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Microresonator-based Kerr frequency comb for high-speed optical communications and signal processing
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Microresonator-based Kerr frequency comb for high-speed optical communications and signal processing
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Content
MICRORESONATOR-BASED KERR FREQUENCY COMB FOR HIGH-SPEED
OPTICAL COMMUNICATIONS AND SIGNAL PROCESSING
by
Peicheng Liao
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
May 2020
Copyright 2020 Peicheng Liao
ii
Dedication
This dissertation is dedicated to my parents, Huaying Luo and Pingan Liao,
for their love and endless support,
and to my siblings, Xiaoqin, Xiaoyan and Peizhou Liao,
for their patience and encouragement.
iii
Acknowledgements
The journey towards my PhD is long, and I can never accomplish it without the
help of many people. I am sincerely grateful for the support and encouragement that
help me grow and shape me into a professional researcher today.
First of all, I would like to deeply thank my thesis advisor, Professor Alan E.
Willner, for his enthusiastic support and guidance. His wisdom, sense of responsibility
and serious attitude have always enlightened me in doing good research and being a
better person. It is one of my most precious experiences to work with him at Optics
Communications Laboratory (OCLab). In addition, I would like to express my
gratitude to Professor Moshe Tur from Tel-Avis University in Israel. I have learned so
much from his broad knowledge and extensive experience. In particular, he made me
realize the importance of optimism and lifelong learning. I would also like to thank
Professor Andrea M. Armani and Professor Wei Wu for severing on my dissertation.
I would also like to acknowledge the continuous support and advice from our
collaborators at EPFL. Specifically, I want to thank Professor Tobias J. Kippenberg,
Dr. Martin Pfeiffer, Maxim Karpov, and Arne Kordts. Also, I would like to thank Dr.
Andrey Matsko from OEwaves Inc., Dr. Youichi Akasaka from Fujitsu, Professor
Kent Choquette and Dave Harshil from UIUC for helpful discussions.
My grateful thanks are also extended to my colleagues Dr. Lin Zhang, Dr.
Changjing Bao, and Kaiheng Zou for their insightful discussions and collaborations.
Moreover, I am grateful for other current and past OCLab members, Dr. Bishara
Shamee, Dr. Hao Huang, Dr. Yan Yan, Dr. Yongxiong Ren, Dr. Morteza Ziyadi, Dr.
iv
Guodong Xie, Dr. Ahmed Almaiman, Dr. Amirhossein Mohajerin-Ariaei, Dr. Yinwen
Cao, Dr. Long Li, Zhe Zhao, Zhe Wang, Cong Liu, Ahmad Fallahpour, Fatemeh
Alishahi, Kai Pang, Haoqian Song, Runzhou Zhang, Hao Song, Huibin Zhou, Karapet
Manukyan, Nanzhe Hu, Amir Minoofar, and Xinzhou Su for all their helpful
discussions. I also want to appreciate the tremendous support from USC staff,
particularly, Ms. Diane Demetras, Ms. Corine Wong, Ms. Gerrielyn Ramos, Ms. Susan
Wiedem, and Mr. Theodore Low.
Finally, I want to thank my warm and loving family for their precious help and
support in my life.
v
Table of Contents
Dedication ................................................................................................................... ii
Acknowledgements .................................................................................................... iii
List of Figures ........................................................................................................... vii
Abstract .................................................................................................................. xii
Chapter 1 Introduction .............................................................................................. 1
1.1 Microresonator-based Optical Kerr Frequency Comb ................................... 1
1.2 High-Speed Optical Communications ............................................................ 4
1.3 Advanced Optical Signal Processing .............................................................. 6
1.4 Thesis Outline ................................................................................................. 8
Chapter 2 Dependence of Microresonator-based Kerr Comb on the Pump
Linewidth ................................................................................................ 10
2.1 Introduction .................................................................................................. 10
2.2 Linewidth Broadening and Characterization ................................................ 11
2.3 Dependence of Kerr Comb on the Pump Linewidth .................................... 13
2.4 Coherent System Performance of Kerr Comb Lines .................................... 16
2.5 Conclusion .................................................................................................... 17
Chapter 3 Effect of EDFA-induced Pump Noise on Soliton Kerr Combs for
64-QAM Transmission .......................................................................... 19
3.1 Introduction .................................................................................................. 19
3.2 Effect of EDFA-induced Pump Noise on the Comb Line Noise .................. 20
3.3 Transmission of 64-QAM Using a Soliton Kerr Comb ................................ 25
3.4 Conclusion .................................................................................................... 27
Chapter 4 Generation of Multiple Kerr Combs from Another Remote Kerr
Comb ....................................................................................................... 28
4.1 Introduction .................................................................................................. 28
4.2 Concept of Multiple Kerr Comb Generation ................................................ 29
4.3 Multiple Kerr Comb Generation Using Different Master Comb Lines ........ 30
4.4 Characterization of the Master and Multiple Slave Combs .......................... 33
4.5 Discussion and Conclusion ........................................................................... 38
Chapter 5 Pump-linewidth-tolerant Wavelength Multicasting Using Soliton
Kerr Frequency Comb ........................................................................... 40
5.1 Introduction .................................................................................................. 40
5.2 Concept of Pump-linewidth-tolerant Wavelength Multicasting based on
Coherent Kerr Comb .................................................................................... 41
vi
5.3 Demonstration of Pump-linewidth-tolerant Wavelength Multicasting ........ 42
5.4 Conclusion .................................................................................................... 48
Chapter 6 Scalable and Reconfigurable Optical Tapped-delay-line for
Multichannel Optical Signal Processing with a Kerr Frequency
Comb ....................................................................................................... 50
6.1 Introduction .................................................................................................. 50
6.2 Concept of Optical TDL for Multichannel Signal Processing ..................... 51
6.3 Demonstration of Optical TDL for Equalization and Correlation ................ 53
6.4 Discussion and Conclusion ........................................................................... 57
Chapter 7 Deterministic Generation of a Controllable Breathing Soliton by
a Second Pump or Pump Modulation .................................................. 59
7.1 Introduction .................................................................................................. 59
7.2 Deterministic Generation of a Controllable Breathing Soliton .................... 60
7.3 Experimental Results .................................................................................... 61
7.4 Simulation Results ........................................................................................ 66
7.5 Conclusion .................................................................................................... 69
Chapter 8 Dual Microcomb Source Using a Controllable Breathing Soliton .... 70
8.1 Introduction .................................................................................................. 70
8.2 Concept of Dual Micro-Comb Source Utilizing a Controllable
Breathing Soliton .......................................................................................... 70
8.3 Experimental Results .................................................................................... 71
8.4 Discussion and Conclusion ........................................................................... 74
References ................................................................................................................. 76
vii
List of Figures
Figure 1.1 The spectrum of an optical frequency comb. ................................................. 2
Figure 1.2 The generation of Kerr frequency comb in a microresonator. ....................... 4
Figure 1.3 Typical optical communication systems exploiting wavelength-division
multiplexing. Tx: transmitter; PC: polarization controller. ................................... 4
Figure 1.4 The waveform of different modulation formats and their corresponding
signal constellations. ............................................................................................. 5
Figure 1.5 A general structure of coherent detection with the post digital signal
processing. ............................................................................................................. 6
Figure 1.6 Different physical dimensions of optical carriers for signal processing
through nonlinear wave mixing. ............................................................................ 7
Figure 1.7 Sum and difference frequency generation in a PPLN waveguide. ................. 7
Figure 2.1 Experimental setup for generating the frequency comb and characterizing
the corresponding linewidth. ECDL: external cavity diode laser; BPF: band
pass filter; LF: lensed fiber; FBG: fiber Bragg grating; ESA: Electrical
spectrum analyzer; AOM: acousto-optic modulator; .......................................... 12
Figure 2.2 (a) Schematic setup of the pump linewidth broadening using an AWG
and comb linewidth characterization. AWG: arbitrary waveform generator;
(b) and (c) Linewidth measurement of the pump without broadening and with
a broaden linewidth of 500 kHz. ......................................................................... 13
Figure 2.3 (a), (b) and (c) The optical spectra and the corresponding linewidth (LW)
measurements of the comb line at the wavelength of 1534.54 nm without
broadening the pump. The linewidths of the primary and low-phase-noise
combs are close to that of the pump. ................................................................... 14
Figure 2.4 (a) The comb line linewidth as a function of pump linewidth in the
primary and low-phase-noise states. The inset is the optical spectrum of the
low-phase-noise comb at C-band. (b) The RF beat note of the low-phase-noise
comb with various pump linewidths (LWs). The single narrow peaks indicate
the comb maintains low phase noise. .................................................................. 15
Figure 2.5 (a) Experimental setup for demonstrating QPSK signal transmission with
Kerr frequency combs. (b) BER as a function of OSNR for the pump and
primary comb with different pump linewidths. The inset is the constellation
of the QPSK signal with a linewidth of 10 MHz; (c) BER as a function of
viii
OSNR for the pump and the low-phase-noise comb. The inset is the
constellation of the QPSK signal with a linewidth of 2 MHz. ............................ 17
Figure 3.1 (a) Experimental setup for cavity-soliton Kerr comb generation and
characterization. (b) Optical spectrum of the single-soliton comb. The left and
right insets show a microscope image of the integrated microresonator and
the RF spectrum of the beat note, respectively. (c) Autocorrelation trace of
the single-soliton pulse. (d) Optical spectrum of the single-soliton comb
across C-band. (e) Optical spectrum of Kerr combs in the three-soliton states.
............................................................................................................................. 21
Figure 3.2 (a) Optical spectrum (Res: 100 MHz) of Kerr comb in the breather soliton
state (inset: comb line at ~1550 nm). (b) Optical spectrum of a stable soliton
Kerr comb (inset: ~1550 nm). (c) Pump-induced noise level, comb line power
and (d) comb optical OCNR at different wavelengths or three pump OCNRs
(inset) for the single-soliton comb. (e) Comb OCNR under different
bandwidths of the TOF. (f) Comb OCNR at different pump OCNRs for a
three-soliton crystal. ............................................................................................ 24
Figure 3.3 (a) The setup for linewidth measurement using the self-heterodyne
method. (b) Comb linewidths at two pump OCNRs. .......................................... 25
Figure 3.4 (a) Experimental setup for four-channel 20 Gbaud 64-QAM data
transmission using single-soliton Kerr comb. (b) Optical spectrum of the
received modulated signals. (c) Comb OCNR and the EVM versus the pump
OCNR (before modulation) for channels 2 and 3. (d) The constellation
diagrams of four signals with 52-dB pump OCNR. ............................................ 26
Figure 4.1 Concept of multiple Kerr comb generation using different lines from
another Kerr comb for optical communication systems. ..................................... 30
Figure 4.2 Experimental setup for demonstrating the generation of multiple Kerr
combs from a remote Kerr comb. ........................................................................ 32
Figure 4.3 (a-d) Spectra of the master and slave combs. The left and right insets of
(a) are the optical microscope image of the microresonator and the
autocorrelation trace of the soliton pulse. The inset in (b) shows the
corresponding RF beat note. ................................................................................ 33
Figure 4.4 (a) Spectra of the master and slave comb 1 (The comb lines in the box
are selected for beat note measurement). (b) Beat notes of the master and slave
comb lines after 50-km SMF transmission. (c) is the zoom-in spectrum of the
10
th
RF beat note. ................................................................................................. 34
ix
Figure 4.5 (a) The linewidths of both the master and slave comb 1 for back-to-back
(B2B) and 25-km fiber transmission. (b) The received pump power and pump
OSNR in the second microresonator at different transmission losses. ................ 36
Figure 4.6 (a) and (b) are the RF spectrum and the zoom-in of the 10
th
beat note of
the two combs with the slave comb generated by an independent pump laser.
(c) The frequency error at different counts of the regenerated comb line and
independent unstabilized laser separately serving as the LO. ............................. 37
Figure 5.1 The concept of pump-linewidth-tolerant wavelength multicasting based
on coherent Kerr frequency comb. ...................................................................... 42
Figure 5.2 Experimental setup for pump-linewidth-tolerant wavelength multicasting
based on coherent Kerr frequency comb. ............................................................ 43
Figure 5.3 (a) The optical spectrum of single-soliton Kerr combs and (b) its spectrum
across C-band. (c) The autocorrelation trace of a single-soliton pulse. The
optical spectrum at the PPLN output when (d) eight Kerr comb lines are used
or when (e) the free-running ECL is used to generate multicast signals or
converted signal. .................................................................................................. 44
Figure 5.4 (a) and (b) The experimentally measured normalized power spectrum
density (PSD) of the signal laser and multicast signal 1. (c) The linewidth
(LW) of multicast signal 1 almost stay unchanged at different comb pump
linewidths. (d) The normalized PSD of the converted signal. ............................. 45
Figure 5.5 (a) The EVM performance of eight multicast signals with (w/) and
without (w/o) Kalman filtering (KF) algorithm when coherent Kerr combs are
used as pumps. The EVM performance of the multicast signal 1 and converted
signal 1 at different comb pump linewidths (b) with (w/) and (c) without (w/o)
the KF algorithm in the receiver. ......................................................................... 47
Figure 5.6. System performance of the original signal and multicast copies (a) The
constellations as well as the measured EVM and BER. (b) EVM and BER as
a function of the OSNR. ...................................................................................... 48
Figure 6.1(a) Concept of an optical TDL for independent multichannel signal
processing using (a) k stages and (b) two stages to generate k taps. QPM:
quasi-phase matching; SFG: sum frequency generation; DFG: difference
frequency generation. .......................................................................................... 52
Figure 6.2 Experimental setup for multichannel signal processing using an optical
TDL. AWG: arbitrary waveform generator; BPG: bit pattern generator; FBG:
fiber Bragg grating; TOF: tunable optical filter; DCF: dispersion
compensation fiber. ............................................................................................. 54
x
Figure 6.3 (a) Optical spectrum of a single-soliton Kerr comb. The inset is the
autocorrelation trace. (b) The output spectrum of PPLN 1. (c, d) The spectra
of PPLN 2 output with two or three taps. Eq.: equalization; Cor.: correlation. .. 55
Figure 6.4 (a1-a4) show the in-phase and quadrature (IQ) constellation diagrams of
Ch1 input signal and the output Ch1 signals after the two- or three-tap
equalization. ........................................................................................................ 56
Figure 6.5 (a) The constellation diagrams of Ch2 input symbols. (b) Two-tap
correlation outputs and the correlation peaks corresponding to matched
patterns [A B]. (c, d) Three-tap correlation outputs and the correlation peaks
corresponding to matched patterns [A B C] and [A B D]. .................................. 57
Figure 7.1 The two approaches to generate a controllable breathing soliton by
injecting a second pump or modulating the CW pump. CW: continuous-wave;
Mod.: modulation. ............................................................................................... 60
Figure 7.2 (a) Experimental setup to demonstrate the deterministic generation of a
breathing soliton by injecting a second pump. (b) Optical spectrum of the
single soliton along with Pump II. (c) Zoom-in spectrum of Pump II located
at the soliton resonance of the comb line at 1543.85 nm. ................................... 62
Figure 7.3 (a) Zoom-in spectra of comb lines at 1540.81 and 1559.28 nm from the
high-res. OSA. (b) RF spectrum of the breathing soliton. (c) 1
st
sideband
power (labeled in Figure 7.3(a)) as a function of Pump II power. (d, e) The
spectrum of the comb line (1540.81 nm) under period doubling and the
corresponding RF spectrum. ................................................................................ 63
Figure 7.4 (a) Experimental setup for the deterministic generation of a breathing
soliton by modulating the CW pump. (b, c) The optical spectra of the
breathing soliton and the modulated pump. (d) The zoom-in spectrum of the
comb line at 1542.14 nm and its sidebands from the high-res. OSA. (e) The
spectrum of the comb line at 1542.14 nm under period doubling. (f) The RF
spectrum of the breathing soliton. ....................................................................... 64
Figure 7.5 (a) and (b) are the power of 1
st
sideband (labeled in Figure 7.4(d)) as a
function of RF signal power and frequency (freq.), respectively. (c) The
power evolution for different comb line groups located at different center
wavelengths. ........................................................................................................ 65
Figure 7.6 Simulated dynamics of the breathing soliton. (a) The narrowest (red) and
widest (blue) spectra of the breathing soliton. (b) The spectrum of the comb
line at 1579.04 nm in the breathing soliton. (c) The spectral dynamics,
intracavity peak power, and pulse width of the breathing soliton. ...................... 67
xi
Figure 7.7 (a) and (b) The effects of the RF signal power and frequency on the pulse
peak power, respectively. (c) The power evolution for different comb line
groups. ................................................................................................................. 68
Figure 8.1 Dual micro-comb source utilizing a controllable breathing soliton with
an increased resolution. f s: RF modulation frequency; Δp: pump frequency
difference; Δf rep1, Δf rep2, and Δf r: repetition rates of comb 1 and 2, and their
difference. ............................................................................................................ 71
Figure 8.2 Experimental setup to demonstrate on-chip dual-comb source using a
controllable breathing and a stable soliton. ......................................................... 72
Figure 8.3 (a) A single RF comb generated by heterodyning two stable soliton
combs. (b) Five RF combs generated by heterodyning a breathing soliton and
a stable soliton. (c) Optical spectra of the signal and reference paths with one
soliton comb in the breathing state. (d) Waveshaper filtering shape measured
by the dual-comb source without (w/o) and with (w/) use of the breathing
soliton. ................................................................................................................. 74
xii
Abstract
Optical frequency combs, which comprise a multitude of equidistant spectral
lines in their spectrum, have become an indispensable tool in optical and photonics
technology. They have been widely used in optical metrology, spectroscopy, remote
sensing, arbitrary waveform generation and telecommunication due to its broad
spectrum of the precisely controlled optical carriers. In the past decade, a noticeable
development in frequency comb technology is the use of integrated microring
resonators to produce combs based on Kerr nonlinearity. Such Kerr frequency combs
can be fabricated with a small footprint enabling large comb line spacings over broad
optical bandwidths. Depending on the pump power and wavelength, the formation of
Kerr combs consists of several dynamic regimes, which exhibit different degrees of
coherence as well as distinct noise properties. Kerr combs in a low-noise state are
promising to enhance many applications including optical frequency synthesis,
spectroscopy, optical communications and signal processing.
This thesis will study the generation of optical Kerr frequency combs and explore
their use as coherent light sources for high-speed optical communications and as pump
lasers for advanced optical signal processing functions. In the first part, the
applications of the Kerr comb in optical communication systems are experimentally
investigated and demonstrated, which include (i) the generation of Kerr combs as well
as their characterization in terms of the comb line linewidth and noise; (ii) the effect
of erbium-doped fiber amplifier (EDFA) induced pump noise on soliton Kerr
frequency comb for 64-quadrature amplitude modulation (QAM) transmission; (iii)
the generation of multiple Kerr combs from another remote Kerr comb and their
potential applications as mutually coherent light sources and local oscillators in inter-
datacenter communications.
The experimental demonstrations of different optical signal processing functions
using Kerr frequency comb are covered in the second part of the dissertation. There
are mainly two topics. One is the proposed pump-linewidth-tolerant wavelength
xiii
multicasting using mutually coherent Kerr comb lines, and the other is a scalable
optical tapped-delay-line (TDL) for simultaneous and independent processing on
multiple data channels using Kerr frequency comb and nonlinear wave mixing. In
addition, two deterministic approaches are numerically and experimentally
demonstrated to generate a controllable breathing soliton and its potential application
in dual-comb source is briefly discussed.
1
Chapter 1 Introduction
Optical frequency combs, which comprise a series of equidistant spectral lines
in their spectrum, have become an indispensable tool in optical and photonics
technology [1, 2]. They have been used as optical “rulers” for high-precision optical
metrology and frequency synthesis since the first demonstration in 2000 [3, 4]. Beyond
the usage of metrology and synthesis, as optical frequency combs exhibit a broad
spectrum of the precisely controlled optical carriers, their applications have been
dramatically extended to include spectroscopy [5], remote sensing [6], arbitrary
waveform generation [7], optical communications and signal processing [8]. These
various applications have led to increasing requirements on the performance of optical
frequency combs. For example, it would be desirable to have a large repetition rate
above 10 GHz in a compact device for many uses. In the past decade, a noticeable
development in frequency comb technology is the use of integrated microring
resonators to produce combs based on Kerr nonlinearity [9]. Such frequency combs
are typically termed as Kerr frequency comb or microcomb. They can be fabricated
with a small footprint enabling high repetition rates over broad optical bandwidths.
These new features are promising to enhance many potential applications including
optical frequency synthesis [10], spectroscopy [11], telecommunications [12, 13], and
optical signal processing [14].
This chapter will first introduce the basic concept of the optical Kerr frequency
comb generated in a microresonator. Then, a brief overview of high-speed optical
communications and advanced optical signal processing will be presented. Finally, the
outline of the rest of the dissertation will be explained.
1.1 Microresonator-based Optical Kerr Frequency Comb
An optical frequency comb is a light source that consists of a series of equidistant
frequency lines in their spectrum [15]. Each of these lines occupying a frequency f is
similar to a laser source. A bunch of these equally spaced lines form a “comb” shape,
2
and each of them becomes a tooth as shown in Figure 1.1, which is a typical
representation of a frequency comb in the wavelength domain. The wavelength of any
tooth can be obtained by 𝜆 𝑛 =(𝑛 −1)×𝜆 𝑠 +𝜆 1
, where m is an integer, λs is the tooth
spacing, and λ1 is the wavelength of the first tooth.
Figure 1.1 The spectrum of an optical frequency comb.
There are different mechanisms to generate optical frequency combs, such as
mode-locking and electro-optical modulation [15, 16]. Recently, Kerr frequency comb
has gained significant interest in frequency comb technology [9, 17, 18]. Kerr comb is
based on the optical microresonator, which is a high Q cavity with a small mode
volume. Such microresonators have been made from different materials with a Kerr
nonlinearity and low dispersion in various structures. Kerr comb is first demonstrated
with a 500-nm span around 1550 nm in a Silica toroid microcavity [19]. They are able
to achieve a high Q factor over 10
8
owing to the low absorption loss of Silica. Other
whispering gallery mode (WGM) resonators (e.g., microdisks and microspheres) with
comparable Q factors are also used as the platforms for Kerr comb generation [20, 21].
Particularly, Kerr combs have been produced in more compact integrated
microresonators made of silicon nitride (Si3N4) [22, 23]. Although the optical Q factor
is much lower (~10
6
) than that of silica resonator, this approach can allow for chip-
scale integration of the fabricated devices. Silicon as the foundation of integrated
photonics can be another platform for comb generation [24]. However, because of the
strong two-photon absorption near 1550, efficient comb generation in silicon is only
achieved in mid-infrared wavelength range. Besides, there are other platforms such as
Power
λ
s
λ
n
= (n-1)λ
s
+ λ
1
Power
Wavelength
λ
1
: wavelength of the 1
𝑠
tooth
λ
1
λ
3
AlN and diamond that can be used to extend the operation wavelength range of the
generated Kerr comb [25, 26].
The generation of Kerr frequency comb is achieved by parametric frequency
conversion via coupling a continuous-wave (CW) pump into a microresonator [9] as
shown in Figure 1.2. Basically, there are mainly two processes during comb formation.
At first, when the microresonator is pumped by a high-power CW light, two photons
at the pump wavelength (wp) annihilate and both a signal (ws) and idler (wi) photon are
created, in which the conservation of energy is met (2wp = ws + wi). As the parametric
process is further enhanced in the cavity, the signal and idler sidebands become
stronger and themselves serve as the secondary pumps. This results in the second
process where cascaded four-wave-mixing (FWM) is initiated to generate a serious of
new sidebands. Depending on the pump power and wavelength, the formation of Kerr
combs consists of several dynamic regimes, including Turing patterns, chaos, low-
phase-noise combs, and soliton combs [27-33]. Turing patterns result from the
modulation instability (MI) of the pump at the initial state of comb formation [34].
They are also referred as primary combs in the frequency domain, which exhibit high
coherence and robustness to external perturbations. Chaos can appear following the
primary comb when the pump wavelength is increased. Although chaotic combs have
a broad spectrum, they have been shown with high intensity and phase noise because
of multiple comb lines within one resonance. Therefore, chaotic combs should be
avoided in applications that require high coherence. Further increasing the pump
wavelength can result in the low-phase-noise comb, which have been experimentally
demonstrated in different microresonator platform [33, 35, 36]. In addition, soliton
combs can be obtained by sweeping the pump wavelength or thermally tuning the
cavity resonance [32, 37-39]. They have a stable pulsed waveform in the time domain
leading to a smooth spectral envelope in a broad bandwidth. Both the low-phase-noise
and soliton combs are in the phase-locked state that inherently has low noise. There is
also breathing soliton in which additional sidebands are generated around soliton Kerr
comb lines, which can be uesful for certain applications [40-42].
4
Figure 1.2 The generation of Kerr frequency comb in a microresonator.
1.2 High-Speed Optical Communications
Optical communications, which use light to carry information, have dominated
the backbone network owing to its capability and potential for high-speed data
transmission [43-45]. The transmission distance can range from several meters for data
center connection to thousands of kilometers for long-haul communication. As shown
in Figure 1.3, an optical communication system mainly consists of a transmitter,
transmission media, and a receiver. In general, the information is encoded in the
amplitude/phase of the optical carrier. To increase the capacity in a data link, a large
number of optical carriers/wavelengths carrying different information are combined
together into a single data link, which is known as wavelength-division multiplexing
[46]. These data channels propagate together along the link. At the receiver, different
data channels are separately detected in a photodiode to decode the information.
Figure 1.3 Typical optical communication systems exploiting wavelength-division multiplexing. Tx:
transmitter; PC: polarization controller.
λ
λ
Microresonator
CW Laser
Waveguide
Kerr frequency comb
Optical
amplifier
IQ modulator
Laser 2
Data 2 Tx 2
IQ modulator Laser 1
Data 1
Coherent
Receiver 1
PC
PC
PC
Tx1
IQ modulator
Laser n
Data n
Tx n
Multiplexer
Demultiplexer
Coherent
Receiver 2
PC
Coherent
Receiver n
PC
Optical
fiber
PC
5
As mentioned above, the data sequence is generally encoded on the
amplitude/phase of the optical waveform, which results in different modulation
formats [47]. Figure 1.4 shows the waveforms of different modulation formats and
their corresponding signal constellation. Originally, only the amplitude of the
waveform is used to encode the information, which is called on-off-keyed (OOK). In
this case, each symbol carries only 1-bit information. To efficiently make use of the
spectrum, the phase of the waveform has also been exploited to carry the data
information. For example, φ=0 denotes the information “0” while φ= π denotes the
information “1”. As such, the data information is represented by distinctive discrete
phase values. The set size of the amplitudes and phases can be increased for the data
encoding, which can encode more information on each symbol. This results in
spectrum-efficient advanced modulation formats such as quadrature-phase-shift-
keyed (QPSK) and 16 quadrature-amplitude-modulation (16-QAM). For higher-order
modulation formats, as the symbols get closer to each other, they become more
sensitive to the intensity and phase noise of the light sources [48, 49].
Figure 1.4 The waveform of different modulation formats and their corresponding signal constellations.
Coherent detection is widely used to demodulate the signals with advanced
modulation formats in optical communications [50, 51]. Compared to direct detection,
coherent detection exhibits higher receiver sensitivity by using a local laser to amplify
the received signal. Figure 1.5 shows a general structure of coherent detection with
the post digital signal processing (DSP). The incoming optical signal beats with a local
0 1 1 0 1 0
0 1
01 10 00 11
0110 0011
0 1 1 0 0 0 1 1
BPSK
QPSK
OOK
16-QAM
Waveform Constellation
I
Q
I
Q
I
Q
I
Q
t
I: in-phase Q: quadrature
( φ=0) ( φ= π)
t
t
t
Waveform Constellation
6
oscillator (LO) after a 90° optical hybrid. The direct current (DC) components from
the precious beating process can be canceled by using balanced detection.
Consequently, only the I and Q components of the received signal are remained. After
being digitized by analog-to-digit converters (ADCs), different DSP algorithms
including chromatic dispersion compensation, channel equalization, and carrier phase
recovery are used to recover the data information [52].
Figure 1.5 A general structure of coherent detection with the post digital signal processing.
1.3 Advanced Optical Signal Processing
With the potential to achieve high-speed signal processing functions, optical
signal processing (OSP) has gained much interest for high-capacity data transmission
[53-55]. It brings together different fields of optics and signal processing ranging from
nonlinear devices and processes, analog and digital signals to advanced modulation
formats. As shown in Figure 1.6, data information can be encoded in different physical
dimensions of optical carriers including amplitude, phase, wavelength, polarization,
and spatial features. Various optical nonlinearities have been shown to enable high-
speed optical processing for signals that are encoded in different dimensions [56-58].
As a result, different signal processing functions including wavelength multicasting,
correlation and equalization can be achieved in the optical domain.
Polarization
Controller
90
0
Hybrid
Balanced
detector
Balanced
detector
ADC
ADC
DSP
E
s
(t)
E
LO
(t)
ADC: analog-to-digital converter; DSP: digital signal processing; LO: local oscillator .
Input
signal
Local
laser
7
Figure 1.6 Different physical dimensions of optical carriers for signal processing through nonlinear
wave mixing.
One fundamental processing in OSP is nonlinear wave mixing, which is the
interaction among multiple optical carriers at different wavelengths in a nonlinear
media. In this process, a new optical wave at another wavelength is typically generated.
There are different kinds of nonlinear devices such as highly nonlinear fiber (HNLF)
and periodically poled lithium niobate (PPLN) waveguide [57, 58]. A PPLN
waveguide has second-order susceptibility χ
(2)
, which enables three-wave mixing (e.g.,
sum frequency generation (SFG) and difference frequency generation (DFG)). The
cascaded process of SFG and DFG can generate a signal copy (idler) close to the
original signal as shown in Figure 1.7. The efficiency of these processes depends on
many factors. One of them is the phase-matching among the multiple interacting
waves, which is the reason why the signal and pump laser should be placed
symmetrically regarding the quasi-phase matching (QPM) frequency.
Figure 1.7 Sum and difference frequency generation in a PPLN waveguide.
Amplitude Phase Frequency Polarization Space
Nonlinear wave mixing (e.g., three-wave
mixing, four-wave mixing)
•
❖ Wavelength conversion
❖ Wavelength multicasting
❖ Correlation
❖ Equalization
❖ Regeneration
❖ Aggregation/Deaggregation
Optical Signal Processing Functions
SFG
f
dummy
f
pump
f
SFG
QPM
(2)
DFG
f
signal
f
idler
SFG: Sum frequency generation DFG: Difference frequency generation
QPM: Quasi-phase matching
f
pump
f
SFG
QPM
f
signal
(2)
SFG
8
Except for three-wave mixing, there is four-wave mixing (FWM) resulting from
the 3
rd
order nonlinearity. This process is similar to cascaded SFG and DFG, in which
a fourth optical wave is generated from the nonlinear wave mixing of three waves.
Generally, there are two FWM processes depending on the number of pumps, one is
degenerate FWM (a single pump) and the other non-degenerate FWM (two pumps).
HNLF is one of the commonly used materials for FWM and its frequency conversion
efficiency reaches the maximum when the two pumps are symmetrically located
around the zero-dispersion wavelength (ZDW) [59].
1.4 Thesis Outline
This dissertation mainly focuses on the generation of microresonator-based Kerr
frequency comb and its applications in optical communications and signal processing.
The rest of the dissertation is organized in the following manner. The generation of
Kerr combs, as well as their characterization in terms of the comb line linewidth and
noise, will be covered from Chapter 2 to 4, which will also discuss the applications of
Kerr combs as coherent light sources and local oscillators in WDM communication
systems. Chapters 5 and 6 will present the use of Kerr combs as multiple mutually
coherent pumps to achieve different optical signal processing functions. Finally, the
deterministic generation of a controllable breathing soliton and its application in the
dual-comb source will be discussed in Chapters 7 and 8.
To be specific, Chapter 2 investigates the dependence of Kerr comb generation
and the comb line linewidth on the pump linewidth in a coherent communication
system. Chapter 3 studies the effect of the EDFA-induced pump noise on soliton Kerr
comb for the transmission of 64-QAM signals. Chapter 4 presents the generation of
multiple Kerr combs from different comb lines of another remote comb and their
potential applications in inter-datacenter communications. Chapter 5 proposes pump-
linewidth-tolerant wavelength multicasting by exploiting Kerr comb lines as mutually
coherent pumps. Chapter 6 describes a scalable optical tapped-delay-line for
simultaneous and independent processing on multiple data channels using Kerr
9
frequency comb and nonlinear wave mixing. Chapter 7 discussed the deterministic
generation of a controllable breathing soliton by either injecting a second pump at the
soliton resonance or modulating the CW pump in simulation and experiment. Chapter
8 briefly illustrates one potential use of the controllable breathing soliton in the dual-
comb source.
10
Chapter 2 Dependence of Microresonator-based
Kerr Comb on the Pump Linewidth
2.1 Introduction
The optical frequency comb is of significant interest for a wide range of potential
applications including time and frequency metrology, RF signal generation and optical
communications [60-65]. Recently, the use of integrated microring resonators to
produce combs based on Kerr nonlinearity has attracted much interest because of its
small footprint and broadband operation [9, 19].
The approach to generating the chip-scale Kerr frequency combs is realized by
cascaded FWM via coupling a CW pump into a high-quality (Q) microresonator.
Depending on the pump power and wavelength, the formation of Kerr combs consists
of several dynamic regimes, including Turing patterns (primary combs), chaos, low-
phase-noise combs and soliton combs [28-32]. These comb states could exhibit
different degrees of coherence between comb lines leading to distinct noise properties
[27, 66, 67]. Moreover, since the comb lines are derived from the pump, the pump
phase noise could also affect the noise performance of different comb states, which
might limit their applications such as being used as coherent light sources in optical
communication systems.
An important feature and figure-of-merit for the system utility of the comb lines
themselves is their individual linewidths, which is expected to be influenced by the
pump noise for different kinds of combs. For example, the linewidths of fiber laser
frequency comb away from the comb center is dominated by the pump-induced noise
[68]. In terms of chaotic Kerr comb, the relation between the comb linewidth and the
pump phase noise is studied as well [69]. However, questions remain about the
dependence of the individual comb lines in the primary and low-phase-noise states as
the Kerr comb pump linewidth is increased, and about how tolerant these two states of
Kerr combs are to increasing levels of the pump phase noise.
11
In this chapter, we experimentally study the effect of the pump linewidth on the
generation of Kerr comb lines, as well as on their linewidths and performance in a
coherent communication system. In the primary and low-phase-noise comb states, the
linewidths of the generated combs are found to be linearly dependent on the pump
linewidth with a slope close to 1, as it increases from 60 kHz to 10 MHz. However,
when the pump linewidth is broadened beyond 5 MHz, the formation of the low-phase-
noise comb could not be achieved, and only the primary comb is generated, potentially
indicating its larger tolerance to the pump linewidth. Furthermore, serving as coherent
light sources, there is less than 0.2 dB optical signal-to-noise ratio (OSNR) penalty
between the pump and the generated Kerr combs at the bit-error rate (BER) of 10
-3
in
both primary and low-phase-noise states, demonstrating similar coherent system
performance of Kerr combs and the pump [70].
2.2 Linewidth Broadening and Characterization
The Kerr frequency comb is generated by a microring resonator, which is made
of silicon nitride with a cross section of 1.5 μm × 0.9 μm. The resonator dispersion at
the pump wavelength of 1552.3 nm is anomalous [71]. The free spectral range (FSR)
is ~71.7 GHz and the cavity linewidth and quality factor of the resonator cavity are
300 MHz and 4 x 10
5
. Figure 2.1 is a schematic of the experimental setup to generate
the frequency comb and measure the comb linewidth. The CW light of a narrow-
linewidth (<100 kHz) external cavity diode laser (ECDL) is used as the pump. A high-
power erbium-doped fiber amplifier (EDFA) is used to amplify the pump with a total
output power of 34.5 dBm, and the out-of-band noise is filtered by a 2-nm bandpass
filter (BPF). The pump goes through an isolator and a polarization controller (PC)
before it is coupled to the chip through the lensed fiber. The coupling loss is
approximately 3 dB per facet. Different comb states can be obtained when the pump
wavelength is carefully tuned as described in [72]. The light out of the chip is divided
into two parts. One is used to characterize the comb by measuring the optical spectrum
using an optical spectrum analyzer (OSA) and by monitoring the RF beat note using
12
an electrical spectrum analyzer (ESA). It should be noted that when measuring the RF
spectrum, the residual strong CW pump is attenuated by 25 dB with a fiber Bragg
grating (FBG). On the other path, the comb is sent to a 0.4-nm tunable filter (BPF 2)
to separately extract individual comb lines for measuring their corresponding
linewidths using the self-heterodyne approach [73]. The selected comb line is split into
two paths. On the upper arm, the light frequency is shifted by 590 MHz using an
acoustic-optical modulator (AOM) to allow for self-heterodyne detection. An optical
fiber is added on the lower arm with a length of 12.7 km, which is longer than the
coherence length of the ECDL. The combined signals are amplified by an EDFA and
detected by a photodiode (PD). A 50-GS/s real-time oscilloscope is used to measure
the power spectral density (PSD) of the signal.
Figure 2.1 Experimental setup for generating the frequency comb and characterizing the corresponding
linewidth. ECDL: external cavity diode laser; BPF: band pass filter; LF: lensed fiber; FBG: fiber Bragg
grating; ESA: Electrical spectrum analyzer; AOM: acousto-optic modulator;
Linewidth emulation of the semiconductor laser is employed to investigate the
effect of the pump linewidth on the Kerr comb generation and linewidth [74]. Figure
2.2(a) shows the experimental setup to broaden the linewidth of the pump and
characterize the comb linewidth. The output of the pump is phase-modulated to
broaden its linewidth, ∆𝜐 , through an IQ modulator driven by an arbitrary waveform
generator (AWG). Theoretical phase noise as a Wiener process is digitally generated
based on the equation 𝜙 (𝑛 )=√2𝜋 Δ𝜈𝑑𝑡 ∑𝑋 (𝑛 )
𝑛 0
, where dt is the reciprocal of the
sampling frequency, Fs, and X(n) is a Gaussian random variable. Note that a 1 GHz
frequency shift is imposed on the I and Q drive signals by adding a linearly increasing
phase to exclude improperly amplified low-frequency noise components from the
13
input to the high power EDFA in the comb generation. Figure 2.2(b) and (c) show the
experimentally measured normalized PSD of the pump without broadening and with
a 500 kHz broadening as well as the corresponding fittings of Lorentzian shaped
spectrum. It can be observed that both field spectra have a Lorentzian shape. For higher
accuracy, the linewidth is measured at its -20 dB (with respect to its maximum value)
points and the full-width half maximum (FWHM) linewidth is obtained by dividing
the -20 dB value by 2√99 [75]. The linewidth of the pump without broadening is
measured to be approximately 60 kHz. With a broadening design value of 500 kHz,
the resulting linewidth is estimated to be ~505 kHz, which is in good agreement with
the theoretical value.
Figure 2.2 (a) Schematic setup of the pump linewidth broadening using an AWG and comb linewidth
characterization. AWG: arbitrary waveform generator; (b) and (c) Linewidth measurement of the pump
without broadening and with a broaden linewidth of 500 kHz.
2.3 Dependence of Kerr Comb on the Pump Linewidth
The optical spectra and the corresponding linewidths of the comb line at the
wavelength of 1534.54 nm in different comb states without pump broadening are
shown in Figure 2.3(a), (b) and (c). As can be seen in the primary and low-phase-noise
states, the field spectra of the generated combs maintain the Lorentzian line shape, and
the linewidths are close to that of the pump. However, in the chaotic state (Figure
2.3(b)), the field spectrum broadens up and becomes non-Lorentzian. The reason for
this difference is that in the chaotic state, multiple lines are oscillating in one resonance,
which results in a broad RF spectrum.
14
Figure 2.3 (a), (b) and (c) The optical spectra and the corresponding linewidth (LW) measurements of
the comb line at the wavelength of 1534.54 nm without broadening the pump. The linewidths of the
primary and low-phase-noise combs are close to that of the pump.
The dependence of the comb linewidth and comb generation on the pump
linewidth in the primary and low-phase-noise comb states is further investigated by
broadening the pump linewidth from 60 kHz to 10 MHz. The linewidths of selected
combs with high power from 1534.54 nm to 1536.94 nm are measured. Figure 2.4(a)
shows the linewidth of comb lines as a function of the pump linewidth in the primary
and low-phase-noise states. The inset is the optical spectrum of the low-phase-noise
comb at C-band with five labeled high-power comb lines. It can be seen that in both
states, the comb linewidth linearly increases with and is almost equal to the pump
linewidth. This indicates that the linewidth of the generated comb lines is linearly
dependent on the pump (as long as it is larger than the minimum value influenced by
other noise sources, including the thermorefractive and thermoelastic ones) [69]. This
observation of linear dependence between the output and input linewidths may also be
extended to other phase-locked states, including cavity soliton states, as the phase
(b)
1520 1540 1560 1580
-60
-40
-20
0
Wavelength [nm]
Power [dBm]
Chaotic comb
585 590 595
-40
-30
-20
-10
0
10
Normalized amplitude [dB]
Frequency [MHz]
Field spectrum
(c)
1520 1540 1560 1580
-60
-40
-20
0
Wavelength [nm]
Power [dBm]
Low-phase-noise comb
585 590 595
-40
-30
-20
-10
0
10
Normalized amplitude [dB]
Frequency [MHz]
Field spectrum
Lorenzian fit Lorentzian
LW 60 kHz
(a)
1520 1540 1560 1580
-60
-40
-20
0
Power [dBm]
Wavelength [nm]
Primary comb
585 590 595
-40
-30
-20
-10
0
10
Normalized amplitude [dB]
Frequency [MHz]
Field spectrum
Lorenzian fit Lorentzian
LW 60 kHz
15
relationship between the pump and comb lines is well-defined. In addition, the RF beat
notes maintain a single narrow peak with different pump linewidths, as shown in
Figure 2.4(b). When the pump linewidth is 2 MHz, the peak of the RF beat note drops
due to the variance of the comb spectrum.
It should be noted that when the pump linewidth is larger than 5 MHz, there is
no low-phase-noise comb being generated. One reason for this could be that the pump
power in the cavity becomes lower than the threshold for forming the low-phase-noise
combs due to the reduced coherence length of the pump. Another reason might be that
as the phase noise becomes higher at wider pump linewidths, the excess noise prevents
phase locking among the pump and comb lines. Nevertheless, primary combs could
still be generated even with pump linewidth higher than 5 MHz, which demonstrates
that for our Si3N4 micro-resonator, the generation of the primary comb has a larger
tolerance to the pump linewidth compared to the low-phase-noise comb. This agrees
with the finding that primary combs exhibit a strong and robust phase locking in [76].
Note that the tolerance of 5 MHz pump linewidth is specific to our microresonator.
The tolerance of the pump linewidth for the comb generation could depend on many
factors including the quality factor, pump detuning, and resonator dispersion.
Figure 2.4 (a) The comb line linewidth as a function of pump linewidth in the primary and low-phase-
noise states. The inset is the optical spectrum of the low-phase-noise comb at C-band. (b) The RF beat
note of the low-phase-noise comb with various pump linewidths (LWs). The single narrow peaks
indicate the comb maintains low phase noise.
10
-1
10
0
10
1
10
-1
10
0
10
1
Pump linewidth [MHz]
Comb line linewidth [MHz]
10
-1
10
0
10
1
10
-1
10
0
10
1
Pump linewidth [MHz]
Comb line linewidth [MHz]
Primary Comb Comb line 1 Comb line 2 Comb line 3 Comb line 4 Comb line 5
10
-1
10
0
10
1
10
-1
10
0
10
1
Pump linewidth [MHz]
Comb line linewidth [MHz]
Primary Comb Comb line 1 Comb line 2 Comb line 3 Comb line 4 Comb line 5
Wavelength [nm]
1530 1540 1550 1560
Power [dBm]
-40
-20
0
20
pump
1
2
5
3
4
Primary and low-
phase-noise comb
Primary comb
(a)
71.1084 71.1089
-100
-80
-60
-40
Frequency [GHz]
71.1083 71.1088
-100
-80
-60
-40
Frequency [GHz]
Power [dB]
71.1084 71.1088
-100
-80
-60
-40
Frequency [GHz]
71.1081 71.1086
-100
-80
-60
-40
Frequency [GHz]
Pump LW
= 60 kHz
Pump LW
= 500 kHz
Pump LW
= 1 MHz
Pump LW
= 2 MHz
(b)
16
2.4 Coherent System Performance of Kerr Comb Lines
The coherent system performance of generated comb lines and the pump as light
sources for optical communications are studied with different pump linewidths. The
back-to-back (B2B) experimental setup is shown in Figure 2.5(a). The extracted single
comb line is amplified by an EDFA, and the out-of-band noise is filtered by a narrow-
band filter. An IQ modulator driven by the pulse pattern generator in the transmitter is
used to modulate the comb line with 20-GBaud QPSK signals. By using a local
oscillator in a coherent receiver, the signals are demodulated and the BER
measurements are performed as well as the EVM measurements.
Figure 2.5(b) shows the BER as a function of the optical signal-to-noise ratio for
the pump and the primary comb with different pump linewidths. The inset is the
constellation of the signal carried by the transmitted primary comb with a linewidth of
about 10 MHz. Similarly, Figure 2.5(c) shows the BER as a function of the OSNR for
the pump and comb line 1 in the low-phase-noise state. For the various pump
linewidths, both the primary comb and comb line 1 have nearly the same BER
performance as the pump. When the pump linewidth is lower than 2 MHz, less than
0.2 dB OSNR penalty can be observed between the pump and generated comb lines.
When the pump is broadened beyond 5 MHz, there is no low-phase-noise comb and
only the primary comb is generated. In addition, the BER performance of the pump,
as well as the primary comb is degraded as a result of the higher phase noise, as can
be seen in the inset of the constellation diagram. As such, the system performance of
Kerr combs for optical communications in the primary and low-phase-noise states
could be comparable to that of the pump. It is essential to use a narrow-linewidth pump
laser to generate the Kerr frequency comb used as coherent light sources for phase
noise sensitive applications, including higher-order QAM transmission.
17
Figure 2.5 (a) Experimental setup for demonstrating QPSK signal transmission with Kerr frequency
combs. (b) BER as a function of OSNR for the pump and primary comb with different pump linewidths.
The inset is the constellation of the QPSK signal with a linewidth of 10 MHz; (c) BER as a function of
OSNR for the pump and the low-phase-noise comb. The inset is the constellation of the QPSK signal
with a linewidth of 2 MHz.
2.5 Conclusion
In conclusion, we demonstrate the strong tie between the linewidths of Kerr
comb lines and that of the pump in multiple comb states. The linewidths of Kerr combs
almost remain identical to the pump linewidth as the latter is digitally broadened from
60 kHz to 10 MHz. We also find that only the primary comb could be generated with
the pump linewidth beyond 5 MHz using our resonator, indicating the larger tolerance
of this type of comb to broad pump linewidth. Furthermore, the difference in BER
performance between the pump and comb lines with the same OSNR is negligible at
different pump linewidths, which indicates Kerr frequency combs can have similar
Coherent
Receiver
BPF 2
EDFA BPF 1
Modulator
20 GBaud
Kerr comb
PPG
EDFA
PC
TX
(a)
9 10 11 12 13 14
10
-6
10
-5
10
-4
10
-3
10
-2
BER
OSNR [dB]
9 10 11 12 13 14
10
-6
10
-5
10
-4
10
-3
10
-2
BER
OSNR [dB]
Pump(60kHz)
Primary comb
Pump(500kHz)
Primary comb
Pump(1MHz)
Primary comb
9 10 11 12 13 14
0
1
2
3
4
5
6
x 10
-3
BER
OSNR [dB]
Pump(2MHz)
Primary comb
Pump(5MHz)
Primary comb
Pump(10MHz)
Primary comb
(b)
9 10 11 12 13 14
10
-6
10
-5
10
-4
10
-3
10
-2
BER
OSNR [dB]
Pump(60kHz)
Comb line 1
Pump(500kHz)
Comb line 1
Pump(1MHz)
Comb line 1
Pump(2MHz)
Comb line 1
(c)
(b) (c)
18
coherent system performance to the pump in the primary and low-phase-noise states.
Therefore, a narrow-linewidth pump laser is essential for Kerr frequency combs to
transmit high-speed, higher-order data signals in optical communications.
19
Chapter 3 Effect of EDFA-induced Pump Noise on
Soliton Kerr Combs for 64-QAM Transmission
3.1 Introduction
An optical frequency comb with a multitude of equidistant frequency lines has
gained much interest as a potential tool in high-precision frequency metrology, high-
capacity data transmission and optical signal processing [1, 9, 63, 77]. Recently,
microresonator-based Kerr frequency combs have received attention in optical
communication systems because of their broadband operation and chip-scale
integration [12, 13, 19]. Such combs are compact and provide multiple optical carriers
that have low phase noise and are mutually coherent in several dynamic regimes [30,
66, 78]. One comb state is the dissipative Kerr soliton resulting from the balance
between dispersion and Kerr nonlinearity [32, 37-39]. Such a soliton comb is
potentially important because of its deterministic generation and smooth spectral
envelope. In one notable experiment with two interleaving soliton combs, transmission
of a data stream beyond 50 Tb/s over a distance of 75 km has been achieved [12].
An important feature of the comb lines for high-speed transmission is the carrier
power compared to the noise power, which is known as optical signal/carrier-to-noise
ratio (OSNR/OCNR) [79, 80]. Typically, Kerr frequency combs are generated using a
microresonator that is pumped by an external laser. A recent work is the soliton comb
generation directly from a laser in a high-quality (Q) silica micro-disk resonator [81].
To achieve efficient comb generation in a lower-Q ring resonator, the pump laser is
usually amplified by an EDFA before being injected into the chip. The EDFA-
generated amplified spontaneous-emission (ASE) noise beats with the pump, leading
to stochastic intensity variations, which could be transferred to the generated comb
lines [82, 83]. As a result, there remain questions regarding the effect that the ASE
noise of the amplified pump may have on the quality of Kerr comb lines, including the
comb noise level and linewidth. Such effects might limit the applications in optical
20
communications using higher-order modulation formats (e.g., 64-quadrature
amplitude modulation (QAM)).
In this chapter, we experimentally investigate the effects of EDFA-induced
pump noise on soliton Kerr combs for 64-QAM transmission. It is found that the
OCNRs of the comb lines across C-band change almost linearly with the pump OCNR
and their values are close to each other when the pump OCNR is kept at certain values.
Compared to a single soliton, a three-soliton crystal shows slightly lower OCNR
despite having higher comb line power. We also observe that when the ASE noise on
the pump varies within a 10-dB range in the single-soliton state, there is a very small
effect on the comb linewidth. Furthermore, a pump light with OCNR higher than 52
dB has generated a single-soliton Kerr comb, in which four lines are used as coherent
light sources to transmit 20-Gbaud 64-QAM signals over a 25-km fiber with below
forward-error correction (FEC) performance [84].
3.2 Effect of EDFA-induced Pump Noise on the Comb Line Noise
The microresonator consists of a silicon nitride waveguide with a cross section of
1.5 μm × 0.9 μm. It is pumped near 1555.0 nm light in the anomalous dispersion region.
The corresponding quality (Q) factor of the resonator and the cavity linewidth are 1.3
x 10
6
and 150 MHz, respectively. Figure 3.1(a) illustrates the experimental setup for
soliton Kerr comb generation and characterization. An external cavity diode laser as
the pump combined with an ASE broadband source is filtered by a narrow bandpass
filter (BPF: 0.4 nm) and amplified by a high power EDFA with a total output power of
35 dBm. The output is filtered by a tunable optical filter (TOF) and coupled to the chip
through a lensed fiber. The measured coupling loss is about 2.5 dB per facet. The output
of the generated comb is sent to a fiber Bragg grating to suppress the residual strong
pump line and then split into several paths for different characterizations. The intensity
autocorrelation is measured using an autocorrelator, and the optical spectrum as well
as the OSNR are measured by a conventional OSA with 12.5-GHz (0.1 nm) resolution
(Res). It should be noted that because the bandwidth of the ASE noise for the pump and
21
generated comb lines is limited by the narrow cavity linewidth, the OCNR is used as a
figure of merit to characterize the additive ASE noise, which is measured by a high-
resolution OSA in a bandwidth of 100 MHz (0.008 nm).
Figure 3.1 (a) Experimental setup for cavity-soliton Kerr comb generation and characterization. (b)
Optical spectrum of the single-soliton comb. The left and right insets show a microscope image of the
integrated microresonator and the RF spectrum of the beat note, respectively. (c) Autocorrelation trace
of the single-soliton pulse. (d) Optical spectrum of the single-soliton comb across C-band. (e) Optical
spectrum of Kerr combs in the three-soliton states.
Temporal cavity solitons can be obtained by sweeping the pump wavelength
using an arbitrary function generator. In general, multiple soliton states, such as soliton
crystals, appear first during the pump tuning for comb generation. Further decrease in
the pump wavelength (backward tuning) results in a transition to the single-soliton state
[85]. Figure 3.1(b) shows the full optical spectrum of the single-soliton comb, which
has a broad span of 250 nm and exhibits a sech
2
shape (Res: 12.5 GHz). The left inset
shows a microscope image of the integrated microresonator, and the right one shows
the measured RF beat note of adjacent comb lines using amplitude modulation down-
mixing [86]. The autocorrelation trace of the soliton pulse in Figure 3.1(c) shows a
pulse period of 5.2 ps, which corresponds to a repetition rate of ~192.0 GHz. The zoom-
in spectrum of the single-soliton comb across C-band is shown in Figure 3.1(d). It can
ECDL
EDFA
Isolator PC
LF Resonator
ASE
source
BPF
FBG
High
res. OSA
Comb
Att
Autoco-
rrelator
(a)
AFG
TOF PC
-5 0 5
0
0.5
1
Delay (ps)
Intensity (a.u.)
5.2 ps
1500 1550 1600 1650
-60
-40
-20
Power (dBm)
Wavelength (nm)
Ring
1
Power (20 dB/div)
(10 dB/div)
Span=20 MHz
(b)
(c)
(d)
1500 1550 1600 1650
-60
-40
-20
Wavelength (nm) (e)
Res: 12.5 GHz
Res: 12.5 GHz
Spacing = ~576 GHz
FSR = ~192 GHz
1530 1540 1550 1560
-60
-40
-20
Power (dBm)
Wavelength (nm)
47.97 47.975 47.98 47.985
-80
-70
-60
fc = ~192
GHz
22
be seen that most lines have OSNR higher than 35 dB (Res: 12.5 GHz) except the ones
close to the pump. In addition, comb lines can have higher power if there is more than
one soliton in the cavity. Those solitons co-propagate and exhibit different spectra due
to the spectral interference between them [87]. Figure 3.1(e) shows one specific
spectrum with the comb spacing (~576 GHz) equal to three resonator FSRs, indicating
a train of three solitons evenly separated in time.
In general, the efficient generation of cavity-soliton combs in the S3N4
microresonator requires high pump power around 1 W (inside the waveguide). The
ASE noise (in-band and out-of-band) on the pump could increase considerably after
being amplified by the high-power EDFA. Given that comb lines are generated from
the amplified pump, the impact of EDFA-induced pump noise on the noise performance
of the comb lines is experimentally investigated using the above setup as shown in
Figure 3.1(a). In the experiment, instead of using EDFAs with different noise figures
(NFs) or changing the input pump power to the high-power EDFA, the in-band ASE
noise on the pump is varied using a broadband ASE source, whose power is tuned using
an attenuator (Att). Moreover, the out-of-band ASE noise on the pump can be tuned by
changing the bandwidth of the TOF. Thus, different ASE levels can be obtained, while
the power of the amplified pump is maintained at the chip input. It should be noted that
when the pump laser wavelength is decreased to some extent during the backward
tuning, the breather soliton state occurs, as shown in Figure 3.2(a) and its inset (Res:
100 MHz): Both multiple sub teeth and a noticeable change in the comb noise floor
could be observed [88]. Also, taking the impact of pump detuning on the comb
spectrum into account, the pump wavelength should be finely tuned to maintain a
soliton comb with stable comb line power. Through applying a 1-nm bandwidth TOF,
the in-band noise of comb lines is measured.
Figure 3.2(b) is the optical spectrum of the stable single-soliton Kerr comb across
C-band at 46-dB pump OCNR. The inset is the zoom-in spectrum of the comb line at
~1550.0 nm. The broad pedestal at the bottom of the inset shows the in-band noise for
each individual comb line. Similar to the OSNR, the OCNR could be measured by
23
linearly interpolating the noise level at the corresponding wavelength [89]. The pump-
induced noise level (i.e., comb noise generated from the ASE noise of the pump), comb
line power, and the OCNR of Kerr comb corresponding to different comb lines and
three pump OCNRs are shown in Figure 3.2(c), (d) and its inset, respectively. It can be
seen that the comb noise level increases and their OCNRs decrease almost linearly with
a slope of about 0.8 when the pump OCNR deteriorates. In the experiment, when the
pump OCNR is less than 43 dB (~23 dB OSNR), no soliton Kerr comb could be
generated. Compared to that of the pump, there is about 5 dB OCNR degradation for
the comb lines, which is caused by the noisy pump-induced gain. At a given pump
OCNR, the noise profile of the comb exhibits similar shape to its spectral envelope.
This results in nearly identical OCNRs of Kerr comb lines across C-band, as indicated
in Figure 3.2(d). The reason could be the cascaded parametric interaction between the
generated comb lines, which are different-order sidebands of the pump.
The effect of the out-of-band ASE noise on the amplified pump is also studied by
varying the bandwidth of the TOF at 56-dB pump OCNR. As seen in Figure 3.2(e),
when the bandwidth of TOF changes from 1 nm to 9 nm, the OCNRs are close to each
other for comb lines located where the EDFA ASE noise is filtered. However, the comb
OCNRs are reduced for comb lines close to the pump owing to the residual ASE noise.
The effect of in-band EDFA-induced pump ASE noise is also investigated in the
three-soliton state, as shown in Figure 3.1(e). Figure 3.2(f) is the corresponding comb
OCNR at three pump OCNRs. Compared to the single-soliton comb, the three-soliton
comb has fewer comb lines but with higher power. However, their OCNR is slightly
lower than those of the single-soliton comb at the same pump OCNR. This means that
nearly no improvement in the comb OCNR can be obtained despite higher comb line
power for the three-soliton crystal. The reason could be the interference between the
three uniformly distributed solitons that are generated from the same pump. As their
noise is somewhat correlated, adding them together increases the noise level.
24
Figure 3.2 (a) Optical spectrum (Res: 100 MHz) of Kerr comb in the breather soliton state (inset: comb
line at ~1550 nm). (b) Optical spectrum of a stable soliton Kerr comb (inset: ~1550 nm). (c) Pump-
induced noise level, comb line power and (d) comb optical OCNR at different wavelengths or three
pump OCNRs (inset) for the single-soliton comb. (e) Comb OCNR under different bandwidths of the
TOF. (f) Comb OCNR at different pump OCNRs for a three-soliton crystal.
The effect of EDFA-induced pump noise on the Kerr comb linewidth is of equal
importance. Figure 3.3(a) depicts the self-heterodyne approach to measure the comb
1530 1540 1550 1560
-80
-60
-40
-20
0
Power (dBm)
Wavelength (nm)
1530 1540 1550 1560
-80
-60
-40
-20
0
Power (dBm)
Wavelength (nm)
Res: 100 MHz Res: 100 MHz
1549.92 1549.94
-80
-60
-40
-20
Power (dBm)
Wavelength (nm)
(a)
(b)
Noise
1549.94 1549.96
-80
-60
-40
-20
Power (dBm)
Wavelength (nm)
Sub teeth
1530 1540 1550 1560
40
45
50
55
60
Wavelength (nm)
Comb OCNR (dB)
Pump
(c) (d)
46 51 56
40
45
48
Pump OCNR (dB)
1530.2 nm
1545.4 nm
1560.8 nm
1530 1540 1550 1560
-80
-74
-68
-62
-56
-50
Pump-induced noise level (dBm)
Wavelength (nm)
1530 1540 1550 1560
-42
-36
-30
-24
-18
-12
1530 1540 1550 1560
-42
-36
-30
-24
-18
-12
1530 1540 1550 1560
-42
-36
-30
-24
-18
-12
Comb line power (dBm)
46 dB Pump OCNR
51 dB Pump OCNR
56 dB Pump OCNR
Pump
1530 1540 1550 1560
40
45
50
55
Wavelength [nm]
Comb OCNR [dB]
56 dB Pump OCNR
51 dB Pump OCNR
46 dB Pump OCNR
Pump
(f)
1530 1540 1550 1560
35
40
45
50
55
Wavelength (nm)
Comb OCNR (dB)
1nm TOF
2nm TOF
5nm TOF
9nm TOF
Pump
(e)
25
linewidth. The individual comb line is extracted and split into two paths. On the upper
arm, the light frequency is shifted by 590 MHz using an acoustic-optical modulator.
An optical fiber is added on the lower arm with a length of 20 km, which is longer than
the coherence length of the pump laser. The combined signals are amplified by an
EDFA and detected by a photodiode. A real-time oscilloscope is used to measure the
power spectral density of the signal. The linewidths of 10 comb lines (in Figure 3.2(b))
at both 46- and 56-dB pump OCNRs are shown in Figure 3.3(b). When the pump
OCNR is decreased from 56 to 46 dB, there is only small variation in the comb
linewidths, which are comparable to the pump linewidth. The reason for nearly
unchanged comb linewidths could be that they mainly depend on the given pump
linewidth in the phase-locked soliton states.
Figure 3.3 (a) The setup for linewidth measurement using the self-heterodyne method. (b) Comb
linewidths at two pump OCNRs.
3.3 Transmission of 64-QAM Using a Soliton Kerr Comb
Considering the high spectral purity and OCNR of soliton Kerr frequency comb
lines (Figure 3.2(b)), a 64-QAM transmission experiment is performed to evaluate the
effect of the pump-induced noise when the comb lines are used as coherent light
sources. The experimental setup is illustrated in Figure 3.4(a). Four comb lines from
1544.0 to 1549.0 nm are extracted by a 5-nm filter (BPF1). After amplification by a
low-noise EDFA, the comb lines are modulated with 64-QAM signals using an IQ
modulator driven by an arbitrary waveform generator at 20 Gbaud. The signals are
transmitted through a 25-km single-mode fiber before they are demodulated in the
coherent receiver, where the EVM and BER measurements are performed to assess
1550 1555 1560
10
20
30
40
Wavelength (nm)
Comb linewidth (kHz)
46 dB pump OCNR
56 dB pump OCNR
AOM
590 MHz
EDFA
Oscillo
scope
PD
Optical delay
PC
BPF
EDFA
(a)
20 km SMF
(b)
Pump
26
the signal quality. Figure 3.4(b) presents the optical spectrum of the received
modulated signals. The measured comb OCNR (before modulation) and EVM
performance versus the pump OCNR are shown in Figure 3.4(c) for channels 2 and 3.
The OCNR of the comb line becomes higher and the corresponding EVM decreases
as the pump OCNR is increased. When the pump OCNR is greater than 52 dB (Figure
3.4(d)), all four channels have their estimated BERs lower than the FEC limit (4.5 x
10
-3
), indicating the error-free performance of the transmitted signals [90]. Therefore,
a pump light with the OCNR beyond 52 dB is required for soliton Kerr frequency
combs to transmit high-speed 64-QAM data signals.
Figure 3.4 (a) Experimental setup for four-channel 20 Gbaud 64-QAM data transmission using single-
soliton Kerr comb. (b) Optical spectrum of the received modulated signals. (c) Comb OCNR and the
EVM versus the pump OCNR (before modulation) for channels 2 and 3. (d) The constellation diagrams
of four signals with 52-dB pump OCNR.
1548 1550 1552
-40
-30
-20
-10
Power (dBm)
Wavelength (nm)
50 52 54 56 58
44
46
48
50
52
54
Comb OCNR (dB)
Pump OCNR (dB)
50 52 54 56 58
4.4
4.8
5.2
5.6
6
6.4
50 52 54 56 58
4.4
4.8
5.2
5.6
6
6.4
50 52 54 56 58
4.4
4.8
5.2
5.6
6
6.4
EVM (%)
OCNR @1548.3nm
OCNR @1549.9nm
EVM @1548.3nm
EVM @1549.9nm
EVM of Pump
Res: 100 MHz
Ch3:1549.9 nm
EVM: 5.8%,
BER = 4.0E-3
Ch4:1551.4 nm
EVM: 5.83%,
BER = 4.2E-3
Ch2:1548.3 nm
EVM: 5.76%,
BER = 3.9E-3
Ch1:1546.8 nm
EVM: 5.89%,
BER = 4.4E-3
(b)
(c)
(d)
BPF2
IQ modulator
20 Gbaud
BPF1
AWG
EDFA
PC
TX
Kerr comb
Coherent
receiver
BPF3 EDFA
25 km
SMF
(a)
Res: 1.25 GHz
Ch1 Ch2 Ch3 Ch4
27
3.4 Conclusion
In this chapter, we investigate the effects of EDFA-induced pump noise on
soliton Kerr frequency combs for 64-QAM transmission. We find that the OCNRs of
the comb lines across C-band almost linearly depend on the pump OCNR and are
similar for a constant input pump power and noise. For a specific three-soliton state,
despite higher comb line power, there is no noticeable OCNR improvement compared
to the single-soliton comb. When the ASE noise on the pump is varied by 10 dB in the
stable single-soliton state, the comb linewidths remain relatively unchanged and
similar to the pump linewidth. Furthermore, four lines of the single-soliton Kerr comb
produced by a pump light at an OCNR larger than 52 dB are used as coherent light
sources to transmit 20-Gbaud 64-QAM signals over a 25-km fiber with BER below
FEC threshold.
28
Chapter 4 Generation of Multiple Kerr Combs from
Another Remote Kerr Comb
4.1 Introduction
Recently, the implementation of different states of Kerr frequency combs as
coherent light sources in a WDM system and as multi-wavelength local oscillators
(LOs) in a coherent detection system have gained much attention. A notable
demonstration is the transmission of a data stream beyond 50 Tb/s over a distance of
75 km using two interleaving soliton combs [12].
Of interest is another potential use of Kerr combs in optical systems: a selection
of multiple lines from a “master” comb could each be used to generate a “slave” Kerr
comb at multiple receiver sites, which can also be exploited as both light sources and
LOs in high-capacity intra- or inter-datacenter communications [91, 92]. Previously,
it has been reported that the pump line from one Kerr comb can be used subsequently
to generate another comb on the same chip [93]. Exploiting the comb lines located in
different bands of one Kerr comb might be of interest to subsequently generate
multiple other combs at different remote locations for certain applications.
In this chapter, we experimentally investigate the generation of multiple Kerr
frequency combs using different lines from another Kerr comb located at different
distances. A series of master comb lines have been individually used to pump distinct
microresonators to produce slave combs at different receiver sites. The coherence time
between the master comb and different slave combs is close to each other around 40
μs while it slightly decreases for the comb lines whose wavelength are far away from
the pump because of the temporal decorrelation caused by the dispersive walk-off. In
addition, it is found that the slave comb lines have similar linewidth to the master comb
pump and more than 23 dB pump OSNR is required for slave comb generation. When
both the slave comb lines and the comb lines generated by an independent unstabilized
29
laser serve as LOs in a coherent receiver, the former ones have a smaller variation of
frequency error compared to the latter [94].
4.2 Concept of Multiple Kerr Comb Generation
The concept of multiple Kerr frequency comb generation using different lines
from another Kerr comb for optical communication systems is illustrated in Figure
4.1. At the Tx site, a master comb is generated by coupling a strong CW pump into a
microresonator. The master comb is then split into different bands, each of which is
sent to the corresponding receiver site. In each band, all comb lines are modulated with
different data signals except one comb line that is left unmodulated to be used as the
pump of the slave comb. The signals combined with the slave comb pump are
transmitted to the Rx site through a certain length of a single-mode fiber (SMF). In Rx
i, the slave comb pump is extracted and sent to microresonator i to generate slave comb
i. Considering that the pump and different low-noise comb lines have a well-defined
phase relationship, this configuration might enable some potential applications. For
example, in optical communication systems and networks, (i) the master comb lines
can replace multiple pump lasers to excite different slave combs, (ii) the generated
slave comb can serve as coherent light sources or as multi-wavelength LOs,
additionally reducing the number of discrete lasers, and (iii) the mutual coherence
between the master and slave combs can be beneficial for phase recovery in
multichannel coherent detection [95], where phase-locking requirements could be
reduced. Such mutual coherence between the two Kerr combs could be obtained by
using a single pilot seed from a master comb to generate the slave comb. Note that the
mutual coherence among different CW lasers can be achieved by using multiple phase-
locking loops (PLLs). In addition, the master and slave combs can be employed as two
comb sources for other applications [96]. It should also be noted that the
microresonators need to have close resonance wavelengths and FSRs to ensure a small
frequency offset among different comb line pairs of the master and slave combs in
most cases.
30
Figure 4.1 Concept of multiple Kerr comb generation using different lines from another Kerr comb for
optical communication systems.
4.3 Multiple Kerr Comb Generation Using Different Master Comb
Lines
The experimental setup to demonstrate multiple Kerr comb generation using
different master comb lines is presented in Figure 4.2. An external cavity diode laser
as the pump is amplified by high-power EDFA 1 and coupled to a microresonator
consisting of a silicon nitride waveguide. It is pumped near 1553.4 nm in the
anomalous dispersion region. The corresponding quality (Q) factor of the resonator is
1.3 x 10
6
. The master comb in the single soliton state is generated by controlling the
pump wavelength using an arbitrary function generator. At the output of the chip, a
tunable fiber Bragg grating is used to suppress the residual pump. In the TX side, the
master comb is first split into two paths. The comb line used to pump the slave comb
is individually selected by a tunable optical filter, amplified, and then attenuated using
a tunable attenuator on the lower arm. The attenuator is used to vary the slave comb
pump power input to EDFA 2, which enables the study of the effect of the pump
OSNR. On the upper arm, a 30-nm bandpass filter (BPF 1) is used to extract around
20 comb lines on the blue side of the slave comb pump and eliminate the slave comb
Master
comb
Data mod.: data modulation;
Pump
laser
Kerr
comb
Demux
50 km
SMF
Microresonator
Data
Mod.
Mux
Data
Mod.
Mux
25 km
SMF
Demux
Kerr
comb 1
Slave comb
Receiver
Rx 1
Demux
Kerr
comb i
Slave comb
Receiver
Rx i
LO
LO
TX
Band 1
Slave comb pump
LS
LS
31
pump to avoid its interference. The selected comb lines can be amplified to achieve
higher OSNR after fiber propagation. The extracted comb lines and the slave comb
pump are then combined and transmitted through a span of SMF. At the receiver site,
the slave comb pump is individually selected again. Because the microresonators are
polarization-sensitive [97], the polarization of the pump is optimized manually before
being sent to the second microresonator. As the wavelength of the selected comb line
is fixed, thermally controlled comb generation is utilized to generate the slave comb
[39]. Consequently, the cavity resonance of the second microresonator is thermally
tuned by using a micro Peltier temperature controller (TEC) module. Due to the limited
tuning speed of the TEC, the slave comb is generated in the low-phase-noise state
instead of in the soliton state.
The regenerated comb lines and their corresponding master ones are combined
and interfered on a photodetector. The repetition rate difference between the two
combs creates a time-domain interferogram (digitalized waveform) on a 20-GHz
oscilloscope. Multiheterodyne beat notes of the two combs can be obtained by the
Fourier transform of the time-domain waveform, which is similar to linear optical
sampling [5, 98]. Consequently, we can simultaneously characterize these beat notes.
The frequency resolution, determined by the sampling rate and the number of samples,
is 10 kHz. The linewidths of the beat notes in the RF domain are measured the same
way as the optical linewidth using a Lorentzian fit [99]. The linewidth is measured at
its -10 dB points and the FWHM linewidth is obtained by dividing the -10-dB value
by three. In addition, there are other approaches that might separately measure the
individual beat note linewidth more accurately, such as using a frequency counter or
phase noise analyzer [28]. Note that the setup is potentially applied to conventional
WDM systems, in which different master comb lines are used as distinct slave comb
pumps or employed to carry independent data channels. The comb line as the slave
comb pump can also be in the middle of the data channels. In this case, it should be
individually extracted by using, for example, an FBG or a liquid crystal on silicon
32
(LCoS) filter. Although the master comb lines might be used to generate a
superchannel, that is not the case we are dealing with.
Figure 4.2 Experimental setup for demonstrating the generation of multiple Kerr combs from a remote
Kerr comb.
The spectra of the master and generated slave combs are shown in Figure 4.3(a-
d). The master comb in the soliton state (Figure 4.3(a)) has a broad span of 250 nm
and a smooth spectral envelope. However, the slave combs in the low-phase-noise
state (Figure 4.3(b-d)) exhibit a large power variation among the different comb lines.
The optical microscope image of the integrated Si3N4 microresonator and the
autocorrelation trace of the soliton pulse are shown in the left and right insets of Figure
4.3(a). Figure 4.3(b) is the spectrum of the low-phase-noise slave comb generated in
Ring 2 pumped by the master comb line at 1558.2 nm after a 25-km fiber transmission.
Figure 4.3(c) is the spectrum of the one pumped by the master comb line at 1559.8 nm
after a 50-km fiber transmission. The inset of Figure 4.3(b) shows the measured RF
beat note of adjacent comb lines using amplitude modulation down-mixing. The
repetition rate or comb spacing of the master and slave combs (1&2) are measured as
191.88 and 191.99 GHz, respectively. The repetition rate difference results from the
EDFA2
LOs or
reference
BPF2
EDFA4
Received signal
Comb generation
Microresonator
FBG
TX
ECDL
PC1
Master comb
Slave comb
0 ~ 50 km
SMF
TEC
Real-time Scope
BPF1
RX
TOF
EDFA3 BPF3
BPF6
AFG
Att
EDFA1
PC2
33
slightly different ring resonator lengths in fabrication. Additionally, by replacing ring
2 with a much larger ring 3, slave comb 3 (Figure 4.3(d)), with a repetition rate of
~71.50 GHz, is produced through the master comb line at 1551.8 nm as the pump. The
power of different comb lines fluctuates in the low-phase-noise state. Consequently,
some comb lines show >35 dB OSNR while some others have a poor OSNR. The
comb lines with high OSNR in the low-phase-noise comb can be used as LOs in
coherent detection. However, it might be beneficial to generate the slave combs in the
soliton state, which have predictable spectra and high OSNR for most comb lines. This
could be achieved with better thermal- or RF-controlled comb generation [39, 100].
Figure 4.3 (a-d) Spectra of the master and slave combs. The left and right insets of (a) are the optical
microscope image of the microresonator and the autocorrelation trace of the soliton pulse. The inset in
(b) shows the corresponding RF beat note.
4.4 Characterization of the Master and Multiple Slave Combs
Given that the slave combs are generated from different master comb lines, the
relationship between the master and slave combs (1&2) is investigated through the
beat notes of the corresponding comb line pairs. Importantly, the degree of mutual
coherence between the master and slave combs can be estimated from the linewidths
of their beat notes. Figure 4.4(a) shows the combined spectra of the master and slave
comb 1, in which comb lines from 1530 to 1553 nm are extracted for characterization.
Figure 4.4(b) shows the beat notes of the selected comb lines from the two combs after
1480 1500 1520 1540 1560 1580 1600 1620 1640 1660
Wavelength (nm)
Power (20 dB/div)
(c) 1500 1550 1600 1650
Wavelength (nm)
Power (20 dB/div)
Pump:
1559.8 nm
Slave comb 2
(low-phase-noise)
1500 1550 1600 1650
Wavelength (nm)
Power (20 dB/div)
r = ~ 119 um
Ring 1
(a)
-5 0 5
0
0.5
1
Delay (ps)
Intensity (a.u.)
5.2 ps
Power (20 dB/div)
Pump:
1553.4 nm
Master
comb
(Soliton)
Repetition rate
= 191.88 GHz
1480 1500 1520 1540 1560 1580 1600 1620 1640 1660
Wavelength (nm)
Power (20 dB/div)
(b)
4.7874 4.7876 4.7878 4.788 4.7882
x 10
10
-90
-80
-70
Frequency (GHz)
Power (10 dB/div)
10 dB/div
Span = 10 MHz
fc = ~191.99 GHz
Pump:
1558.2nm
Slave comb 1
(low-phase-noise)
Ring 2
Ring 2
Repetition rate = ~72 GHz Pump:
1551.8 nm
Slave comb 3
(low-phase-noise)
(d)
Ring 3
Power (20 dB/div)
Repetition rate = ~ 191.99 GHz
Span: 2 MHz
34
50 km fiber transmission. Figure 4.4(c) is the zoom-in of the 10
th
RF beat note, and
the single narrow peak shows a good mutual coherence between the comb lines. The
measured linewidth of the beat note is approximately 20 kHz, which could be narrower
with a higher measurement resolution.
Figure 4.4 (a) Spectra of the master and slave comb 1 (The comb lines in the box are selected for beat
note measurement). (b) Beat notes of the master and slave comb lines after 50-km SMF transmission.
(c) is the zoom-in spectrum of the 10
th
RF beat note.
During fiber transmission, the comb pump could be degraded by nonlinear
effects such as four-wave mixing, self-phase modulation (SPM), and cross-phase
modulation (XPM). To evaluate the nonlinear effects, the linewidths of both the master
and slave comb lines are measured using the self-heterodyne approach for the B2B
and 25-km fiber transmission. The ECDL serving as the original pump has a linewidth
of approximately 20 kHz, which corresponds to a coherence length of ~10 km. In our
measurement, a 12.5-km fiber is used for the decorrelation in the self-heterodyne setup
[101]. As the nonlinear effects depend on power, the power of the slave comb pump
is maintained at about 0 dBm before transmission. The results are presented in Figure
4.5(a), in which the inset is the measured power spectrum density of the master comb
1500 1550 1600 1650
Wavelength (nm)
Power (20 dB/div)
(a)
Master & slave comb 1
0 0.5 1 1.5 2 2.5
-90
-80
-70
-60
-50
-40
-30
Frequency (GHz)
Power (dBm)
Beat notes of
master & slave
comb 1 (50 km)
(b)
10
th
RBW: 10 kHz
1.2585 1.259 1.2595 1.26 1.2605
-80
-70
-60
-50
-40
-30
Frequency (GHz)
Power (dBm)
Power (10 dB/div)
(c)
Linewidth: ~20 kHz
Span = 2 MHz
35
pump and the corresponding fitting of the Lorentzian-shaped spectrum. It can be seen
that the linewidths of comb lines from both the master and slave combs are close to
the original pump linewidth (~ 20 kHz) for the B2B transmission, consistent with the
fixed phase relationship between the pump and comb lines. Even after 25-km
transmission, no obvious linewidth broadening is observed for the master and slave
comb lines. This means that the additional phase noise, induced by the fiber nonlinear
effects, is negligible with appropriate slave comb pump power. Hence, Kerr comb
lines can be regenerated with the linewidth remaining similar to that of the pump laser
in the Tx.
Furthermore, the efficient generation of phase-locked combs in the Si3N4
microresonator generally requires a pump laser with high power. A high power EDFA
is necessary to boost the on-chip pump power leading to high ASE noise on the pump.
In the proposed scenario, as the power of the slave comb pump becomes rather low
due to the transmission loss, its ASE noise will be increased dramatically after being
amplified by the cascaded EDFAs (2&3) in the receiver. This increase greatly reduces
the OSNR of the slave comb pump that could affect the comb generation. Therefore,
the effect of the pump OSNR on the generation of the low-phase-noise slave comb is
investigated. In the experiment, instead of adding extra ASE noise from an ASE source
[84], the pump OSNR is varied by changing the power of the slave comb pump input
to the cascaded EDFAs. This process is achieved by tuning an attenuator added after
the TOF, which can mimic the loss caused by extending the fiber length in the link.
Thus, the total transmission loss includes the loss of the 25-km fiber and the
attenuation. Note that the out-of-band ASE noise of the pump is filtered by BPF 3
(bandwidth: 1 nm), the output power of which is kept the same. Figure 4.5(b) depicts
the received slave comb pump power and the pump OSNR in the second
microresonator at different transmission losses. As the transmission loss is increased,
both the received pump power and the on-chip pump OSNR decrease. Interestingly,
when the pump OSNR is lower than ~23 dB, there is no low-phase-noise comb being
generated, consistent with the result in [84]. This finding may be attributed to the
36
stochastic intensity variations of the comb pump, which prevents the phase locking
between the pump and generated comb lines. The 23 dB OSNR tolerance of the pump
is specific to the microresonator we used in our experiment. Generally, the pump
OSNR tolerance for Kerr comb generation could depend on many other factors
including the Q factor, resonance detuning, and resonator dispersion. Nevertheless,
because the OSNR of the regenerated comb lines depends on the pump OSNR, it is
important for the slave pump to have a higher OSNR. In practical communication
systems, an OSNR about 21 dB is required to reach 1000 km for 200 Gb/s DP-16
QAM signals [102].
Figure 4.5 (a) The linewidths of both the master and slave comb 1 for back-to-back (B2B) and 25-km
fiber transmission. (b) The received pump power and pump OSNR in the second microresonator at
different transmission losses.
As mentioned above, the mutual coherence between the master and slave combs
can potentially enable the latter to serve as efficient LOs. This feature is further
estimated in a coherent receiver. For comparison purposes, the beat notes of the two
combs are also measured with the slave comb generated by an independent
unstabilized pump laser (linewidth: <300 kHz) instead of the selected master comb
line. Figure 4.6(a) and (b) show the corresponding RF spectrum and the zoom-in of
the 10
th
beat note. As can be seen, multiple peaks exist for each beat note because of
different frequency drifts of the two combs generated by two independent lasers. These
peaks also exist in the beat note of the received master comb line and an independent
1530 1535 1540 1545 1550
20
40
60
80
100
Wavelength (nm)
Linewdith (kHz)
Tx comb: B2B
Tx comb: 25km SMF
LO comb 1: B2B
LO comb 1: 25km SMF
(a)
1530 1535 1540 1545 1550
20
40
60
80
100
Wavelength (nm)
Linewdith (kHz)
Master comb: B2B
Master comb: 25km SMF
Slave comb 1: B2B
Slave comb 1: 25km SMF
Pump
Span: 10 MHz
24 26 28 30 32
-38
-34
-30
-26
-22
Received Pump Power (dB)
Transmission Loss (dB)
24 26 28 30 32
20
24
28
32
36
On-chip Pump OSNR (dB)
24 26 28 30 32
-38
-34
-30
-26
-22
Received Pump Power (dB)
Transmission Loss (dB)
24 26 28 30 32
20
24
28
32
36
On-chip Pump OSNR (dB)
Low-phase-noise comb
can be generated
No low-phase-noise comb
(b)
37
unstabilized laser with nearly the same wavelength. The frequency error (frequency
difference between the carrier and LO) is further measured when the regenerated comb
line and the independent unstabilized laser separately serve as the LO. Figure 4.6(c)
shows 30 counts of the frequency error in the two cases. In the former case, the
variation of the frequency error (Δf) is less than 5 MHz, which is about 16 times
smaller than that of the latter using the independent unstabilized laser as the LO. The
5 MHz variation of frequency error could be further decreased if both Kerr frequency
comb oscillators are stabilized [33]. These results demonstrate a certain level of
frequency locking between the master and slave combs, which might reduce the
complexity of digital signal processing in WDM coherent optical communications.
Figure 4.6 (a) and (b) are the RF spectrum and the zoom-in of the 10
th
beat note of the two combs with
the slave comb generated by an independent pump laser. (c) The frequency error at different counts of
the regenerated comb line and independent unstabilized laser separately serving as the LO.
0 5 10 15 20 25 30
-60
-40
-20
0
20
40
60
Counts
Frequency error - offset [MHz]
Free running laser as LO (offset: 70 MHz)
Comb line as LO (offset: 990 MHz)
Δf < 5 MHz
Δf < 80 MHz
(c)
0.8 1 1.2
-90
-80
-70
-60
-50
-40
Frequency (GHz)
Power (dBm)
1 1.1
-90
-80
-70
-60
-50
-40
Frequency (GHz)
Power (dBm)
(a) (b)
RBW: 30 kHz
38
4.5 Discussion and Conclusion
As mentioned in section 4.2, optical coherent detection is one potential
application of our experiment, where the data signals carried by the master comb lines
can be demodulated by using the regenerated slave comb lines as the LOs in the
receiver. In our case, the narrow-linewidth master and slave comb lines can potentially
allow ≥20 Gbaud data transmission using advanced modulation formats such as 16- or
64-QAM modulation [103]. Additionally, mutual coherence might be beneficial for
phase recovery in multichannel coherent detection. Therefore, an interesting and
important extension of this work would be to use the newly generated slave comb lines
as the LOs to coherently detect the data signals, which could enable sharing the phase
noise estimation among different data channels.
It should be noted that there could be an issue on the polarization of the pump
input to the remotely located microresonators. Although the polarization of the slave
pump can be optimized manually in the experiment, the polarization maintenance can
be more challenging for practical links in the field, which could limit the feasibility of
our approach. One potential solution for polarization maintenance is to use an active
fast polarization tracking system [104]. Moreover, in our experiment, we use one
master comb line to excite each individual slave comb. In the future, multiple comb
lines might be used to generate each slave comb. The potential of this approach to
enhance the phase and frequency locking between the master and slave combs needs
to be further studied.
In conclusion, we experimentally demonstrate multiple Kerr frequency comb
generation using different lines from another Kerr comb located up to 50 km away.
Different master comb lines after fiber propagation can be individually selected to
pump distinct microresonators to generate slave combs with different repetition rates.
An approximately 20-kHz linewidth can be obtained for the beat notes of the master
and remote slave combs. Furthermore, results show that the linewidths of the slave
comb lines almost remain the same as that of the master comb pump. A pump light
with an optical signal-to-noise ratio of beyond 23 dB is required for the slave comb
39
generation after transmission. When serving as local oscillators, the slave comb lines
have a smaller variation of frequency error than the comb lines that are generated by
an independent laser.
40
Chapter 5 Pump-linewidth-tolerant Wavelength
Multicasting Using Soliton Kerr Frequency Comb
5.1 Introduction
It is known that different operating regimes have been observed throughout the
formation of Kerr frequency combs by detuning the pump wavelength and power,
including primary combs, chaotic combs, and soliton combs. Of particular interest are
dissipative Kerr soliton combs, which represent a pulsed waveform that maintains its
shape in the time domain leading to a smooth spectral envelope with broad bandwidth.
The inherently low phase noise of soliton combs may serve as mutually coherent light
sources for a number of applications in all-optical signal processing and network
functions, among which is wavelength multicasting that replicates data information to
multiple selected destination wavelengths [53, 105].
Recently, pump-linewidth-tolerant wavelength conversion for high-order QAM
signals, which are sensitive to phase noise, has been reported using two coherent
pumps [106]. Though such a design has been shown to suppress the phase noise
transformation from the pumps to multicast signals, it could be difficult to
simultaneously generate multiple coherent pumps. As such, it might be interesting to
explore the broadband and mutually coherent soliton Kerr combs for pump-linewidth-
tolerant wavelength multicasting.
In this chapter, we experimentally demonstrate pump-linewidth-tolerant
wavelength multicasting using coherent soliton Kerr frequency combs generated in a
microresonator. When the linewidth of the comb pump changes from 100 kHz to 1
MHz, the linewidth of the multicast signal remains relatively unchanged with coherent
Kerr comb lines serving as the pumps in a periodically poled lithium niobate
waveguide while using a free-running (FR) laser as the dummy pump gives rise to a
significantly broadened signal copy. Eight-fold error-free multicasting of 10 Gbaud
16- QAM signals is achieved even when the linewidths of coherent Kerr combs are
41
broadened to 1 MHz (no Kalman filtering (KF) algorithm in the coherent receiver). In
contrast, if the FR laser is used as the pump and KF algorithm is not applied, the EVM
performance of the converted signal dramatically degrades due to severe phase noise.
These results demonstrate the potential of exploiting the broadband phase-locked Kerr
frequency combs for pump-linewidth-tolerant wavelength multicasting [107].
5.2 Concept of Pump-linewidth-tolerant Wavelength
Multicasting based on Coherent Kerr Comb
The concept of pump-linewidth-tolerant wavelength multicasting based on
coherent Kerr combs is illustrated in Figure 5.1. When the pump of the Kerr comb and
the signal are placed symmetrically around the quasi-phase matching (QPM)
wavelength of a PPLN waveguide, multicast signals are simultaneously generated
through the cascaded sum frequency generation and difference frequency generation
in the χ
(2)
nonlinear process of PPLN with Kerr comb lines functioning as dummy
pumps (DPs) . The generated signals at ωsi and the DPs at ωdi are also symmetrically
located with respect to the QPM, and the spacing between signal copies equals the
spacing of the comb lines. The corresponding phase of i-th multicast signal is given
by Eq. (1) in Figure 5.1, in which Φs, Φsi, ΔΦp, ΔΦdi, and Φ are the phases of the input
signal and output signal, the phase noise of the pump and the i-th dummy pump, and
a constant term, respectively. In the conventional multicasting scheme, there is no
phase relationship between the main and FR dummy pumps. Thus, their phase noise
difference (ΔΦpump) is transferred to the signal copy and increases its linewidth.
However, when the generated comb lines serve as the dummy pumps, phase noise
from pumps (ΔΦpump) theoretically cancels out due to the mutual coherence between
Kerr comb lines and the comb pump that has excited the comb. This process introduces
no phase noise from the pumps to multicast signals. To differentiate between the two
cases (i.e. a comb line or an FR laser as the dummy pump), the generated signal is
denoted as multicast or converted signal, respectively.
42
Figure 5.1 The concept of pump-linewidth-tolerant wavelength multicasting based on coherent Kerr
frequency comb.
5.3 Demonstration of Pump-linewidth-tolerant Wavelength
Multicasting
Kerr frequency comb is generated in a silicon nitride microresonator through
parametric four-wave mixing. The resonator is pumped with 1555.6 nm light in the
anomalous dispersion region. The corresponding quality factor of the resonator cavity
is 1.3 × 10
6
and the FSR is approximately 192 GHz. Figure 5.2 shows the schematic
of the experimental setup. The narrow-linewidth (<100 kHz) continuous-wave output
of an external cavity diode laser, serving as the pump, is phase-modulated to broaden
its linewidth (Δυ) through an IQ modulator driven by the arbitrary waveform generator.
The phase noise is digitally generated by assuming a Wiener process. The broadened
pump is amplified by a high-power EDFA and the out-of-band noise is filtered by a
BPF. Next, the pump is coupled to the microresonator through the lensed fiber. At the
output of the chip, an FBG is used to attenuate the remaining CW pump by 25 dB.
Signal
λ
c1
λ λ
d1
λ
p
λ
s
C
1
Kerr comb lines
QPM
DFG
SFG
Phase locked
C
2
C
3
λ
d2
λ
d3
λ
c2
λ
c3
d
1
d
2
d
3
Comb
pump
Phase noise of multicast copies from the pumps
𝜙 𝑠
= 𝜙 𝑠 + ∆𝜙
− ∆𝜙
--- Eq (1)
∆𝜙 𝑠 = ∆𝜙
− ∆𝜙
=1 2 --- Eq (2)
Dummy
pump (di)
Comb line FR laser
∆𝜙 𝑠 = 0 ∆𝜙 𝑠 ≠ 0
FR laser: free-running laser
43
Figure 5.2 Experimental setup for pump-linewidth-tolerant wavelength multicasting based on coherent
Kerr frequency comb.
Figure 5.3(a) and (b) show the optical spectrum of a single-soliton Kerr comb
and its spectrum across C-band, respectively. The corresponding autocorrelation trace
of the single-soliton pulse is shown in Figure 5.3(c). The spectrum of the soliton combs
covers a bandwidth of 250 nm and has a smooth envelope. Through the use of a tunable
optical filter (TOF), the comb pump and the eight generated consecutive comb lines
from 1557.2-1568.4 nm are extracted and combined with the signal before they enter
the PPLN. The input signal is generated by modulating an external cavity laser (ECL
linewidth: ~30 kHz) with 16-QAM at 10 Gbaud. It should be noted that, when
measuring the linewidth of multicast signals, the output of the signal laser (ECL) is
connected to the upper path without being modulated. Figure 5.3(d) represents the
optical spectrum at the PPLN output. As displayed in Figure 5.3(d), eight copies of the
modulated signals from 1533.4-1544.2 nm are generated when eight comb lines on the
right side of the comb pump serve as the DPs. A local oscillator in a coherent receiver
allows proper demodulation of multicast signals and the EVM measurements are
performed. For comparison purposes, when the TOF is tuned to extract only the comb
pump, a narrow-linewidth (<10 kHz) FR ECL replacing comb line 1 (i.e. 1557.2 nm)
is turned on and sent to the PPLN with the comb pump and modulated signal. The
EDFA
Isolator PC LF Resonator
IQ Modulator ECDL
AWG
PC
BPF
IQ modulator
ECL PC
EDFA
TOF
Coherent
Receiver
BPF EDFA
BPF
Pump
broadening
AFG
Free-running
pump laser
PPLN
BPF EDFA
Signal laser
ECL
off
on
λ
λ λ
λ λ
λ
1545.8 nm
1557.2 nm
QPM QPM
44
corresponding spectrum at the PPLN output is shown in Figure 5.3(e), which shows
that merely one copy is generated at the wavelength of 1544.2 nm.
Figure 5.3 (a) The optical spectrum of single-soliton Kerr combs and (b) its spectrum across C-band.
(c) The autocorrelation trace of a single-soliton pulse. The optical spectrum at the PPLN output when
(d) eight Kerr comb lines are used or when (e) the free-running ECL is used to generate multicast signals
or converted signal.
To verify the linewidth or phase noise preservation when soliton Kerr combs
serve as coherent pumps, the linewidth of the multicast signal is measured using the
self-heterodyne approach. The linewidth emulation of the semiconductor lasers is used
to broaden the linewidth of the Kerr comb pump from 100 kHz to 1 MHz, which also
increases the linewidths of the corresponding comb lines due to their linear
dependence on the pump linewidth in the phase-locked state [74]. Figure 5.4(a) and
(a)
(d)
(e)
1530 1540 1550 1560 1570
-60
-40
-20
0
Wavelength (nm)
Power [dBm]
1545 1550 1555
-60
-40
-20
0
Wavelength (nm)
Power [dBm]
1450 1500 1550 1600 1650 1700
-60
-40
-20
Power (dBm)
Wavelength (nm)
FSR = ~192 GHz
(b)
1530 1540 1550 1560
-60
-40
-20
Power (dBm)
Wavelength (nm)
Comb pump Signal
s1 s8
d8 d1
(c)
Signal
Comb pump
d1
c1
dip
dip
Multicast
signals
Comb lines
Converted
signal
FR ECL
-5 0 5
0
0.5
1
Delay (ps)
Intensity (a.u.)
5.2 ps
45
(b) show the experimentally measured normalized power spectrum density of the
signal laser and multicast signal 1 (labeled s1 in Figure 5.3(d)) as well as the
corresponding fittings of Lorentzian shaped spectrum when the comb pump is
broadened to 1 MHz. The linewidth of multicast signal 1 as a function of the comb
pump linewidth is shown in Figure 5.4(c). It is shown that the linewidth of multicast
signal 1 almost remains the same as that of the signal laser, virtually independent of
that the comb lines and comb pump. However, when the FR ECL is used as the dummy
pump and the comb pump is broadened to 1 MHz, the linewidth of the converted signal
(labeled c1 in Figure 5.3(e)) significantly increases to 1.2 MHz as shown in Figure
5.4(d).
Figure 5.4 (a) and (b) The experimentally measured normalized power spectrum density (PSD) of the
signal laser and multicast signal 1. (c) The linewidth (LW) of multicast signal 1 almost stay unchanged
at different comb pump linewidths. (d) The normalized PSD of the converted signal.
585 590 595
-50
-40
-30
-20
-10
0
10
Normalized amplitude [dB]
Frequency [MHz]
Field spectrum
Lorentzian fit
585 590 595
-50
-40
-30
-20
-10
0
10
Normalized amplitude [dB]
Frequency [MHz]
Field spectrum
Lorentzian fit
0 200 400 600 800 1000
20
25
30
35
40
Linewidth of multicasted signal (kHz)
Kerr comb pump linewidth (kHz)
(a)
(b)
(c)
(d)
LW = ~30 kHz LW = ~30 kHz
585 590 595
-50
-40
-30
-20
-10
0
10
Normalized amplitude [dB]
Frequency [MHz]
Field spectrum
Lorentzian fit LW = ~1.2 MHz
0 0
0
Span = 10 MHz Span = 10 MHz
Span = 10 MHz
Pump linewidth
46
In a high bit-rate communication experiment, when the signal laser is modulated
with 16-QAM data at 10 Gbaud, eight-fold multicasting is demonstrated with the
linewidth of Kerr combs equalling 1 MHz. As mentioned in the experimental setup,
the comb pump and the eight consecutive lines of the soliton combs are selected and
then sent into the PPLN waveguide along with the modulated signal. At the PPLN
output, eight signal copies are generated, which can be seen in Figure 5.3(d). The
conversion efficiency of the PPLN waveguide, defined as the power difference
between the comb line and the corresponding multicast signal, is estimated to be -13.5
dB. Thus, the EVM performance of eight multicast signals are measured with and
without the KF algorithm, which normally is used to mitigate the effect of phase noise.
In both cases, the results presented in Figure 5.5(a) show that all EVMs of comb-
generated multicast signals are lower than the EVM-limit (11.1%) for error-free
detection using the second-generation FEC [90].
The EVM performance of multicast signal 1 (s1) and converted signal 1 (c1)
separately generated by comb line 1 and FR ECL as the DP is further investigated at
different comb pump linewidths. As displayed in Figure 5.5(b), due to the phase noise
mitigation of the KF algorithm, the EVM change is less than 0.2% at different comb
pump linewidths for both cases. However, when the KF algorithm is not applied,
Figure 5.5(c) shows that the EVM performance of the converted signal strongly
degrades as the comb pump linewidth increases. The corresponding constellation at
the comb pump linewidth of 500 kHz is shown in the inset, in which significant
spreading of symbols is clearly seen. On the contrary, there is only slight increase of
the EVM of multicast signal 1 when using the comb line as DP. This slight EVM
increase might result from the imperfect phase noise cancellation at large pump
linewidths. Although the KF algorithm could reduce the effect of phase noise in the
experiment, it is of significance to leverage on the use of pump-linewidth-tolerant
wavelength multicasting for higher-order QAM signals, which are more sensitive to
phase noise.
47
Figure 5.5 (a) The EVM performance of eight multicast signals with (w/) and without (w/o) Kalman
filtering (KF) algorithm when coherent Kerr combs are used as pumps. The EVM performance of the
multicast signal 1 and converted signal 1 at different comb pump linewidths (b) with (w/) and (c)
without (w/o) the KF algorithm in the receiver.
In addition, when the signal laser is modulated with 64-QAM data at 20 Gbaud,
three-fold multicasting is demonstrated without broadening the linewidth of Kerr
combs. Figure 5.6(a) shows the constellations as well as the measured EVM and BER
(after equalization) for the original 64-QAM signal and its multicast copies. All three
multicast copies can achieve an EVM of around 5.3% and a BER (<= 3.5 x 10
-3
) lower
than the FEC threshold with 7% overhead, indicating the post-FEC error-free
performance. However, because of the loss induced in the wavelength conversion, the
noise level of the copies is slightly increased after the amplification at the receiver,
which results in higher BER compared to that of the original signal. Figure 5.6(b) and
(c) show the measured EVMs and BERs at different OSNR, respectively. Both the
EVM and BER performances show less than 0.5-dB OSNR penalty difference between
0 200 400 600 800 1000
8
10
12
14
16
18
Comb pump linewidth (kHz)
EVM (%)
Multicast signal 1 w/ KF
Converted signal 1 w/ KF
(b)
0 200 400 600 800 1000
8
10
12
14
16
18
Comb pump linewidth (kHz)
EVM (%)
Multicast signal 1 w/o KF
Converted signal 1 w/o KF
(c)
0 2 4 6 8
6
8
10
12
14
16
18
Channel Number
EVM (%)
Multicast signals w/ KF
Multicast signals w/o KF
11.1 %
(a)
48
the original data signal and the multicast copies. Note that the EVM or BER at certain
OSNR is slightly degraded because of the filtering effect of the narrow bandwidth
filter at the receiver. Besides, compared to the theoretical curve, there is large OSNR
penalty, which could be caused by the imperfect performance of the equipment and
non-optimal DSP algorithms in the receiver. These results demonstrate that there is
little signal distortion in the wavelength multicasting.
Figure 5.6. System performance of the original signal and multicast copies (a) The constellations as
well as the measured EVM and BER. (b) EVM and BER as a function of the OSNR.
5.4 Conclusion
To sum up, we experimentally demonstrate pump-linewidth-tolerant wavelength
multicasting using soliton Kerr frequency combs. When Kerr comb linewidths are
broadened to 1 MHz, the linewidth of the signal copy almost remains that of the
1549.3 nm
EVM: 5.23%,
BER = 3.1E-3
Signal
1547.7 nm
EVM: 5.32%,
BER = 3.4E-3
1546.2 nm
EVM: 5.27%,
BER = 3.3E-3
1544.7 nm
EVM: 5.40%,
BER = 3.5E-3
C1 C2 C3
(a)
FEC threshold
(b)
49
original signal and error-free eight-fold multicasting of 10 Gbaud 16-QAM signals is
achieved without applying KF algorithm for carrier phase recovery. In addition, we
also demonstrate three-fold wavelength multicasting of a 20-Gbaud, 64-QAM signal.
All three multicast copies can have a BER of ~3.5x10
-3
, which is lower than the FEC
threshold. The EVM and BER show less than 0.5-dB penalty difference between the
signal and multicast copies.
50
Chapter 6 Scalable and Reconfigurable Optical
Tapped-delay-line for Multichannel Optical Signal
Processing with a Kerr Frequency Comb
6.1 Introduction
Tapped-delay-lines (TDL) are fundamental building blocks for various signal-
processing functions, such as equalization and correlation [108-110]. If a signal is in
the optical domain, it may be advantageous to perform these functions optically,
considering the potential of having higher processing speeds and avoiding inefficient
optical-to-electrical-to-optical conversion [111-114]. One approach to achieve a
reconfigurable optical TDL is to multicast a signal onto different wavelengths in a
nonlinear element [115], differentially delay these copies [116], and multiplex the
copies together onto a single output wavelength in a second nonlinear element [117].
Important goals for a reconfigurable optical TDL include: (a) efficiently processing
multiple data channels within a single optical element, (b) performing independent
signal processing functions on different wavelength channels, and (c) enabling an
approach that is scalable to more taps, channels, and functions.
Previously, it was reported that multiple channels can be processed
simultaneously with different functions [118]. However, that approach used discrete
pump lasers and was not efficiently scalable in terms of the number of taps, since the
number of taps corresponded to a linear increase in the number of required processing
stages. There is the possibility of utilizing the unique features of optical frequency
combs to potentially achieve the above goals. For example, integrated microresonators
have been shown to produce Kerr frequency combs with large comb spacing, a broad
spectrum, and low noise. Comb lines have been shown to be usable as sources for
optical signals, and the mutual coherence of different comb lines can be utilized for
efficient wave mixing in nonlinear signal-processing elements. We explore using such
51
combs to address the challenge of a scalable optical TDL for processing multiple
channels with different functions.
In this chapter, we experimentally demonstrate a scalable and reconfigurable
optical TDL for multichannel equalization and correlation of 20-Gbaud QPSK signals
using nonlinear wave mixing and a soliton Kerr frequency comb. There are mainly
two stages for the optical TDL: one is multicasting of the input signals in a periodically
poled lithium niobate waveguide with Kerr comb lines serving as coherent pumps, and
the other is coherent multiplexing of the delayed and weighted signal replicas in
another PPLN. The tap number of the optical TDL depends on the number of multicast
copies. We show that such an optical TDL with two- or three- taps can simultaneously
reduce the EVM of a distorted QPSK signal from 22.5% to either 19.9% or 18.2%
after equalization, as well as search two- or three-symbol patterns on another QPSK
signal [119].
6.2 Concept of Optical TDL for Multichannel Signal Processing
The concepts for an optical TDL using the prior [118] and proposed [119]
approaches to achieve independent multichannel signal processing are illustrated in
Figure 6.1. Figure 6.1(a) shows the prior method, in which k stages are required to
achieve N-channel processing with k taps. In each stage, N-channel signals are firstly
wavelength converted in a nonlinear medium (e.g., PPLN). A relative delay is then
induced between each signal and its replica through a dispersive element, along with
the amplitude/phase adjustment in a liquid crystal on silicon filter [120]. This stage in
the prior method functions as a “tap” building block and the number of taps
corresponds to the number of stages, which is not particularly scalable.
In our proposed approach shown in Figure 6.1(b): (i) only two stages (i.e.,
multicasting and multiplexing) are needed to simultaneously and independently
process multiple signals, (ii) the number of taps corresponds to the number of multicast
copies in the nonlinear elements. The Kerr frequency comb lines, with a large comb
spacing, are exploited as mutually coherent pumps in both stages. At the first stage,
52
when the input signals and one comb line are placed symmetrically around the QPM
wavelength of a PPLN waveguide, the k-1 replicas for all signals are generated through
the sum and difference frequency generation with other comb lines serving as dummy
pumps [57]. Then, the signals and their replicas are sent through a dispersive element
to induce relative delays. The complex weights to achieve different functions are
applied using an LCoS filter, which can adjust the amplitude/phase of different taps.
At the second stage, these weighted and delayed signal copies are coherently
multiplexed together onto the corresponding wavelengths in a similar PPLN. Note that
the Kerr comb pump is efficiently reused as another pump during the multiplexing
stage. Therefore, different optical processing functions can be simultaneously and
independently performed on different individual channels, including equalization and
correlation. The realization of either an individual equalizer or a coherent correlator is
explained in detail in [117, 118].
Figure 6.1(a) Concept of an optical TDL for independent multichannel signal processing using (a) k
stages and (b) two stages to generate k taps. QPM: quasi-phase matching; SFG: sum frequency
generation; DFG: difference frequency generation.
Prior approach
N-channel processes with K taps 1 2 1’ 2’
λ
s1
λ
s2
λ
sn
λ
s1
λ
s2
λ
sn
k fold N channel
multicasting, delay,
amplitude/phase adjust
k fold N channel
multiplexing
A B
C
D
Pattern symbol
Equalization
N-channel processes with K taps
Input Data Channels
Processed Data Output
1 2 1’ 2’
λ
s1
λ
s2
λ
sn
λ
s1
λ
s2
λ
sn
N λ-conversion
delay, amplitude
/phase adjust
N
1st stage 2nd stage kth stage
N’
N’
N
(a)
(b)
1st stage
2nd stage
Distorted
signal
N λ-conversion
delay, amplitude
/phase adjust
N λ-conversion
delay, amplitude
/phase adjust
Correlation
Proposed approach
Kerr comb lines
QPM
SFG
Copies
DFG
Outputs
Signals
Pump
53
6.3 Demonstration of Optical TDL for Equalization and
Correlation
The experimental setup for the demonstration of multichannel signal processing
using an optical TDL is depicted in Figure 6.2. Two narrow-linewidth external cavity
lasers (1&2) spaced by 50 GHz are used as light sources to carry data channels. The
output of each laser is individually modulated with a 20-Gbaud QPSK signal generated
by either an AWG or a bit pattern generator. Ch1 signal from the AWG output is
digitally distorted with a chromatic dispersion equaling to a propagation of 15-km
SMF. The two channels are then combined together and sent into PPLN 1 with three
Kerr comb lines ranging from 1551.2 to 1554.4 nm. These comb lines are generated
through cascaded four-wave mixing by pumping a silicon nitride microresonator via a
CW light at 1557.5 nm. The generated comb lines are separated from the high-power
comb pump by a tunable fiber Bragg grating, and the three lines are selected by a
tunable optical filter. Two multicast copies are created for each of the two channels in
PPLN 1 and the output of PPLN 1 is sent to the LCoS filter, which can independently
adjust the amplitude/phase of the multicast copies for both channels. The relative delay
between different taps is added by passing through a 200-m dispersion compensation
fiber (D = ~160 ps/nm/km). The signals, the weighted and delayed multicast copies as
well as the comb lines are amplified again before being injected into PPLN 2 with the
Kerr comb pump. The signals and their delayed copies are coherently multiplexed
together through the cascaded SFG & DFG in the χ2 nonlinear wave mixing. The
output multiplexed signals at λMux1 and λMux2 are individually extracted by a narrow-
band filter (BW: 0.4 nm) and demodulated in a coherent receiver.
54
Figure 6.2 Experimental setup for multichannel signal processing using an optical TDL. AWG: arbitrary
waveform generator; BPG: bit pattern generator; FBG: fiber Bragg grating; TOF: tunable optical filter;
DCF: dispersion compensation fiber.
Figure 6.3(a) shows the full optical spectrum of the single-soliton comb, which
has a wide spectrum of around 250 nm and exhibits a sech
2
shape (Res: 0.1 nm). The
inset is the autocorrelation trace of the soliton pulse, which has a pulse duration of ~5.2
ps corresponding to a repetition rate of ~192.0 GHz. Figure 6.3(b) presents the output
spectrum of PPLN 1. The two multicast copies are created at wavelengths in symmetry
to the corresponding comb line 2&3 with respect to the QPM, and the spacing between
them equals the comb spacing. The conversion efficiency of PPLN 1, defined as the
power difference between the signal and the multicast copies, is approximately -14 dB.
The spectra of PPLN 2 output with two or three taps are shown in Figure 6.3(c) and (d),
respectively. By applying different weights and delays on different taps, the outputs for
the two- or three-tap equalization (Ch1) and correlation (Ch2) are simultaneously
generated at around 1542.1 and 1542.5 nm.
It should be noted that the number of input channels that can be accommodated
will be limited by the wavelength range of efficient wavelength conversion of the PPLN.
Moreover, the aggregate spectrum of the input signals should be smaller than the
frequency comb spacing in order to avoid spectrum overlap among the taps of the
different input signals. However, if the aggregate spectrum of the input signals is larger
PPLN 1
Coherent
Receiver
BPF4 EDFA
EDFA BPF1
μResonator
Kerr comb
TOF BPF2 EDFA
λ
DCF
(~200 m)
LCoS
Filter
PPLN 2
FBG
λ
λ
IQ modulator
Laser 2
BPG
Ch2
IQ modulator Laser 1
PC
AWG
Ch1
EDFA BPF3
QPM
Kerr comb pump
1548.1 nm
1548.5 nm
PPLN 1 output
QPM
PPLN 2 output
λ
Mux1 λ
Mux2
Signals
Copies Comb lines
55
than the comb spacing, the prior approach in [118] might exhibit certain
implementation advantages. In addition, the number of possible taps could be limited
by the wavelength range of the PPLN device, which is around 20 nm.
Figure 6.3 (a) Optical spectrum of a single-soliton Kerr comb. The inset is the autocorrelation trace. (b)
The output spectrum of PPLN 1. (c, d) The spectra of PPLN 2 output with two or three taps. Eq.:
equalization; Cor.: correlation.
The equalization on Ch1 and the correlation on Ch2 are simultaneously and
independently implemented in the experiment. The performance of the two- or three-
tap optical equalization is illustrated in Figure 6.4. Figure 6.4(a1-a4) show the in-phase
and quadrature (IQ) constellation diagrams of a distorted input data signal of Ch1 and
the output signals of Ch1 after one-, two- or three-tap equalization, respectively.
Chromatic dispersion of ~15-km SMF propagation is digitally added to the data signal
in Figure 6.4(a1). The EVM of the distorted data signal is 22.5%, which can be reduced
to 19.9% or 18.2% following the two- or three-tap equalization. Note that the
degradation on the one-tap output results from the system penalty as no equalization
has been actually implemented. The equalization performance and EVM reduction of
the optical TDL will depend on several factors, including the number of taps and the
nonlinear conversion efficiency. We note that there could be a BER system power
1500 1550 1600 1650
Power (20 dB/Div)
Wavelength (nm)
Pump: 1557.5 nm
Res: 0.1 nm
(a)
(b)
1540 1545 1550 1555 1560
-40
-20
0
20
Power (dBm)
Wavelength (nm)
PPLN 1
output
1 2 3 Comb lines
Copies
Signals
1540 1545 1550 1555 1560
-60
-40
-20
0
Power (dBm)
Wavelength (nm)
PPLN 2
output
2 taps
Eq. & Cor.
Suppressed
Comb
pump
(c)
1540 1545 1550 1555 1560
-60
-40
-20
0
Power (dBm)
Wavelength (nm)
PPLN 2
output
3 taps
Comb
pump
(d)
Comb spacing:
~192 GHz
Eq. & Cor.
-5 0 5
0
0.5
1
Delay (ps)
Intensity (a.u.)
R
in
g
~5.2 ps
56
penalty due to the PPLN properties, e.g., limited conversion efficiency of -14 dB or
limited wavelength range of ~20 nm.
Figure 6.4 (a1-a4) show the in-phase and quadrature (IQ) constellation diagrams of Ch1 input signal
and the output Ch1 signals after the two- or three-tap equalization.
In addition, the results of the coherent correlation with two or three taps are shown
in Figure 6.5. Figure 6.5(a) shows the constellation diagrams of Ch2 input, which has
an EVM of 13.5%. The 9-QAM constellation with an EVM of 9.41% in Figure 6.5(b)
is the 2-tap correlator output, and the target pattern [A B] appears on the top-right corner.
For the output of the three-tap correlator, the target pattern [A B C] and [A B D] are
shown in the 16-QAM with an EVM of 9.38% and 9.42%, respectively (Figure 6.5(c1)
and (d1)). The correlation peaks (level 1) corresponding to the two matched patterns on
1000 QPSK symbols are depicted in Figure 6.5(c2) and (d2).
EVM: 22.5% EVM: 19.9% EVM: 18.2% (a1) (a2) (a3) (a4) EVM: 23.2%
Equalized signal
with 1 tap
Distorted signal
Equalized signal
with 2 taps
Equalized signal
with 3 taps
57
Figure 6.5 (a) The constellation diagrams of Ch2 input symbols. (b) Two-tap correlation outputs and
the correlation peaks corresponding to matched patterns [A B]. (c, d) Three-tap correlation outputs and
the correlation peaks corresponding to matched patterns [A B C] and [A B D].
6.4 Discussion and Conclusion
The proposed optical TDL can potentially achieve in-line processing of multiple
independent data channels. However, a key issue for further study is the power-
consumption scaling of this optical approach compared to systems based on electrical
signal processing, especially when operating at ≥100 Gbit/s per channel.
Input Signal
EVM: 13.5 %
-1 0 1
-1
0
1
A = 1+j B = -1+j
C = -1-j D = 1-j
(a)
-1 -0.5 0 0.5 1
-1
-0.5
0
0.5
1
EVM: 9.41 %
(b1)
0 200 400 600 800 1000
0
1
Peak Level (a.u.)
Symbol
Pattern: [A B]
(b2)
-1 -0.5 0 0.5 1
-1
-0.5
0
0.5
1
EVM: 9.38 %
(c1)
0 200 400 600 800 1000
0
1
Peak Level (a.u.)
Symbol
Pattern: [A B C]
(d1) (d2)
EVM: 9.42 %
(c2)
0 200 400 600 800 1000
0
1
Peak Level (a.u.)
Symbol
-1 -0.5 0 0.5 1
-1
-0.5
0
0.5
1
Pattern: [A B D]
Matched
Matched
Matched
58
To sum up, we experimentally demonstrate a scalable and reconfigurable optical
TDL for multichannel equalization and correlation of 20-Gbaud QPSK signals using
nonlinear wave mixing and a microresonator Kerr frequency comb. The optical TDL
mainly consists of two stages: one being a multicasting of the original signals in a
PPLN waveguide with Kerr comb lines functioning as mutually coherent pumps, while
the other is a coherent multiplexing of the delayed and weighted signal replicas in a
second PPLN. A two- or three-tap optical TDL is demonstrated to simultaneously
equalize a distorted QPSK data signal, reducing the EVM from 22.5% to either 19.9%
or 18.2%, and search two- or three-symbol patterns on another QPSK signal.
59
Chapter 7 Deterministic Generation of a
Controllable Breathing Soliton by a Second Pump
or Pump Modulation
7.1 Introduction
There are different operating regimes of Kerr combs depending on the pump
conditions [27, 29, 31]. Of interest are temporal cavity soliton combs, which have
pulsed waveforms in the time domain due to the balance between dispersion and Kerr
nonlinearity [32, 37]. These soliton combs are relatively stable and exhibit a fairly
uniform and predictable spectral envelope. Apart from the stable solitons, “breathing”
solitons in microresonators have recently been reported [40-42]. Once a stable soliton
state is achieved, the breathing soliton can be excited by fine tuning the pump
wavelength or power. Importantly, the breather exhibits a temporal periodic oscillation
that induces additional lines (sidebands) around soliton comb lines. The newly created
sidebands might be exploited for certain applications [121].
However, the characteristics of breathing soliton depend on the microresonator
properties. The breathing frequency and amplitude could be fluctuating for the
breathers excited by tuning the pump wavelength [40-42]. Therefore, it might be
beneficial for potential applications if the generation of breathing solitons can be more
controllable and deterministic.
In this chapter, we experimentally demonstrate two approaches in which the
sidebands of the breathing soliton can be controllably and deterministically produced.
The breathing soliton is excited by either injecting a second pump at the soliton
resonance or modulating the CW pump over a wide range of RF frequencies. Similar
breathing behavior is observed for both approaches. When implementing the second
approach, we have found the breathing amplitude increases almost linearly at low RF
signal power and saturates at high RF signal power. The breathing amplitude reaches
60
the maximum when the RF modulation frequency is close to the breathing frequency
of “native” breathers generated by tuning the CW pump wavelength. Numerical
simulations on the generation of breathing solitons agree with the experimental
observations.
7.2 Deterministic Generation of a Controllable Breathing Soliton
The two approaches to generate a controllable breathing soliton by (i) injecting
a second pump or (ii) modulating the CW pump are depicted in Figure 7.1 [121, 122].
In Figure 7.1(a), when a stable soliton circulates in a microresonator, a breathing
soliton can be excited by injecting a second pump around the soliton resonance.
Through changing the second pump wavelength and power, the breathing frequency
and amplitude can be tuned. Moreover, a breathing soliton can also be generated by
modulating the CW pump before it is coupled into the chip (Figure 7.1(b)). Since the
breathing soliton is excited by modulating the pump with an RF sine wave instead of
by tuning the pump wavelength, the breathing frequency and amplitude can be
determined by the corresponding RF modulation signal.
Figure 7.1 The two approaches to generate a controllable breathing soliton by injecting a second pump
or modulating the CW pump. CW: continuous-wave; Mod.: modulation.
μResonator
(a)
CW
laser I
CW
laser II
λ
λ
λ
Controllable
breathing solitons
Deterministic breathing
frequency & amplitude
Optical
amplifier
Pump modulation
Signal
generator
λ λ
f
s
Intensity
Mod.
μResonator
λ
Deterministic breathing
frequency & amplitude
Controllable
breathing solitons
CW
laser
(b)
Optical
amplifier
61
7.3 Experimental Results
The experimental setup to demonstrate the generation of a controllable breathing
soliton by injecting a second pump is illustrated in Figure 7.2. Two external cavity
diode lasers serve as two CW pumps for Microresonator I. They are separately
amplified by high-power EDFAs and then combined by an optical coupler before
being coupled into the resonator. The microresonator made of a Si3N4 waveguide is
pumped by ~1553.4 nm light (ECDL 1) in the anomalous dispersion region. The
corresponding quality (Q) factor of the resonator and the cavity linewidth are 1.3 x 10
6
and 150 MHz, respectively. At first, when Pump I is controlled by the arbitrary
function generator to generate the single-soliton comb, Pump II power should be kept
low. As the cavity exhibits the double-resonance feature in the soliton state [85], the
wavelength of Pump II (~1543.86 nm) can be finely tuned around the soliton
resonance, and the generation of sidebands can be observed with higher Pump II
power. The output of the generated breathing soliton is sent to a fiber Bragg grating to
suppress the strong pump line. The optical spectra are measured by a conventional
OSA with 12.5-GHz (0.1 nm) resolution as well as a high-resolution OSA (Res: 100
MHz) to resolve the sidebands. In addition, the output breathing soliton is sent to a 5-
GHz photodiode which is connected to an electrical spectrum analyzer for RF
spectrum measurement.
Figure 7.2(b) is the optical spectrum of the generated single soliton along with
Pump II. The soliton has a broad span of 250 nm and exhibits a sech
2
shape. The inset
is the autocorrelation trace of the soliton with a pulse separation of ~5.2 ps, which
corresponds to a repetition rate of ~191.88 GHz. The zoom-in spectrum of Pump II
located at the soliton resonance of the comb line at 1543.85 nm is shown in Figure
7.2(c) with a resolution of 100 MHz. The zoom-in spectra of Kerr comb lines at
1540.81 and 1559.28 nm are shown in Figure 7.3(a). It can be seen that different orders
of sidebands are generated asymmetrically around these two comb lines, which occurs
at other Kerr comb lines as well. The power of the sidebands decreases when they are
away from the main Kerr comb line. Note that Pump II can also be placed around the
62
soliton resonance of different soliton comb lines to excite the sidebands. However,
these sidebands exhibit the highest power when the second pump is located at the
soliton resonance. Figure 7.3(b) shows the RF spectrum of the breathing soliton, which
exhibits a similar low noise floor to that in the stable soliton state. The spacing of the
sidebands is ~500 MHz. Multiple peaks can exist in the RF spectral lines, indicating
that the sidebands are not phase-locked with the main comb lines. The effect of Pump
II power on the sidebands is also studied, as shown in Figure 7.3(c). The power of the
1
st
sideband almost grows linearly with Pump II power, which applies to other
sidebands. As Pump II power becomes rather high (>14 dBm) in the experiment, sub-
teeth could be observed (Figure 7.3(d)) in the middle of the sidebands, which could be
related to the double period in the time domain [85]. The corresponding RF spectrum
is shown in Figure 7.3(e). The soliton eventually disappears, as do the sidebands at
high Pump II power.
Figure 7.2 (a) Experimental setup to demonstrate the deterministic generation of a breathing soliton by
injecting a second pump. (b) Optical spectrum of the single soliton along with Pump II. (c) Zoom-in
spectrum of Pump II located at the soliton resonance of the comb line at 1543.85 nm.
ECDL1 EDFA BPF
AFG
EDFA BPF ECDL2
PC
PC
FBG
High res.
OSA
PD ESA
OSA
μResonator I
(a)
1543.84
Pump 2 Comb line
Res:100 MHz
(b)
(c)
Pump 1
Pump 2
Delay (ps)
Intensity(a.u)
Power (dBm)
Res: 0.1 nm
63
Figure 7.3 (a) Zoom-in spectra of comb lines at 1540.81 and 1559.28 nm from the high-res. OSA. (b)
RF spectrum of the breathing soliton. (c) 1
st
sideband power (labeled in Figure 7.3(a)) as a function of
Pump II power. (d, e) The spectrum of the comb line (1540.81 nm) under period doubling and the
corresponding RF spectrum.
We further investigate the deterministic generation of a breathing soliton by
modulating the CW pump. Figure 7.4(a) shows the corresponding experimental setup.
The output of an ECDL (1554.95 nm) is sent to an intensity modulator driven by an
800 MHz RF sinusoidal signal. The modulated pump is amplified and filtered by a
bandpass filter with a bandwidth of 15 nm before being coupled into the chip.
Similarly, when cavity solitons are generated by sweeping the pump wavelength, the
RF modulation signal power should be kept low at first. The generated breathing
soliton is characterized by measuring its optical and electrical spectra as well. Note
that the 15-nm filter instead of a narrow one is used to increase the overall power on
chip including the out-of-band ASE noise. Microresonator II, with different coupling
between the straight waveguide and ring waveguide from Microresonator I, is
employed here.
The optical spectra of the breathing soliton and the modulated pump are shown
in Figure 7.4(b) and (c). Figure 7.4(d) is the zoom-in spectrum of the comb line at
1540.82
(a)
sidebands
Soliton
comb line
1st
2nd
Res:100 MHz
Res: 30 kHz
(b)
1
st
sideband power(dBm)
(c)
(d) (e)
Double
Period
Res: 30 kHz
64
1542.14 nm, where multiple sidebands can be seen. The sidebands are also observed
around other comb lines, and their frequencies and amplitudes depend on the RF signal
driving the pump light. When the RF signal power is increased to some extent, sub-
teeth are observed (Figure 7.4(e)). Figure 7.4(f) shows the RF spectrum with the zoom-
in of the first beat note in the inset. The narrow spectral lines (linewidth: 40 kHz)
indicate that the main comb lines and their sidebands are phase-locked.
Figure 7.4 (a) Experimental setup for the deterministic generation of a breathing soliton by modulating
the CW pump. (b, c) The optical spectra of the breathing soliton and the modulated pump. (d) The
zoom-in spectrum of the comb line at 1542.14 nm and its sidebands from the high-res. OSA. (e) The
spectrum of the comb line at 1542.14 nm under period doubling. (f) The RF spectrum of the breathing
soliton.
Figure 7.5(a) and (b) show the power of the 1
st
sideband (labeled in Figure 7.4(d))
as a function of RF signal power and frequency, respectively. The 1
st
sideband power
μResonator II
EDFA BPF
AFG
PC
MZI
ECDL
f
s
FBG
High res.
OSA
PD ESA OSA
(a)
Sidebands
Res: 100 MHz
1
st
sideband
(d) (e)
Double
Period
1555
(b)
Pump
(c)
(f)
800 MHz
Res: 30 kHz
2MHz span
LW 0 kHz
1554.95
Res: 0.1 nm
Res: 100
MHz
1st
65
increases almost linearly at low RF signal power, while it is saturated at high RF signal
power. When the RF signal power is too high (> 20 dBm), the breathing soliton finally
disappears. Different orders of sidebands can be generated at various breathing
frequencies equal to modulation frequencies. The 1
st
sideband reaches the highest
power at ~700 MHz, which is close to the measured breathing frequency of “native”
breathers (i.e. breathing solitons generated by fine tuning the pump wavelength). This
breathing frequency is comparable with the cavity linewidth. Furthermore, the
temporal evolution of different breathing comb line groups is examined with the
method described in [40]. About 10 comb lines located at different center wavelengths
are extracted to record the fast evolution (with numerical filtering), as shown in Figure
7.5(c). It can be seen that the power change of comb lines around the pump has a phase
difference of nearly π/2 from that of comb lines centered at 1525 nm, meaning that
different groups of comb lines experience modulations with different relative phases.
Figure 7.5 (a) and (b) are the power of 1
st
sideband (labeled in Figure 7.4(d)) as a function of RF signal
power and frequency (freq.), respectively. (c) The power evolution for different comb line groups
located at different center wavelengths.
Breathing Freq. (MHz)
(a) (b)
(c)
Breathing freq. of native breather
66
These experimental results indicate that a breathing soliton can be controllably
generated by modulating the pump over a wide range of RF frequencies. The reason
could be that the stable solitons are susceptible to oscillations around the breathing
frequency of “native” breathers. This assumption can be confirmed by the breathing
soliton excitation resulting from injecting a second pump at the soliton resonance. It
should be noted that an electro-optical modulator can be used to modulate the stable
soliton combs to generate the sidelines, which are typically symmetrical with respect
to the soliton comb lines [123]. However, this is different from what we see with the
breathers in this work.
7.4 Simulation Results
Generation of a breathing soliton by modulating the pump is numerically
simulated using the modified Lugiato-Lefever equation (LLE) [30, 124, 125], as
presented below:
[𝜏 0
𝜕 𝜕 𝑡 +
𝛼
2
+
𝜃 2
−𝑗 𝛿 0
+𝑗𝐿 ∑
(−𝑗 )
𝛽
𝑚 !
𝜕 𝜕 𝜏
∞
=2
]𝐸 (𝑡 𝜏 )=√𝜃 𝐸 𝑛
′
−𝑗𝛾 𝐿𝐸 (𝑡 𝜏 )|𝐸 (𝑡 𝜏 )|
2
where τ0 is the roundtrip time, t and τ are the slow and fast times, E(t,τ) is the
intracavity field, and 𝐸 𝑛
′
is the total input field after the intensity modulation. 𝐸 𝑛
′
is
assumed to be Ein[1+rcos(ωst)], where r is the modulation depth and ωs is the angular
modulation frequency on the pump. The pump power is defined as Pin = |𝐸 𝑛
′
|
2
, δ0 is
the phase detuning of the pump frequency from the adjacent resonance frequency, L
is the cavity length, and αi and θ represent the power loss per round-trip and power
coupling coefficient, respectively. βm is the m
th
-order dispersion coefficient.
The dispersion profile is obtained on the basis of the Si3N4 ring resonator with a
waveguide height of 900 nm and a width of 1500 nm. The free spectral range is 191.8
GHz, and the radius of the cavity is ~ 120 μm. The pump wavelength is 1.556 μm
(192.67 THz). The calculated second-order dispersion β2 is -112 ps
2
/km. The nonlinear
coefficient γ is 0.89 /(W·m) and the propagation loss is assumed to be 0.15 dB/cm.
The quality factor of the microresonator is 1.3 x 10
6
.
67
The breathing soliton can be excited under different pump power and pump
detuning [34, 126]. Figure 7.6(a) shows the narrowest (red) and widest (blue) spectra
of the breathing soliton when the pump power is 0.8 W, and the normalized pump
detuning Δ (Δ is defined as 2δ0/(αi + θ) [127]) is 28. Figure 7.6(b) is the spectrum of
the comb line at 1579.04 nm in the breathing soliton, which is calculated from a pulse
train with 4,000 pulses using Fourier transform. Multiple sidebands are generated
around the main comb line due to the temporal oscillation. As depicted in Figure 7.6(c),
the spectral dynamics, intracavity peak power, and pulse width of the soliton show the
periodic duration and amplitude oscillation. The breathing period (1 ns) is equal to the
inverse of the RF modulation frequency (fs = 1 GHz), which is exactly the spacing
between sidebands. The peak power variation is around 250 W, and the pulse width
also changes periodically from 30 fs to 65 fs.
Figure 7.6 Simulated dynamics of the breathing soliton. (a) The narrowest (red) and widest (blue)
spectra of the breathing soliton. (b) The spectrum of the comb line at 1579.04 nm in the breathing
soliton. (c) The spectral dynamics, intracavity peak power, and pulse width of the breathing soliton.
In addition, the effects of the RF signal power and frequency on the pulse peak
power are investigated, as shown in Figure 7.7(a) and (b). Similar to the experimental
Sidebands
1 GHz
Main comb
line
10 15 20
0
200
400
1GHz 0.3*Amp. Modbreather
Slowtime (ns)
Peak power (W)
10 15 20
20
40
60
80
1GHz 0.3*Amp. Modbreather
Slowtime (ns)
Pulsewidth (fs)
(a)
(b)
(c)
Narrowest pulse
Widest pulse
68
observation, the breathing amplitude increases with the RF signal power and the
breathing soliton disappears when the RF signal power is too high. The amplitude
variation changes with the RF signal frequency, and it reaches the maximum at 1 GHz
for the simulated device, which is different from 700 MHz in the experiment. Such
difference is also observed for the native breathing frequency, which could result from
the difference of waveguide parameters between the simulation and experiment. The
power evolution for different comb line groups is also numerically studied. Figure
7.7(c) shows the power evolution for two comb line groups centered at 1525 nm and
the pump. A phase difference of ~π/2 can be observed between the modulations of the
two comb line groups. These simulation results are consistent with the experimental
measurements.
Figure 7.7 (a) and (b) The effects of the RF signal power and frequency on the pulse peak power,
respectively. (c) The power evolution for different comb line groups.
(c)
200 250 300 350 400 450 500
360
420
480
540
600
Peak Power (W)
Slowtime (ns)
200 250 300 350 400 450 500
-200
-100
0
100
200
Power Variation (W)
(b)
0.7 GHz 0.8 GHz 0.9 GHz 1.1 GHz1.2 GHz 1.3 GHz1.4 GHz1.5 GHz
1 GHz
(a)
0 50 100 150 200 250 300 350 400 450 500
0
100
200
300
400
500
Slowtime (ns)
Peak Power (W)
RF signal power is unevenly increased
-10
-5
0
5
10
15
Intensity (a.u.)
Time (2ns/Div)
Center WL: 1525 nm
Center WL: 1555 nm
69
7.5 Conclusion
In summary, we demonstrate two deterministic approaches to generate the
controllable breathing soliton in a microsresonator, including injecting a second pump
at the soliton resonance or modulating the CW pump. In the second case, we find that
the breathing frequency and amplitude can be determined by the RF modulation signal.
Our experimental observation is supported by numerical simulations. These two
approaches are of significance to the understanding of breather soliton dynamics and
their potential applications.
70
Chapter 8 Dual Microcomb Source Using a
Controllable Breathing Soliton
8.1 Introduction
Most of the applications mentioned above focus on the use of one Kerr comb. In
addition to single combs, integrated dual-Kerr-comb sources have recently attracted
much attention due to their ability to realize a one-to-one mapping of optical comb
lines to RF beat notes by coherent mixing in the photodetector [93, 128-130]. These
reports typically exploit stable solitons that have only one comb line within each
resonance interval. A question remains to potentially utilize breathing solitons for
enhanced dual-comb performance for which more lines in both optical and electrical
domains can be produced. However, because the breathing frequency and amplitude
are fluctuating depending on the microresonator properties, it would be beneficial to
apply the breathing solitons which is generated in a more controllable way.
In this chapter, we experimentally demonstrate a chip-scale dual-comb source
consisting of the controllable breathing soliton and another stable soliton. The
breathing soliton is excited by modulating the CW pump over a wide range of RF
frequencies. We show that when the breathing soliton combined with another stable
soliton are applied in the dual-comb source, the additional sidebands can obtain more
spectral information, achieving an increased resolution.
8.2 Concept of Dual Micro-Comb Source Utilizing a Controllable
Breathing Soliton
Figure 8.1 illustrates the principle of on-chip dual-comb source utilizing a
controllable breathing soliton with an increased resolution [121]. The dual-comb
source includes a controllable breathing soliton as well as a stable soliton. The
breathing soliton with a repetition rate of frep1 is generated by a modulated pump in
Microresonator I while the stable soliton is excited in Microresonator II with a slightly
71
different repetition rate (frep2). When the breathing and stable solitons are combined
together and interfered on a photodiode, not only is an RF comb composed of the
heterodyne beats between the pairs of main comb lines generated, but also many other
RF comb lines can be produced, which are the heterodyne beats between different
orders of sidebands and their corresponding stable soliton comb line. Ideally, if the
repetition rate difference (Δfr) between two soliton combs is far less than the RF
modulation frequency fs, different RF combs will have no spectral overlap and can be
easily distinguished from each other. Therefore, when the breathing and stable solitons
are exploited as a dual-comb source in spectroscopy, more spectral information can be
obtained in the measurement and the resolution will be increased accordingly. Note
that the maximum modulation frequency fs cannot significantly exceed the cavity
linewidth of the microresonator.
Figure 8.1 Dual micro-comb source utilizing a controllable breathing soliton with an increased
resolution. f s: RF modulation frequency; Δp: pump frequency difference; Δf rep1, Δf rep2, and Δf r: repetition
rates of comb 1 and 2, and their difference.
8.3 Experimental Results
The experimental setup to demonstrate dual-comb source consisting of a
controllable breathing and a stable soliton is illustrated in Figure 8.2. Two ECDLs are
used as the pumps, which are individually connected to an arbitrary function generator
(AFG). The output of ECDL I is sent to an intensity modulator driven by an 800 MHz
RF sinusoidal signal. The modulated pump is amplified by a high-power EDFA and
filtered by a bandpass filter (BPF 1) with a bandwidth of 15 nm. The pump is then
Signal
Reference
Sample or
waveshaper
λ
Dual micro-comb source
λ
λ
f
s
Δp
Δf
r
= f
rep2
-f
rep1
f
Δp Δp-f
s
Δp+f
s
Δp-2f
s
Δp+2f
s
f
s
Electrical
spectrum
Main RF comb
Additional
RF combs
Δf
r
Optical spectrum
CW
Pump
Modulated
Pump
λ
μResonator I
μResonator II
72
coupled to the chip through a lensed fiber with ~2.5 dB coupling loss. Cavity solitons
are generated by sweeping Pump I wavelength using the AFG. Note that the RF
modulation signal power should be kept low to obtain the soliton state. The output of
the generated breathing soliton is sent to a fiber Bragg grating to suppress the strong
pump line. Meanwhile, another stable soliton is generated by injecting Pump II into
Microresonator II. The breathing and stable solitons are then combined together by a
2-by-1 coupler and about 15 comb line pairs are selected by BPF 3 before amplified
by another EDFA. The amplified output is split into two paths. The upper path is sent
to a waveshaper before detected by a photodetector while the bottom one is directly
coupled to a PD as the reference. The waveshaper, with a predefined filtering shape,
is used to mimic the test sample in the measurement. The beat notes are recorded by
an oscilloscope with a sampling rate of 80 GS/s.
Figure 8.2 Experimental setup to demonstrate on-chip dual-comb source using a controllable breathing
and a stable soliton.
As mentioned in chapter 7, the main comb lines and their sidebands exhibit high
spectral purity for the controllable breathing soliton. The performance of the dual-
comb source using a controllable breathing soliton is investigated by measuring the
predefined filtering shape of a waveshaper. Figure 8.3(a) shows a single RF comb
Wave-
shaper
PD
Signal
Reference
BPF 3
Oscillo-
scope
EDFA 3
μResonator I
FBG
EDFA 1 BPF 1
AFG
PC
MZI
FBG
EDFA 2 BPF 2
AFG
PC
ECDL I
f
s
ECDL II
μResonator II
TEC
73
generated by heterodyning two stable soliton combs on the reference path while Figure
8.3(b) presents five RF combs generated by heterodyning two soliton combs, one of
which is in the breathing state. The additional RF combs in Figure 8.3(b) are the
heterodyne beats between the sidebands (1
st
and 2
nd
orders) and their corresponding
stable soliton comb lines. The optical spectra of the reference and signal paths are
shown in Figure 8.3(c). The waveshaper filtering functions measured by the dual-
comb source without (red) or with (blue) the breathing soliton are presented in Figure
8.3(d), where the grey curve is the programmed filtering function. It can be seen that
a limited number of comb lines have been selected to measure the waveshaper filtering
function. The reason for this is to avoid the spectral overlap between the main RF
comb and other RF combs produced by heterodyning different orders of sidebands and
their corresponding main soliton comb lines. As expected, three times more data points
(blue circle) are obtained with the 1
st
sidebands of the breathing soliton, which provide
more spectral information. For example, the sharp edges (the insets in Figure 8.3(d))
in the transmission can be better resolved where there are main comb lines and their
breathing sidebands. Hence, the dual-comb source including a breathing soliton can
achieve an increased resolution when they are used for applications such as
spectroscopy.
74
Figure 8.3 (a) A single RF comb generated by heterodyning two stable soliton combs. (b) Five RF
combs generated by heterodyning a breathing soliton and a stable soliton. (c) Optical spectra of the
signal and reference paths with one soliton comb in the breathing state. (d) Waveshaper filtering shape
measured by the dual-comb source without (w/o) and with (w/) use of the breathing soliton.
8.4 Discussion and Conclusion
A frequency comb with a smaller line spacing results in a finer grid in the
measurement. Instead of applying the controllable breathing soliton, there is another
approach to insert more comb lines by modulating the stable soliton combs using an
electro-optical modulator [86]. However, the modulators are usually not suitable to
19 19.5 20 20.5 21 21.5 22 22.5 23 23.5
Power (20 dB/Div)
Frequency (GHz)
Power(20 dB/Div)
18.5 19 19.5 20 20.5 21 21.5 22 22.5 23 23.5
Power (20 dB/Div)
Frequency (GHz)
(a)
(b)
W/o breathing
W/ breathing
Δf
r
=~60 MHz
f
s
= 900 MHz
(c)
(d)
1530 1535 1540 1545
-15
-10
-5
0
Transmission (dB)
Wavelength (nm)
Waveshaper filtering function
Dual-comb w/o breathing
Dual-comb w/ breathing
1536 1537 1538 1539 1540
-14
-12
-10
-8
Transmission (dB)
Wavelength (nm)
Waveshaper filtering function
Dual-comb w/o breathing
Dual-comb w/ breathing
1539 1540 1541 1542 1543 1544 1545 1546 1547 1548
-8
-6
-4
Transmission (dB)
Wavelength (nm)
Waveshaper filtering function
Dual-comb w/o breathing
Dual-comb w/ breathing
f
Δf
r
f
s
… … …
…
1530 1535 1540 1545
-50
-40
-30
-20
-10
Power (dB)
Wavelength (nm)
Reference
Signal
Res: 12.5 GHz
Power (dBm)
75
modulate short optical pulses for several reasons. For instance, firstly, a modulator
typically has a bandwidth of less than 100 nm, which is less than the Kerr comb
bandwidth. Secondly, the modulators, especially power-efficient ones, are
characterized by large dispersion deteriorating the pulse quality. Thirdly, the
modulators might not work properly if the pulse length is smaller than the modulator
length. If a pulse entirely enters to a modulator, the electro-optical effect changes the
periodicity of the pulse train but not its amplitude. This is not what we see with the
breathers. Finally, placing a modulator after the microresonator introduces higher loss
to the generated comb lines, making it less power efficient.
In this chapter, we experimentally demonstrate a microresonator-based dual-
comb source consisting of a controllable breathing soliton and a stable soliton. Our
technique is free from the disadvantages of the direct comb modulation, indicated
above. We further show that such a breathing soliton can be applied in a dual-comb
source to achieve an increased resolution as the additional sidebands can obtain more
spectral information.
76
References
[1] T. Udem, R. Holzwarth, and T. W. Hansch, "Optical frequency metrology,"
Nature, vol. 416, no. 6877, pp. 233-237 (2002).
[2] S. T. Cundiff and J. Ye, "Colloquium: Femtosecond optical frequency combs,"
Rev Mod Phys, vol. 75, no. 1, pp. 325-342 (2003).
[3] S. A. Diddams et al., "Direct link between microwave and optical frequencies
with a 300 THz femtosecond laser comb," Phys Rev Lett, vol. 84, no. 22, pp. 5102-
5105 (2000).
[4] R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P.
S. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys Rev
Lett, vol. 85, no. 11, pp. 2264-2267 (2000).
[5] I. Coddington, W. C. Swann, and N. R. Newbury, "Coherent multiheterodyne
spectroscopy using stabilized optical frequency combs (vol 100, art no 013902,
2008)," Phys Rev Lett, vol. 101, no. 4 (2008).
[6] A. Schliesser, M. Brehm, F. Keilmann, and D. W. van der Weide, "Frequency-
comb infrared spectrometer for rapid, remote chemical sensing," Optics Express, vol.
13, no. 22, pp. 9029-9038 (2005).
[7] T. M. Fortier et al., "Generation of ultrastable microwaves via optical
frequency division," Nature Photonics, vol. 5, no. 7, pp. 425-429 (2011).
[8] D. Hillerkuss et al., "26 Tbit/s line-rate super-channel transmission utilizing
all-optical fast Fourier transform processing," Nature Photonics, vol. 5, no. 6, pp. 364-
371 (2011).
[9] T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, "Microresonator-Based
Optical Frequency Combs," Science, vol. 332, no. 6029, pp. 555-559 (2011).
[10] D. T. Spencer et al., "An optical-frequency synthesizer using integrated
photonics," Nature, vol. 557, no. 7703, pp. 81-85 (2018).
[11] M. G. Suh, Q. F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, "Microresonator
soliton dual-comb spectroscopy," Science, vol. 354, no. 6312, pp. 600-603 (2016).
[12] P. Marin-Palomo et al., "Microresonator-based solitons for massively parallel
coherent optical communications," Nature, vol. 546, no. 7657, pp. 274-279 (2017).
77
[13] A. Fulop et al., "High-order coherent communications using mode-locked
dark-pulse Kerr combs from microresonators," Nature Communications, vol. 9 (2018).
[14] A. E. Willner et al., "All-optical signal processing techniques for flexible
networks," Journal of Lightwave Technology, vol. 37, no. 1, pp. 21-35 (2019).
[15] S. A. Diddams, "The evolving optical frequency comb," J Opt Soc Am B, vol.
27, no. 11, pp. B51-B62 (2010).
[16] R. Wu, V. R. Supradeepa, C. M. Long, D. E. Leaird, and A. M. Weiner,
"Generation of very flat optical frequency combs from continuous-wave lasers using
cascaded intensity and phase modulators driven by tailored radio frequency
waveforms," Optics Letters, vol. 35, no. 19, pp. 3234-3236 (2010).
[17] A. L. Gaeta, M. Lipson, and T. J. Kippenberg, "Photonic-chip-based frequency
combs," Nature Photonics, vol. 13, no. 3, pp. 158-169 (2019).
[18] J. Y. Wu, X. Y. Xu, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A.
Mitchell, and D. J. Moss, "RF photonics: An optical microcombs' perspective," IEEE
Journal of Selected Topics in Quantum Electronics, vol. 24, no. 4 (2018).
[19] P. Del'Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J.
Kippenberg, "Optical frequency comb generation from a monolithic microresonator,"
Nature, vol. 450, no. 7173, pp. 1214-1217 (2007).
[20] I. H. Agha, Y. Okawachi, and A. L. Gaeta, "Theoretical and experimental
investigation of broadband cascaded four-wave mixing in high-Q microspheres,"
Optics Express, vol. 17, no. 18, pp. 16209-16215 (2009).
[21] H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala,
"Chemically etched ultrahigh-Q wedge-resonator on a silicon chip," Nature Photonics,
vol. 6, no. 6, pp. 369-373 (2012).
[22] J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta,
and M. Lipson, "CMOS-compatible multiple-wavelength oscillator for on-chip optical
interconnects," Nature Photonics, vol. 4, no. 1, pp. 37-40 (2010).
[23] L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and
D. J. Moss, "CMOS-compatible integrated optical hyper-parametric oscillator,"
Nature Photonics, vol. 4, no. 1, pp. 41-45 (2010).
[24] A. G. Griffith et al., "Silicon-chip mid-infrared frequency comb generation,"
Nature Communications, vol. 6 (2015).
78
[25] H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, "Green, red, and IR
frequency comb line generation from single IR pump in AlN microring resonator,"
Optica, vol. 1, no. 6, pp. 396-399 (2014).
[26] B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Loncar,
"Diamond nonlinear photonics," Nature Photonics, vol. 8, no. 5, pp. 369-374 (2014).
[27] T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R.
Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, "Universal formation dynamics
and noise of Kerr-frequency combs in microresonators," Nature Photonics, vol. 6, no.
7, pp. 480-487 (2012).
[28] J. Li, H. Lee, T. Chen, and K. J. Vahala, "Low-pump-power, low-phase-noise,
and microwave to millimeter-wave repetition rate operation in microcombs," Phys Rev
Lett, vol. 109, no. 23 (2012).
[29] A. B. Matsko, W. Liang, A. A. Savchenkov, and L. Maleki, "Chaotic dynamics
of frequency combs generated with continuously pumped nonlinear microresonators,"
Optics Letters, vol. 38, no. 4, pp. 525-527 (2013).
[30] S. Coen and M. Erkintalo, "Universal scaling laws of Kerr frequency combs,"
Optics Letters, vol. 38, no. 11, pp. 1790-1792 (2013).
[31] M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, "Route to stabilized
ultrabroadband microresonator-based frequency combs," Optics Letters, vol. 38, no.
18, pp. 3478-3481 (2013).
[32] T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L.
Gorodetsky, and T. J. Kippenberg, "Temporal solitons in optical microresonators,"
Nature Photonics, vol. 8, no. 2, pp. 145-152 (2014).
[33] S. W. Huang, J. H. Yang, M. B. Yu, B. H. McGuyer, D. L. Kwong, T.
Zelevinsky, and C. W. Wong, "A broadband chip-scale optical frequency synthesizer
at 2.7 x 10
-16
relative uncertainty," Sci Adv, vol. 2, no. 4 (2016).
[34] Y. K. Chembo and C. R. Menyuk, "Spatiotemporal Lugiato-Lefever formalism
for Kerr-comb generation in whispering-gallery-mode resonators," Phys Rev A, vol.
87, no. 5 (2013).
[35] M. J. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, "Mode-
locked mid-infrared frequency combs in a silicon microresonator," Optica, vol. 3, no.
8, pp. 854-860 (2016).
79
[36] J. S. Levy, K. Saha, Y. Okawachi, M. A. Foster, A. L. Gaeta, and M. Lipson,
"High-Performance Silicon-Nitride-Based Multiple-Wavelength Source," IEEE
Photonic Technology Letters, vol. 24, no. 16, pp. 1375-1377 (2012).
[37] X. Yi, Q. F. Yang, K. Y. Yang, M. G. Suh, and K. Vahala, "Soliton frequency
comb at microwave rates in a high-Q silica microresonator," Optica, vol. 2, no. 12, pp.
1078-1085 (2015).
[38] P. H. Wang, J. A. Jaramillo-Villegas, Y. Xuan, X. X. Xue, C. Y. Bao, D. E.
Leaird, M. H. Qi, and A. M. Weiner, "Intracavity characterization of micro-comb
generation in the single-soliton regime," Optics Express, vol. 24, no. 10, pp. 10890-
10897 (2016).
[39] C. Joshi, J. K. Jang, K. Luke, X. C. Ji, S. A. Miller, A. Klenner, Y. Okawachi,
M. Lipson, and A. L. Gaeta, "Thermally controlled comb generation and soliton
modelocking in microresonators," Optics Letters, vol. 41, no. 11, pp. 2565-2568
(2016).
[40] C. Y. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. H. Qi, and A.
M. Weiner, "Observation of Fermi-Pasta-Ulam Recurrence Induced by Breather
Solitons in an Optical Microresonator," Phys Rev Lett, vol. 117, no. 16 (2016).
[41] M. J. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. C.
Ji, M. Lipson, and A. L. Gaeta, "Breather soliton dynamics in microresonators,"
Nature Communications, vol. 8 (2017).
[42] E. Lucas, M. Karpov, H. Guo, M. L. Gorodetsky, and T. J. Kippenberg,
"Breathing dissipative solitons in optical microresonators," Nature Communications,
vol. 8 (2017).
[43] G. P. Agrawal, "Lightwave Technology Telecommunication Systems
Introduction," Lightwave Technology: Telecommunication Systems, pp. 1-25 (2005).
[44] E. Agrell et al., "Roadmap of optical communications," J Optics-Uk, vol. 18,
no. 6 (2016).
[45] P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, "Fiber-optic transmission
and networking: the previous 20 and the next 20 years," Optics Express, vol. 26, no.
18, pp. 24190-24239 (2018).
[46] C. A. Brackett, "Dense wavelength division multiplexing networks - principles
and applications," IEEE J Sel Area Comm, vol. 8, no. 6, pp. 948-964 (1990).
80
[47] P. J. Winzer and R. J. Essiambre, "Advanced modulation formats for high-
capacity optical transport networks," Journal of Lightwave Technology, vol. 24, no.
12, pp. 4711-4728 (2006).
[48] M. Seimetz, "Laser linewidth limitations for optical systems with high-order
modulation employing feed forward digital carrier phase estimation," 2008
Conference on Optical Fiber Communication/National Fiber Optic Engineers
Conference, Vols 1-8, pp. 2470-2472 (2008).
[49] M. Karlsson and E. Agrell, "Which is the most power-efficient modulation
format in optical links?," Optics Express, vol. 17, no. 13, pp. 10814-10819 (2009).
[50] K. Kikuchi, "Coherent optical communication systems," Optical Fiber
Telecommunications V B: Systems and Networks, pp. 95-129 (2008).
[51] E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in
optical fiber systems," Optics Express, vol. 16, no. 2, pp. 753-791 (2008).
[52] K. Kikuchi, "Digital coherent optical communication systems: fundamentals
and future prospects," IEICE Electron Expr, vol. 8, no. 20, pp. 1642-1662 (2011).
[53] A. E. Willner, S. Khaleghi, M. R. Chitgarha, and O. F. Yilmaz, "All-Optical
Signal Processing," Journal of Lightwave Technology, vol. 32, no. 4 (2014).
[54] M. Saruwatari, "All-optical signal processing for terabit/second optical
transmission," IEEE Journal of Selected Topics in Quantum Electronics, vol. 6, no. 6,
pp. 1363-1374 (2000).
[55] C. Koos et al., "All-optical high-speed signal processing with silicon-organic
hybrid slot waveguidesx," Nature Photonics, vol. 3, no. 4, pp. 216-219 (2009).
[56] G. P. Agrawal, "Nonlinear Fiber Optics," Lect Notes Phys, vol. 542, pp. 195-
211 (2000).
[57] C. Langrock, S. Kumar, J. E. McGeehan, A. E. Willner, and M. M. Fejer, "All-
optical signal processing using chi((2)) nonlinearities in guided-wave devices,"
Journal of Lightwave Technology, vol. 24, no. 7, pp. 2579-2592 (2006).
[58] S. Radic, "Parametric Signal Processing," IEEE Journal of Selected Topics in
Quantum Electronics, vol. 18, no. 2, pp. 670-680 (2012).
[59] G. W. Lu and T. Miyazaki, "Optical phase erasure based on FWM in HNLF
enabling format conversion from 320-Gb/s RZ-DQPSK to 160-Gb/s RZ-DPSK,"
Optics Express, vol. 17, no. 16, pp. 13346-13353 (2009).
81
[60] D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall,
and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers
and direct optical frequency synthesis," Science, vol. 288, no. 5466, pp. 635-639
(2000).
[61] S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, "Standards of
time and frequency at the outset of the 21st century," Science, vol. 306, no. 5700, pp.
1318-1324 (2004).
[62] N. R. Newbury, "Searching for applications with a fine-tooth comb," Nature
Photonics, vol. 5, no. 4, pp. 186-188 (2011).
[63] F. Ferdous, H. X. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T.
Varghese, and A. M. Weiner, "Spectral line-by-line pulse shaping of on-chip
microresonator frequency combs," Nature Photonics, vol. 5, no. 12, pp. 770-776
(2011).
[64] W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D.
Seidel, and L. Maleki, "High spectral purity Kerr frequency comb radio frequency
photonic oscillator," Nature Communications, vol. 6 (2015).
[65] J. Pfeifle et al., "Coherent terabit communications with microresonator Kerr
frequency combs," Nature Photonics, vol. 8, no. 5, pp. 375-380 (2014).
[66] P. H. Wang, F. Ferdous, H. X. Miao, J. Wang, D. E. Leaird, K. Srinivasan, L.
Chen, V. Aksyuk, and A. M. Weiner, "Observation of correlation between route to
formation, coherence, noise, and communication performance of Kerr combs," Optics
Express, vol. 20, no. 28, pp. 29284-29295 (2012).
[67] J. Pfeifle et al., "Optimally Coherent Kerr Combs Generated with Crystalline
Whispering Gallery Mode Resonators for Ultrahigh Capacity Fiber Communications,"
Phys Rev Lett, vol. 114, no. 9 (2015).
[68] N. R. Newbury and W. C. Swann, "Low-noise fiber-laser frequency combs
(Invited)," J Opt Soc Am B, vol. 24, no. 8, pp. 1756-1770 (2007).
[69] P. Del'Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J.
Kippenberg, "Octave Spanning Tunable Frequency Comb from a Microresonator,"
Phys Rev Lett, vol. 107, no. 6 (2011).
[70] P. Liao, C. Bao, A. Kordts, M. Karpov, M. H. P. Pfeiffer, L. Zhang, A.
Mohajerin-Ariaei, Y. Cao, A. Almaiman, M. Ziyadi, S. R. Wilkinson, M. Tur, T. J.
Kippenberg, and A. E. Willner, "Dependence of a microresonator Kerr frequency
comb on the pump linewidth," Optics Letters, vol. 42, no. 4, pp. 779-782 (2017).
82
[71] M. H. P. Pfeiffer, A. Kordts, V. Brasch, M. Zervas, M. Geiselmann, J. D. Jost,
and T. J. Kippenberg, "Photonic Damascene process for integrated high-Q
microresonator based nonlinear photonics," Optica, vol. 3, no. 1, pp. 20-25 (2016).
[72] P. Liao et al., "Wavelength and Pump Power Characterization of Low-phase-
noise Kerr Frequency Comb Lines," Optical Fiber Communications Conference and
Exhibition (OFC) (2016).
[73] H. Ludvigsen, M. Tossavainen, and M. Kaivola, "Laser linewidth
measurements using self-homodyne detection with short delay," Opt Commun, vol.
155, no. 1-3, pp. 180-186 (1998).
[74] Z. Zan and A. J. Lowery, "Experimental demonstration of a flexible and stable
semiconductor laser linewidth emulator," Optics Express, vol. 18, no. 13, pp. 13880-
13885 (2010).
[75] L. B. Mercer, "1/F Frequency Noise Effects on Self-Heterodyne Linewidth
Measurements," Journal of Lightwave Technology, vol. 9, no. 4, pp. 485-493 (1991).
[76] A. Coillet and Y. Chembo, "On the robustness of phase locking in Kerr optical
frequency combs," Optics Letters, vol. 39, no. 6, pp. 1529-1536 (2014).
[77] V. Ataie, E. Temprana, L. Liu, E. Myslivets, B. P. P. Kuo, N. Alic, and S.
Radic, "Ultrahigh Count Coherent WDM Channels Transmission Using Optical
Parametric Comb-Based Frequency Synthesizer," Journal of Lightwave Technology,
vol. 33, no. 3, pp. 694-699 (2015).
[78] Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta,
"Octave-spanning frequency comb generation in a silicon nitride chip," Optics Letters,
vol. 36, no. 17, pp. 3398-3400 (2011).
[79] M. Pelusi, H. N. Tan, K. Solis-Trapala, T. Inoue, and S. Namiki, "Low Noise
Frequency Combs for Higher Order QAM Formats Through Cross-Phase Modulation
of Modelocked Laser Pulses," IEEE Journal of Selected Topics in Quantum
Electronics, vol. 24, no. 3 (2018).
[80] P. Kylemark, P. O. Hedekvist, H. Sunnerud, M. Karlsson, and P. A.
Andrekson, "Noise characteristics of fiber optical parametric amplifiers," Journal of
Lightwave Technology, vol. 22, no. 2, pp. 409-416 (2004).
[81] N. Volet, X. Yi, Q. F. Yang, E. J. Stanton, P. A. Morton, K. Y. Yang, K. J.
Vahala, and J. E. Bowers, "Micro-Resonator Soliton Generated Directly with a Diode
Laser," Laser Photonics Rev, vol. 12, no. 5 (2018).
83
[82] J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury,
"Suppression of pump-induced frequency noise in fiber-laser frequency combs leading
to sub-radian f (ceo) phase excursions," Appl Phys B-Lasers O, vol. 86, no. 2, pp. 219-
227 (2007).
[83] A. B. Matsko and L. Maleki, "Noise conversion in Kerr comb RF photonic
oscillators," J Opt Soc Am B, vol. 32, no. 2, pp. 232-240 (2015).
[84] P. Liao, C. Bao, A. Kordts, M. Karpov, M. H. P. Pfeiffer, L. Zhang, Y. Cao,
A. Almaiman, A. Mohajerin-Ariaei, F. Alishahi, A. Fallahpour, K. Zhou, M. Tur, T.
J. Kippenberg, and A. E. Willner, "Effects of erbium-doped fiber amplifier induced
pump noise on soliton Kerr frequency combs for 64-quadrature amplitude modulation
transmission," Optics Letters, vol. 43, no. 11, pp. 2495-2498 (2018).
[85] H. Guo et al., "Universal dynamics and deterministic switching of dissipative
Kerr solitons in optical microresonators," Nat Phys, vol. 13, no. 1, pp. 94-102 (2017).
[86] P. Del'Haye, S. B. Papp, and S. A. Diddams, "Hybrid Electro-Optically
Modulated Microcombs," Phys Rev Lett, vol. 109, no. 26 (2012).
[87] D. C. Cole, E. S. Lamb, P. Del'Haye, S. A. Diddams, and S. B. Papp, "Soliton
crystals in Kerr resonators," Nature Photonics, vol. 11, no. 10, pp. 671-676 (2017).
[88] C. J. Bao et al., "Effect of a breather soliton in Kerr frequency combs on optical
communication systems," Optics Letters, vol. 41, no. 8, pp. 1764-1767 (2016).
[89] H. Suzuki and N. Takachio, "Optical signal quality monitor built into WDM
linear repeaters using semiconductor arrayed waveguide grating filter monolithically
integrated with eight photodiodes," Electron Lett, vol. 35, no. 10, pp. 836-837 (1999).
[90] R. Schmogrow et al., "Error Vector Magnitude as a Performance Measure for
Advanced Modulation Formats," IEEE Photonic Technology Letters, vol. 24, no. 23,
pp. 2198-2198 (2012).
[91] A. Napoli et al., "Next Generation Elastic Optical Networks: The Vision of the
European Research Project IDEALIST," IEEE Commun Mag, vol. 53, no. 2, pp. 152-
162 (2015).
[92] T. Inoue, T. Kurosu, K. Ishii, H. Kuwatsuka, and S. Namiki, "Exabit optical
network based on optical comb distribution for high-performance datacenters:
challenges and strategies," in Frontiers in Optics, p. FTh3C. 3 (2015).
[93] A. Dutt, C. Joshi, X. C. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta,
and M. Lipson, "On-chip dual-comb source for spectroscopy," Sci Adv, vol. 4, no. 3,
(2018).
84
[94] P. Liao, C. Bao, A. Almaiman, A. Kordts, M. Karpov, M. H. P. Pfeiffer, L.
Zhang, F. Alishahi, Y. Cao, K. Zou, A. Fallahpour, A. N. Willner, M. Tur, T. J.
Kippenberg, and A. E. Willner, "Demonstration of multiple Kerr-frequency-comb
generation using different lines from another Kerr comb located up to 50 km away,"
Journal of Lightwave Technology, vol. 37, no. 2, pp. 579-584 (2019).
[95] L. Lundberg, M. Karlsson, A. Lorences-Riesgo, M. Mazur, V. Torres-
Company, J. Schroder, and P. A. Andrekson, "Frequency comb-based WDM
transmission systems enabling joint signal processing," Appl Sci-Basel, vol. 8, no. 5
(2018).
[96] I. Coddington, N. Newbury, and W. Swann, "Dual-comb spectroscopy,"
Optica, vol. 3, no. 4, pp. 414-426 (2016).
[97] A. R. Johnson, Y. Okawachi, M. R. E. Lamont, J. S. Levy, M. Lipson, and A.
L. Gaeta, "Microresonator-based comb generation without an external laser source,"
Optics Express, vol. 22, no. 2, pp. 1394-1401 (2014).
[98] C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, "Linear
optical sampling," IEEE Photonic Technology Letters, vol. 15, no. 12, pp. 1746-1748
(2003).
[99] F. Van Dijk, A. Accard, A. Enard, O. Drisse, D. Make, and F. Lelarge,
"Monolithic dual wavelength DFB lasers for narrow linewidth heterodyne beat-note
generation," in 2011 International Topical Meeting on Microwave Photonics jointly
held with the 2011 Asia-Pacific Microwave Photonics Conference, pp. 73-76 (2011).
[100] J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A.
Diddams, and S. B. Papp, "Thermal and Nonlinear Dissipative-Soliton Dynamics in
Kerr-Microresonator Frequency Combs," Phys Rev Lett, vol. 121, no. 6 (2018).
[101] L. E. Richter, H. I. Mandelberg, M. S. Kruger, and P. A. Mcgrath, "Linewidth
Determination from Self-Heterodyne Measurements with Subcoherence Delay
Times," IEEE Journal of Selected Topics in Quantum Electronics, vol. 22, no. 11, pp.
2070-2074 (1986).
[102] K. Roberts, S. H. Foo, M. Moyer, M. Hubbard, A. Sinclair, J. Gaudette, and C.
Laperle, "High Capacity Transport-100G and Beyond," Journal of Lightwave
Technology, vol. 33, no. 3, pp. 563-578 (2015).
[103] T. Pfau, S. Hoffmann, and R. Noe, "Hardware-Efficient Coherent Digital
Receiver Concept With Feedforward Carrier Recovery for M-QAM Constellations,"
Journal of Lightwave Technology, vol. 27, no. 5-8, pp. 989-999 (2009).
85
[104] B. Koch, R. Noe, V. Mirvoda, H. Griesser, S. Bayer, and H. Wernz, "Record
59-krad/s Polarization Tracking in 112-Gb/s 640-km PDM-RZ-DQPSK
Transmission," IEEE Photonic Technology Letters, vol. 22, no. 19, pp. 1407-1409
(2010).
[105] B. P. P. Kuo, E. Myslivets, N. Alic, and S. Radic, "Wavelength Multicasting
via Frequency Comb Generation in a Bandwidth-Enhanced Fiber Optical Parametric
Mixer," Journal of Lightwave Technology, vol. 29, no. 23, pp. 3515-3522 (2011).
[106] G. W. Lu et al., "Pump-linewidth-tolerant optical wavelength conversion for
high-order QAM signals using coherent pumps," Optics Express, vol. 22, no. 5, pp.
5067-5075 (2014).
[107] P. Liao, C. Bao, A. Kordts, M. Karpov, M. H. P. Pfeiffer, L. Zhang, Y. Cao,
A. Almaiman, A. Mohajerin-Ariaei, M. Tur, M. M. Fejer, T. J. Kippenberg, and A. E.
Willner, "Pump-linewidth-tolerant wavelength multicasting using soliton Kerr
frequency combs," Optics Letters, vol. 42, no. 16, pp. 3177-3180 (2017).
[108] J. G. Proakis and M. Salehi, Digital communications. McGraw-hill New York
(2001).
[109] B. Moslehi, J. W. Goodman, M. Tur, and H. J. Shaw, "Fiber-Optic Lattice
Signal-Processing," Proceedings of the IEEE, vol. 72, no. 7, pp. 909-930 (1984).
[110] A. V. Oppenheim, Discrete-time signal processing. Pearson Education India
(1999).
[111] R. W. Boyd, "Nonlinear Optics, 3rd Edition," Nonlinear Optics, 3rd Edition,
pp. 1-613 (2008).
[112] M. Secondini, "Optical equalization: System modeling and performance
evaluation," Journal of Lightwave Technology, vol. 24, no. 11, pp. 4013-4021 (2006).
[113] R. S. Tucker and K. Hinton, "Energy Consumption and Energy Density in
Optical and Electronic Signal Processing," IEEE Photonics Journal, vol. 3, no. 5, pp.
821-833 (2011).
[114] S. Khaleghi et al., "High-Speed Correlation and Equalization Using a
Continuously Tunable All-Optical Tapped Delay Line," IEEE Photonics Journal, vol.
4, no. 4, pp. 1220-1235 (2012).
[115] J. Wang, J. Q. Sun, X. L. Zhang, D. X. Huang, and M. M. Fejer, "Optical phase
erasure and its application to format conversion through cascaded second-order
processes in periodically poled lithium niobate," Optics Letters, vol. 33, no. 16, pp.
1804-1806 (2008).
86
[116] Y. T. Dai, Y. Okawachi, A. C. Turner-Foster, M. Lipson, A. L. Gaeta, and C.
Xu, "Ultralong continuously tunable parametric delays via a cascading discrete stage,"
Optics Express, vol. 18, no. 1, pp. 333-339 (2010).
[117] M. Ziyadi et al., "Tunable optical correlator using an optical frequency comb
and a nonlinear multiplexer," Optics Express, vol. 22, no. 1, pp. 84-89 (2014).
[118] S. Khaleghi et al., "Simultaneous and independent processing of multiple input
WDM data signals using a tunable optical tapped delay line," Optics Letters, vol. 38,
no. 21, pp. 4273-4276 (2013).
[119] A. N. Willner et al., "Scalable and reconfigurable optical tapped-delay-line for
multichannel equalization and correlation using nonlinear wave mixing and a Kerr
frequency comb," Optics Letters, vol. 43, no. 22, pp. 5563-5566 (2018).
[120] G. Baxter, S. Frisken, D. Abakoumov, H. Zhou, I. Clarke, A. Bartos, and S.
Poole, "Highly programmable wavelength selective switch based on liquid crystal on
silicon switching elements," 2006 Optical Fiber Communication Conference/National
Fiber Optic Engineers Conference, Vols 1-6, pp. 94-96 (2006).
[121] P. Liao et al., "Chip-Scale Dual-Comb Source using a Breathing Soliton with
an Increased Resolution," in CLEO: Applications and Technology, p. JTh5A. 4 (2018).
[122] P. Liao et al., "Generation of Multiple Side Lines around Kerr Comb Lines by
a Second Pump Coupled into the Soliton Resonance," in Conference on Lasers and
Electro-Optics (CLEO), pp. 1-2 (2018).
[123] C. J. Bao et al., "Tunable insertion of multiple lines into a Kerr frequency comb
using electro-optical modulators," Optics Letters, vol. 42, no. 19, pp. 3765-3768
(2017).
[124] L. A. Lugiato and R. Lefever, "Spatial Dissipative Structures in Passive
Optical-Systems," Phys Rev Lett, vol. 58, no. 21, pp. 2209-2211 (1987).
[125] M. Erkintalo, H. G. Randle, T. Sylvestre, and S. Coen, "Steady-state and
instabilities of octave-spanning Kerr frequency combs modeled using a generalized
Lugiato-Lefever equation," Conference on Lasers and Electro-Optics Europe and
International Quantum Electronics Conference (CLEO Europe/IQEC) (2013).
[126] P. Parra-Rivas, D. Gomila, M. A. Matias, S. Coen, and L. Gelens, "Dynamics
of localized and patterned structures in the Lugiato-Lefever equation determine the
stability and shape of optical frequency combs," Phys Rev A, vol. 89, no. 4 (2014).
87
[127] F. Leo, L. Gelens, P. Emplit, M. Haelterman, and S. Coen, "Dynamics of one-
dimensional Kerr cavity solitons," Optics Express, vol. 21, no. 7, pp. 9180-9191
(2013).
[128] M. G. Suh and K. J. Vahala, "Soliton microcomb range measurement,"
Science, vol. 359, no. 6378, pp. 884-887 (2018).
[129] P. Trocha et al., "Ultrafast optical ranging using microresonator soliton
frequency combs," Science, vol. 359, no. 6378, pp. 887-891 (2018).
[130] M. J. Yu, Y. Okawachi, A. G. Griffith, N. Picque, M. Lipson, and A. L. Gaeta,
"Silicon-chip-based mid-infrared dual-comb spectroscopy," Nature Communications,
vol. 9 (2018).
Abstract (if available)
Abstract
Optical frequency combs, which comprise a multitude of equidistant spectral lines in their spectrum, have become an indispensable tool in optical and photonics technology. They have been widely used in optical metrology, spectroscopy, remote sensing, arbitrary waveform generation and telecommunication due to its broad spectrum of the precisely controlled optical carriers. In the past decade, a noticeable development in frequency comb technology is the use of integrated microring resonators to produce combs based on Kerr nonlinearity. Such Kerr frequency combs can be fabricated with a small footprint enabling large comb line spacings over broad optical bandwidths. Depending on the pump power and wavelength, the formation of Kerr combs consists of several dynamic regimes, which exhibit different degrees of coherence as well as distinct noise properties. Kerr combs in a low-noise state are promising to enhance many applications including optical frequency synthesis, spectroscopy, optical communications and signal processing. ❧ This thesis will study the generation of optical Kerr frequency combs and explore their use as coherent light sources for high-speed optical communications and as pump lasers for advanced optical signal processing functions. In the first part, the applications of the Kerr comb in optical communication systems are experimentally investigated and demonstrated, which include (i) the generation of Kerr combs as well as their characterization in terms of the comb line linewidth and noise
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Creator
Liao, Peicheng
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Core Title
Microresonator-based Kerr frequency comb for high-speed optical communications and signal processing
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Publication Date
01/08/2020
Defense Date
11/13/2019
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frequency comb,Kerr frequency comb,microresonator,OAI-PMH Harvest,optical communications,optical signal processing
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Willner, Alan (
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), Armani, Andrea (
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), Wu, Wei (
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frequency comb
Kerr frequency comb
microresonator
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