. The received waveform at
the output ports are shown in Figure 7.4 which are captured in a sampling oscilloscope.
For the control signal, we generate the sequence of alternating 0s and 1s with
frequency of 1 MHz and modulate using an intensity modulator. At the remote location,
the control signal is converted to electrical signal and fed into the control port of the
switch. In order to evaluate the quality of the OE converted control signal, we consider
three cases for the power supply: (i) using a local electrical DC power supply, (ii)
using 16 PDs, and (iii) using 12 PDs. As expected from characterization on Figure
7.2(f), using DC supply leads to higher peak-to-peak amplitude compare with using
PDs and 16-PDs outperforms 12-PDs. Furthermore, we observe the rise time is ~50 ns
and higher overshoot at the switching time in the case of using PDs. This is due to the
fact that the PDs in photovoltaic mode has higher internal capacitance which effects
time constant in the RC circuit.
63

Figure 7.4 Captured waveform at two output ports of the switch when the input is an unmodulated CW
laser and the control signal OE converted using electrical DC power supply and photodiodes.

Figure 7.5 shows the switching function when the 1 Gb/s OOK data is
transmitted. The transmitted data channel is shown in Figure 7.5(a), where each frame
contains 450 data bits and 50 empty slots as guard band for switching. Five frames are
shown in Figure 7.5(a) that is aligned with the switching control signal of 01010 as
shown in Figure 7.5(b). In Figure 7.5(c-d), we can observe the data channel is directed
to port 1 when the control is 1 and it is directed to port 2 when the control is 0. Each
of the output ports shows extension ratio of more than 10 dB.
64

Figure 7.5 (a) 1 Gb/s OOK input data channel with 450 data bits and 50 empty slots as guard band for
switching, (b) control signal. (c) and (d) Switch output when it is driven by OE converted control signal
and bias. The data channel is routed to output port 1 when the control intensity is “1” and to output port
2 when the control intensity is “0”.

In order to monitor the switching state, two laser tones (M1 and M2) are
transmitted through SMF into the optical switch at distant location. Each of the
monitoring tones corresponds to one of the output ports. The monitoring tones at λ
𝑀 1

and λ
𝑀 2
can be filtered in bandpass filters and sent back through the same SMF to the
transmitter. Therefore, by comparing the power of M1 and M2 at the transmitter, we
can determine if the switch is in bar state (input is routed to port-1) or cross state (input
is routed to port-2). This comparison can be done by calculation M1/M2 ratio where
if the ratio is greater than 1 the switch is in bar state, otherwise it is on cross state (see
Figure 7.6(a)). Moreover, the switch operates in optimal bias point when there is
highest extension ratio between two output ports, i.e., the ratio M1/M2 is maximum or
minimum in bar or cross states, respectively.
In Figure 7.6(b), we show that the output of two ports are almost constant when
the wavelength of the input signal varies in a wide range. Therefore, the wavelength
separation between M1, M2 and data signal does not impact on the switch state
monitoring. However, if monitoring tones and data signal wavelength separation result
65

in different response of the switch, they should be calibrated to enable proper
monitoring.
Figure 7.6(c) shows that there is a limit for increasing the optical transmitted
power into the SMF fiber. By increasing the optical power higher than a certain limit,
most of the power is reflected back due to SMF nonlinearities and backscattering.
Therefore, the power of the monitoring tones at the transmitter should be in the linear
region in order to perform proper reading of the received tones. The backscattering
effect of the fiber can be reduced by phase modulation of the CW tones.
The measured power of M1 and M2 in bar or cross states are shown in Figure
7.6(d) that varies versus the optical power sent into the PDs connected to bias port of
the switch. Moreover, the ratio of M1/M2 is demonstrated in Figure 7.6(e). When the
optical power to the bias port is smaller than ~10 mW the ratio is greater than 1 in bar
state whereas for higher bias power the ratio is less than 1. Therefore, the state of the
switch can be determined. Furthermore, the switch can be stabilized in case of bias
drift. From Figure 7.6(e), the M1/M2 is maximum or minimum when the optical power
to bias port of the switch is ~34 mW. Therefore, if the value of M1/M2 changes, we
can realize the bias drift and compensate it by changing the optical power at λ
𝐵 1
.
In order to compare the quality of the signal at two output ports, we generate a
40-Gb/s QPSK signal by driving an IQ modulator with the pseudo-random bit
sequence (PRBS) 2
31
-1 to modulate the laser at λ
𝑆 . In bar state, the signal should be
directed to port-1, therefore, the quality of the signal in port-1 is better than port-2.
Similarly, in cross state, the signal is directed to port-2 and the quality of the signal in
port-2 should be better. If the bias of the switch sets at the optimal point, there is much
larger difference in error vector magnitudes (EVMs) of the QPSK signal at two output
ports. For example, in bar state, if the optical power to 16-PDs connected to bias port
is 34 mW the EVM in port-1 and port-2 are 13.7% and 35.3%, respectively; however,
if the optical power is 20 mW, the EVM in port-1 and port-2 are 13.7% and 21.3%,
respectively. The switch state can be changed to cross state by increasing the optical
power to the control port and similar conclusion can be made for the cross state.
66

A common issue of the optical switches is thermal drift that can normally be
handled using a temperature controller to stabilize the temperature. However, we did
not use any temperature controller in this paper, because we do not want to have any
local electrical power supply for temperature controller. One could also address this
issue by remotely powering a thermoelectric cooler and monitoring it.

Figure 7.5 (a) Comparison of two monitoring tones (i.e. M1 and M2) at the transmitter when the switch
at distance location in in bar or cross states, (b) optical switch response at different wavelengths, (c)
67

optical power saturation at optical fiber due to nonlinearities, (d) power measurement of monitoring
tones at bar/cross state when optical power to bias port varies, (e) the ratio of M1/M2 when optical
power to bias port varies, (f) constellation diagram of 40 Gb/s QPSK signal at switch two output ports
with optimal and suboptimal bias points when the switch is in bar/cross state. EVM: error vector
magnitude.

68

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Abstract (if available)

Abstract One of the key functions that can be implemented using optical signal processing is modulation format conversion. Flexible networks should be able to manage heterogeneous channels and various subnetworks with different properties such as different modulation formats, resource allocation, quality of service, etc., depending on their applications. Consequently, future flexible all-optical networks will contain various subnetworks that can speak different languages. In this context, language translators can be used to connect these subnetworks together. In other words, using optical gateways at network access points could be beneficial to perform modulation format conversion in an all-optical fashion, which brings the benefits of avoiding inefficient OEO conversion and enhancing network flexibility, tunability, and spectral efficiency. In this dissertation, we employ optical signal processing to implement some of these modulation format conversions including aggregation (combination of multiple lower order modulation formats to a single higher order one), de-aggregation (reverse function of aggregation), and phase modulation to amplitude modulation format conversion. Furthermore, manipulation of a specific modulation format is demonstrated by optimizing the probability distribution of the transmitting symbols. Finally, the feasibility of remote optical signal processing without using local electrical power supply is investigated by demonstrating a remotely controlled and powered optical switching and monitoring.

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Asset Metadata

Creator Fallahpour, Ahmad (author)

Core Title Reconfigurable high speed optical signal processing for optical communication and modulation format manipulation

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2021-08

Publication Date 07/12/2021

Defense Date 05/05/2021

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

Tag OAI-PMH Harvest,optical communication,optical signal processing

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Willner, Alan (committee chair), Haas, Stephan (committee member), Habif, Jonathan (committee member)

Creator Email fallahpo@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC16255860

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

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