Hybrid Si/III-V Lasers for Next-generation Coherent Optical Communication - CaltechTHESIS

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Hybrid Si/III-V Lasers for Next-generation Coherent Optical Communication
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Zhang, Zhewei
(2021)
Hybrid Si/III-V Lasers for Next-generation Coherent Optical Communication.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/y85t-nj39.
Abstract
The most important application of semiconductor lasers is, without doubt, optical communication, the backbone of the information age. In the past few decades, incoherent optical communication with conventional semiconductor lasers, the III-V distributed feedback (DFB) lasers, has successfully fulfilled the global demand for the data rate. However, in order to support the rapidly growing Internet traffic of the 21st century, the transition from incoherent to coherent optical communication is inevitable, requiring new types of lasers, as the conventional III-V DFB lasers lack the phase coherence needed to serve as the light sources in coherent optical communication. The existent alternatives with high phase coherence are external cavity lasers (ECLs) and fiber lasers, whose high price and bulky size effectively thwart the upgrade of the current communication networks. This is the main motivation for us to develop high-coherence semiconductor lasers.
To achieve the goal, we shall rethink and redesign semiconductor lasers. Advanced modern fabrication technology helps us to turn bold ideas into reality. Not only do we build semiconductor lasers on hybrid platforms, but also engineer elaborately the optical mode to enhance the lasers’ phase coherence. The newly developed semiconductor lasers, hybrid Si/III-V lasers, are the core of the entire thesis. Their design principles, fabrication process, properties and performance in the coherent optical communication system will be presented and discussed. The experimental results show the Si/III-V lasers' superiority to their conventional counterparts.
Aside from possessing high phase coherence, the Si/III-V lasers have great potential to be the light sources on the integrated photonic platforms. The fundamental obstacle thwarting photonic integration is optical feedback, to which the conventional semiconductor lasers are very sensitive. Without the protection provided by optical isolators, which unfortunately cannot be fabricated on chip, the performance of the conventional III-V DFB lasers could get significantly degraded by optical feedback. The Si/III-V lasers, with their built-in high-Q resonators, are very robust against optical feedback and can function properly in the isolator-free coherent optical communication systems. Thus, the cost of future optical networks can be further reduced by monolithically integrating passive photonic devices such as modulators and demodulators with the Si/III-V lasers.
Finally, all the studies centered on laser coherence trigger us to think deeply about the underlying relation between different means of characterizing laser coherence. A rigorous mathematical relation, the Central Relation, has been derived here, which not only unveils the fundamental relation between laser lineshape and frequency noise power spectral density (PSD) but also provides new methods of frequency noise controlling like optical filtering.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Laser coherence; Coherent optical communication
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Yariv, Amnon
Group:
Kavli Nanoscience Institute
Thesis Committee:
Vahala, Kerry J. (chair)
Yariv, Amnon
Faraon, Andrei
Marandi, Alireza
Defense Date:
19 February 2021
Funders:
Funding Agency
Grant Number
Army Research Office (ARO)
W911NF-16-C-0026
Army Research Office (ARO)
W911NF-15-1-0584
Army Research Office (ARO)
W911NF-14-P-0020
Defense Advanced Research Projects Agency (DARPA)
N66001-14-1-4062
Record Number:
CaltechTHESIS:02222021-054057067
Persistent URL:
DOI:
10.7907/y85t-nj39
Related URLs:
URL
URL Type
Description
DOI
Article adapted for Chapter III.
DOI
Article adapted for Chapter III.
DOI
Article adapted for Chapter IV.
DOI
Article adapted for Chapter IV.
DOI
Article adapted for Chapter V.
ORCID:
Author
ORCID
Zhang, Zhewei
0000-0002-1211-7957
Default Usage Policy:
No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
14086
Collection:
CaltechTHESIS
Deposited By:
Zhewei Zhang
Deposited On:
01 Mar 2021 17:38
Last Modified:
12 Jun 2025 00:07
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Hybrid Si/III-V Lasers for Next-generation Coherent
Optical Communication

Thesis by

Zhewei Zhang

In Partial Fulfillment of the Requirements for
the degree of
Doctor of Philosophy

CALIFORNIA INSTITUTE OF TECHNOLOGY
Pasadena, California

2021
(Defended February 19, 2021)

ii

 2021
Zhewei Zhang
ORCID: 0000-0002-1211-7957

iii

ACKNOWLEDGEMENTS
First and foremost, I would like to thank my advisor, Prof. Amnon Yariv, for giving me
opportunities to participate in several great research projects to develop cutting-edge
photonic technologies. Prof. Yariv’s attitudes towards science, work and life have always
inspired me. It is truly my honor and fortune to study in his group.
I would also like to thank Prof. Vahala, Prof. Faraon and Prof. Marandi, three experts on
photonics, for serving on my defense committee.
I am very grateful to all the group members, especially Dr. Mark Harfouche, Dr. Dongwan
Kim and Dr. Huolei Wang, who taught me how to conduct experiments and guided me to
become an independent researcher. I also want to thank Dr. Hetuo Chen, who visited us for
two years, for his collaboration on research and warm friendship.
I would like to express my sincere gratitude to Dr. Naresh Satyan, Dr. George Rakuljic, Dr.
Reginald Lee, Dr. Bruno Crosignani and Dr. Christos Santis for their discussions and
comments in the group meetings. In addition, I would like to thank all the staff at Kavli
Nanoscience Institute and Alireza Ghaffari for their help and training in nanofabrication.
I appreciate all the help from my collaborators, Dr. Peicheng Liao and Kaiheng Zou, from
University of Southern California (USC). I really enjoy working with them and have learned
a lot from them in the collaboration.
Last but not least, I would like to thank my family for their support and love.

iv

ABSTRACT
The most important application of semiconductor lasers is, without doubt, optical
communication, the backbone of the information age. In the past few decades, incoherent
optical communication with conventional semiconductor lasers, the III-V distributed
feedback (DFB) lasers, has successfully fulfilled the global demand for the data rate.
However, in order to support the rapidly growing Internet traffic of the 21st century, the
transition from incoherent to coherent optical communication is inevitable, requiring new
types of lasers, as the conventional III-V DFB lasers lack the phase coherence needed to
serve as the light sources in coherent optical communication. The existent alternatives with
high phase coherence are external cavity lasers (ECLs) and fiber lasers, whose high price and
bulky size effectively thwart the upgrade of the current communication networks. This is the
main motivation for us to develop high-coherence semiconductor lasers.
To achieve the goal, we shall rethink and redesign semiconductor lasers. Advanced modern
fabrication technology helps us to turn bold ideas into reality. Not only do we build
semiconductor lasers on hybrid platforms, but also engineer elaborately the optical mode to
enhance the lasers’ phase coherence. The newly developed semiconductor lasers, hybrid
Si/III-V lasers, are the core of the entire thesis. Their design principles, fabrication process,
properties and performance in the coherent optical communication system will be presented
and discussed. The experimental results show the Si/III-V lasers’ superiority to their
conventional counterparts.
Aside from possessing high phase coherence, the Si/III-V lasers have great potential to be
the light sources on the integrated photonic platforms. The fundamental obstacle thwarting
photonic integration is optical feedback, to which the conventional semiconductor lasers are
very sensitive. Without the protection provided by optical isolators, which unfortunately
cannot be fabricated on chip, the performance of the conventional III-V DFB lasers could
get significantly degraded by optical feedback. The Si/III-V lasers, with their built-in highQ resonators, are very robust against optical feedback and can function properly in the
isolator-free coherent optical communication systems. Thus, the cost of future optical

networks can be further reduced by monolithically integrating passive photonic devices
such as modulators and demodulators with the Si/III-V lasers.
Finally, all the studies centered on laser coherence trigger us to think deeply about the
underlying relation between different means of characterizing laser coherence. A rigorous
mathematical relation, the Central Relation, has been derived here, which not only unveils
the fundamental relation between laser lineshape and frequency noise power spectral density
(PSD) but also provides new methods of frequency noise controlling like optical filtering.

vi

PUBLISHED CONTENT AND CONTRIBUTIONS
[1] M. Harfouche, D. Kim, H. Wang, C. T. Santis, Z. Zhang, H. Chen, et al., "Kicking the
habit/semiconductor lasers without isolators," Optics Express, vol. 28, pp. 36466-36475,
2020.
Z.Z. aided in conducting the experiments and writing the manuscript.
[2] Z. Zhang, K. Zou, H. Wang, P. Liao, N. Satyan, G. Rakuljic, et al., "High-speed Coherent
Optical Communication with Isolator-free Heterogeneous Si/III-V Lasers," Journal of
Lightwave Technology, pp. 1-1, 2020.
Z.Z. participated in designing the experiments, conducting the experiments, analyzing
the data and writing the manuscript.
[3] K. Zou, Z. Zhang, P. Liao, H. Wang, Y. Cao, A. Almaiman, et al., "Higher-order QAM
data transmission using a high-coherence hybrid Si/III–V semiconductor laser," Optics
Letters, vol. 45, pp. 1499-1502, 2020/03/15 2020.
Z.Z. participated in designing the experiments, conducting the experiments, analyzing
the data and writing the manuscript.
[4] Z. Zhang and A. Yariv, "A General Relation Between Frequency Noise and Lineshape
of Laser Light," IEEE Journal of Quantum Electronics, vol. 56, pp. 1-5, 2020.
Z.Z. participated in designing the experiments, conducting the experiments, analyzing
the data and writing the manuscript.
[5] Q.-F. Yang, B. Shen, H. Wang, M. Tran, Z. Zhang, K. Y. Yang, et al., "Microresonator
Spectrometer Using Counter-propagating Solitons," in Conference on Lasers and
Electro-Optics, San Jose, California, 2019, p. AF2K.1.
Z.Z. aided in conducting the experiments and writing the manuscript.
[6] Z. Zhang, H. Wang, N. Satyan, G. Rakuljic, C. T. Santis, and A. Yariv, "Coherent and
Incoherent Optical Feedback Sensitivity of High-coherence Si/III-V Hybrid Lasers," in
Optical Fiber Communication Conference (OFC) 2019, San Diego, California, 2019, p.
W4E.3.
Z.Z. participated in designing the experiments, conducting the experiments, analyzing
the data and writing the manuscript.
[7] K. Zou, Z. Zhang, P. Liao, H. Wang, Y. Cao, A. Almaiman, et al., "Using a Hybrid Si/IIIV Semiconductor Laser to Carry 16- and 64-QAM Data Signals over an 80-km

vii
Distance," in 2019 Optical Fiber Communications Conference and Exhibition (OFC),
2019, pp. 1-3.
Z.Z. participated in designing the experiments, conducting the experiments, analyzing
the data and writing the manuscript.
[8] Q.-F. Yang, B. Shen, H. Wang, M. Tran, Z. Zhang, K. Y. Yang, et al., "Vernier
spectrometer using counterpropagating soliton microcombs," Science, vol. 363, p. 965,
2019.
Z.Z. aided in conducting the experiments and writing the manuscript.

viii

TABLE OF CONTENTS

Acknowledgements…………………………………………………………...iii
Abstract ………………………………………………………………………iv
Published Content and Contributions……………………………………........vi
Table of Contents……………………………………………………………viii
List of Illustrations and/or Tables……………………………………………...x
Chapter 1: Introduction ........................................................................................ 1
1.1 Deployment of coherent optical communication systems ..................... 1
1.2 Desire of the right light sources .............................................................. 2
1.3 Content of this thesis ............................................................................... 3
Chapter 2: Theory of laser coherence and high-coherence Si/III-V lasers ........ 5
2.1 Coherence of semiconductor lasers ........................................................ 5
2.1.1 Spontaneous emission and quantum noise .................................... 5
2.1.2 Coupling between intensity noise and frequency noise ................ 8
2.1.3 Direct current modulation of semiconductor lasers ...................... 9
2.1.4 Laser frequency noise PSD .......................................................... 11
2.2 High-coherence Si/III-V lasers ............................................................. 13
2.2.1 Reduce quantum noise with mode engineering........................... 13
2.2.2 Hybrid Si/III-V lasers ................................................................... 14
2.2.3 Laser characterization: power and spectrum ............................... 19
2.2.4 Laser characterization: relaxation resonance frequency and alpha
parameter ...................................................................................... 20
2.2.5 Laser characterization: frequency noise PSD .............................. 22
2.3 Conclusions ........................................................................................... 25
Chapter 3: Coherent optical communication .................................................... 26
3.1 Fundamental of coherent optical communications............................... 26
3.1.1 Quadrature amplitude modulation ............................................... 27
3.1.2 Demodulation and detection ........................................................ 31
3.1.3 Digital signal processing (DSP) ................................................... 33
3.1.4 System performance ..................................................................... 35
3.2 Si/III-V lasers as the light sources ........................................................ 36
3.2.1 Back-to-Back coherent communications ..................................... 36
3.2.2 Si/III-V laser vs III-V DFB laser vs external cavity laser ........... 37
3.2.3 ZR coherent communications ...................................................... 42
3.3 Conclusions ........................................................................................... 46
Chapter 4: Impacts of optical feedback on laser coherence ............................. 47
4.1 Coherent optical feedback and incoherent optical feedback ................ 48
4.2 Coherent optical feedback effects on laser coherence.......................... 49
4.3 Incoherent optical feedback effects on laser coherence ....................... 52
4.4 Lasers’ sensitivity to optical feedback .................................................. 54
4.5 Sensitivity to coherent optical feedback ............................................... 55

ix
4.6 Sensitivity to incoherent optical feedback ............................................ 59
4.7 System performance under coherent optical feedback ......................... 66
4.8 System performance under incoherent optical feedback ...................... 68
4.9 OSNR penalty due to optical feedback ................................................. 71
4.10 Conclusions.......................................................................................... 72
Chapter 5: A general relation between laser frequency noise and lineshape ... 74
5.1 Derivation of the general relation.......................................................... 74
5.2 Validation of the Central Relation ........................................................ 78
5.3 Insights into the Central Relation .......................................................... 80
5.3.1 Optical filtering of laser frequency noise PSD ............................ 81
5.3.2 Is laser linewidth a good measure for laser coherence ................ 85
5.4 Conclusions............................................................................................ 88
Bibliography ...................................................................................................... 89

LIST OF ILLUSTRATIONS AND/OR TABLES

Figure 2.1 Phasor model of spontaneous emission ............................................. 7
Figure 2.2 Coupling between laser intensity noise and frequency noise ........... 8
Figure 2.3 Normalized direct current modulation response of semiconductor
lasers................................................................................................. 11
Figure 2.4 Frequency noise PSD of semiconductor lasers when (a) photon
lifetime << electron lifetime and (b) photon lifetime ~ electron
lifetime ............................................................................................. 13
Figure 2.5 Structure and mode profile of Si/III-V lasers. The red dash line
indicates that the lasing mode is evanescently coupled to the
quantum wells .................................................................................. 16
Figure 2.6 (a) Flow chart of laser fabrication, (b) SEM image of the silicon
resonators, (c) Optical image of the laser chip after wafer-bonding
and (d) Optical image of the final laser chip................................... 18
Figure 2.7 (a) LIV curves under various temperature and (b) optical spectra of
Si/III-V lasers ................................................................................... 20
Figure 2.8 Measurement setups for laser modulation response ....................... 21
Figure 2.9 Modulation responses and alpha parameters of Si/III-V lasers ...... 22
Figure 2.10 Measure setup for laser frequency noise PSD. RFSA: radio
frequency spectrum analyzer ........................................................... 23
Figure 2.11 Frequency noise PSD of the Si/III-V laser .................................... 24
Figure 2.12 Frequency noise PSD of a commercial III-V DFB laser .............. 24
Figure 3.1 A coherent optical communication link .......................................... 27
Figure 3.2 (a) An optical waveform of QAM, (b) Structure of an IQ modulator
and (c) Constellation diagrams of QAM......................................... 30
Figure 3.3 (a) Structure of coherent receivers (b) Demodulation .................... 32
Figure 3.4 Digital signal processing module .................................................... 34
Figure 3.5 BER as a function of OSNR and phase noise. Black arrows indicate

xi
the direction in which the phase noise increases ............................ 36
Figure 3.6 Measurement setup for coherent optical communications ............. 37
Figure 3.7 Frequency noise PSD of lasers used in the experiments ................ 38
Figure 3.8 20 GBaud 16-QAM (a) system performance and (b) Constellation
diagrams ........................................................................................... 40
Figure 3.9 20 GBaud 64-QAM system performance ....................................... 42
Figure 3.10 ZR communication system performance (a) 16-QAM (b) power
optimization for 16-QAM (c) 64-QAM (d) power optimization for
64-QAM ........................................................................................... 44
Figure 4.1 Optical feedback .............................................................................. 48
Figure 4.2 Schematic diagram of coherent optical feedback ........................... 50
Figure 4.3 Noise coupling (a) w/o coherent optical feedback and (b) w/
coherent optical feedback ................................................................ 51
Figure 4.4 Schematic diagram of incoherent optical feedback ........................ 53
Figure 4.5 Noise coupling (a) w/o incoherent optical feedback and (b) w/
incoherent optical feedback ............................................................. 54
Figure 4.6 Measurement setup for laser frequency noise PSD under coherent
optical feedback ............................................................................... 56
Figure 4.7 Frequency noise PSD of (a) the III-V laser and (b) the Si/III-V
laser under various levels of coherent optical feedback ................. 57
Figure 4.8 Coupling between intensity noise and phase noise ......................... 59
Figure 4.9 Measurement setup for laser frequency noise PSD under incoherent
optical feedback ............................................................................... 60
Figure 4.10 (a) ASE noise spectrum and optical spectra of (b) the hybrid
Si/III-V laser and (c) the III-V laser with ASE noise injected ....... 61
Figure 4.11 Frequency noise PSD of (a) the III-V laser and (b) Si/III-V laser
w/ and w/o the existence of incoherent optical feedback and (c) the
corresponding linewidth as a function of ASE power .................... 63
Figure 4.12 (a) Intensity noise PSD of the III-V DFB laser at various injected
ASE power and (b) the increment of laser intensity noise and laser

xii
frequency noise, respectively ......................................................... 65
Figure 4.13 Measurement setup for coherent optical feedback........................ 66
Figure 4.14 System measurement of (a) the Si/III-V laser and (b) the III-V
DFB laser under coherent optical feedback .................................... 67
Figure 4.15 Constellation diagrams of the III-V DFB laser (a) w/o optical
feedback and (b) with the feedback level beyond -41 dB .............. 68
Figure 4.16 Measurement setup for incoherent optical feedback .................... 69
Figure 4.17 System measurement of (a) the Si/III-V laser and (b) the III-V
DFB laser under incoherent optical feedback ................................. 70
Figure 4.18 Constellation diagrams of the III-V DFB laser (a) w/o optical
feedback and (b) with the ASE power of 0.7 mW.......................... 71
Figure 4.19 Power penalty due to (a) coherent and (b) incoherent optical
feedback ........................................................................................... 72
Figure 5.1 Measurement setups for (a) frequency noise power spectral density
and (b) lineshape. PC: polarization controller; RFSA: radio
frequency spectrum analyzer. A narrow-linewidth fiber laser is used
as the reference laser........................................................................ 79
Figure 5.2 (a) Frequency noise PSD of the laser (b) Corresponding phase noise
PSD and lineshape of the laser ........................................................ 80
Figure 5.3 Measurement setup for the frequency noise PSD of laser output
modified by the MZI with the free spectral range of 203 MHz ..... 82
Figure 5.4 Schematic plot of the laser lineshape and transmission spectrum of
the MZI; the laser frequency aligned to maximum transmission
frequency of the MZI....................................................................... 83
Figure 5.5 (a) Frequency noise PSD of the laser and laser passing through the
MZI (b) Ratio between the two frequency noise PSDs .................. 84
Figure 5.6 Frequency noise PSD of the Si/III-V laser ...................................... 86
Figure 5.7 Frequency noise PSD of the III-V DFB laser w/o and w/ small
coherent optical feedback ................................................................ 86
Figure 5.8 Optical lineshape of the three lasers ................................................ 87

xiii
Figure 5.9 System performance of the three lasers ........................................... 88

Chapter 1

INTRODUCTION
The invention of semiconductor lasers has revolutionized the information technology
industry. It enables high-speed optical communications, leading to the birth of the modern
Internet, which is one of the main engines of the world’s advancement over the past several
decades [1-6]. However, human society has developed to the point when traditional optical
communication technology can no longer satisfy the fast-increasing needs on the data rate.
Hence, it is indispensable to employ new optical communication systems, i.e. coherent
optical communication systems, which require lasers with much higher phase coherence than
the conventional III-V DFB lasers as the light sources. Certainly, the 21st century
communication infrastructure will be powered by new-generation semiconductor lasers.
1.1 Deployment of coherent optical communication systems
We are living in the information age, when a huge amount of data is collected, stored,
analyzed and transmitted on the daily basis. In the upcoming future, more and more users
around the world will have access to the Internet; more electronic devices such as smart
phones, tablets, and computers will be connected to the Internet; new companies based on
big data, cloud computing and artificial intelligence, along with new business models, are
going to emerge; people demand faster and faster Internet speed for both work and personal
enjoyment. The annual global data traffic growth rate is predicted to be 26% by Cisco, which
is a huge burden for the current optical communication systems. At this moment, upgrading
current optical communication networks to meet the ever-increasing demands on the data
rate has become the primary task in the field [7-9].
Conventional optical communications employ 2-level pulse amplitude modulation (PAM2),
where information is encoded in the intensity of semiconductor lasers, with high and low
laser intensity representing 1 and 0, respectively. The simplicity of such a modulation scheme
makes possible the construction of the optical communication systems with inexpensive

optical components such as directly modulated lasers (DMLs) and electro-absorption
modulated lasers (EMLs) [10-12]. Thus, traditional optical networks are exclusively
powered by conventional III-V DFB lasers. However, the spectral efficiency, defined as the
ratio between the data rate and the modulation frequency, of PAM2 is quite low, rendering
it unable to support the ultra-high data rate which the world is demanding.
Coherent optical communications employ more complex modulation schemes such as
quadrature amplitude modulation (QAM), where information is encoded in both the intensity
and the phase of lasers, and therefore have higher spectral efficiency, boosting the capacity
of communication links to meet the increasing demands on the data rate [13, 14]. Currently,
major players in this area are racing towards developing coherent transceivers supporting the
data rate of 400 Gbits/s or even higher. Coherent optical communication networks are likely
to be widely deployed in the next decade or so and we are now witnessing the beginning of
such a transition.
1.2 Desire of the right light sources
Despite the advantages, the construction cost of coherent optical communication systems is
much higher because of the increased complexity of the optoelectronic components,
inevitably slowing down the transition towards coherent optical networks. The key to
reducing the cost is integration, where electronic and photonic devices can be miniaturized
and fabricated massively on a chip. While integrated electronics has moved progressively
towards sub-10nm technology, the development of photonic integration has been far slower.
The major challenge lies at integrating semiconductor lasers with passive photonic devices.
Conventional III-V DFB lasers, the main light sources in the present optical networks, can
be easily fabricated on chip but lack the phase coherence and the feedback insensitivity to
serve as the integrated light sources in coherent optical communications. Instead, what has
been practically used now in commercial coherent transceivers is the Micro Integrable
Tunable Laser Assembly (u-ITLA), an ECL with high phase coherence [15, 16]. Its
fabrication requires extra elaborate assembling, rendering the ECL expensive and unsuitable
for photonic integration. Thus, new types of semiconductor lasers are necessary.

Here, we are going to present heterogeneous semiconductor lasers on silicon, a widely used
platform for integrated photonics [17-21]. Such a new type of semiconductor lasers, i.e. the
hybrid Si/III-V lasers, whose high coherence and feedback insensitivity will be demonstrated
later in the thesis, is exactly the light source needed for the upcoming coherent optical
communication networks.
1.3 Content of this thesis
The core devices discussed in this thesis are, of course, the Si/III-V lasers. Different
experiments have been carried out to characterize various properties of the Si/III-V lasers
and to illustrate their superiority to the commercial counterparts. The whole thesis is
organized as follows.
Chapter 2 starts with the conventional theory of laser coherence, explaining the origin of
quantum noise in semiconductor lasers. The theoretical linewidth and frequency noise PSD,
which are two common measures for laser coherence, of semiconductor lasers will be
introduced. Next, we are going to discuss how to design high-coherence Si/III-V lasers with
mode engineering, focusing on how to reduce quantum noise based on the physics. After
that, the lasers’ fabrication process will be mentioned. Lastly, the properties of the Si/III-V
lasers such as power, threshold and frequency noise PSD will be measured.
Chapter 3 focuses on coherent optical communications. In the first half of this chapter, we
are going to show how a coherent optical communication link is constructed. First, we are
going to explain how the modulation and demodulation processes are done physically. The
two key photonic components, namely the inphase-quadrature (IQ) modulator and
demodulator, will be discussed. Next, we will talk about digital signal processing (DSP),
which is used to recover the information from the distorted signals obtained after
demodulation. We will pay special attention to how the phase information is recovered by
DSP, as it is directly related to the phase coherence of the light sources. In the second half of
this chapter, the system performances of the Si/III-V laser, a conventional III-V DFB laser
and an ECL will be measured, analyzed and compared.

Chapter 4 is about semiconductor lasers’ feedback sensitivity. This old but important
subject regains our attention as large-scale photonic integration faces optical feedback as the
main obstacle. Because optical isolators cannot be integrated on chip, any unwanted optical
feedback can potentially degrade semiconductor lasers, rendering the communication
systems dysfunctional. In this chapter, we will first establish the theories on how optical
feedback affects laser coherence and then measure the feedback sensitivity of the hybrid
Si/III-V lasers in comparison to the conventional III-V DFB laser. Finally, we are going to
show that the Si/III-V lasers can function properly in an isolator-free coherent optical
communication system.
In Chapter 5, we will discuss the relation between different means of characterizing laser
coherence. A general relation between laser frequency noise PSD and lineshape, named as
the Central Relation, will be derived. The Central Relation brings us new insights such as
new methods of tailoring laser frequency noise PSD with optical filtering.

Chapter 2

THEORY OF LASER COHERENCE AND HIGH-COHERENCE
SI/III-V LASERS
In this chapter, we are going to introduce the quantum mechanical theory of laser coherence,
discuss how to apply the theory to designing high-coherence Si/III-V lasers and characterize
the properties of the Si/III-V lasers such as power, threshold and frequency noise PSD.
2.1 Coherence of semiconductor lasers
Coherence, a critical concept in laser physics, describes how far the laser field deviates from
being monochromatic. Mathematically, the laser field can be expressed as
E=
(t ) {E0 + δ (t )}ei{ω0t +ϕ (t )} ,

(2.1)

where E0 and ω0 represent the amplitude and the angular frequency of the laser field,
respectively. δ (t ) and ϕ (t ) are laser amplitude and phase noise. Because of gain saturation in
semiconductor lasers, the amplitude noise in general is largely suppressed so that the
monochromaticity is mainly determined by the phase noise. Later, we will explain where the
laser phase noise arises from with quantum mechanics. In addition, two major means of
quantifying laser coherence, namely laser linewidth and frequency noise PSD, will be
introduced.
2.1.1 Spontaneous emission and quantum noise
The core of semiconductor laser physics lies at the interaction between the laser field and the
semiconductor quantum wells. The interaction Hamiltonian can be written as
  
HI =
−qE (r ) ⋅ x,

(2.2)

where q and x are the charge and the coordinate operator of an electron, respectively. The
 

electric field E (r ) can be further quantized as

 

ω +
E (r ) i
(a − a )u (r )e,
2ε

(2.3)

where ω is the angular frequency of the laser light and ε is the permittivity. a + and a are

the creation and the annihilation operators, respectively. u (r ) represents the normalized

optical mode and e is the unit vector.
The transitions of electrons from the conduction band to the valence band result in the
emission of photons. With time-dependent perturbation theory, the emission rate can be
calculated as
 
π q 2ω
|< V | e ⋅ x | C >|2 ( N p + 1) g (ω ) | u (r ) |2
 
 
π q 2ω
π q 2ω
|< V | e ⋅ x | C >|2 N p g (ω ) | u (r ) |2 +
|< V | e ⋅ x | C >|2 g (ω ) | u (r ) |2

W=

(2.4)

= Wst + Wsp ,

where | C > and | V > represent the quantum states of the conduction band and the valence
band, respectively. N p is the total photon number and g (ω ) , the lineshape function, is a
direct result of Fermi’s golden rule.
The transition rate can be divided it into two terms, namely Wst and Wsp . The former term,
proportional to N p , corresponds to stimulated emission, a process in which new photons are
generated coherently. It provides gain for semiconductor lasers. The latter term is referred to
as spontaneous emission. It is independent on the photon number, suggesting that incoherent
photons are generated in such a process. Interestingly and importantly, the spontaneous
emission rate is always the same as the stimulated emission rate induced by a single photon.
Such a relation sets the ratio between the magnitudes of the coherent and incoherent optical
fields to be N p :1 .
Now, we are going to switch to a classical picture to better describe the laser field, which is
composed of the coherent and incoherent optical fields, as shown schematically in Fig. 2.1.

The incoherent optical field has a fixed magnitude but a random phase relative to the
coherent optical field. The red circle in Fig. 2.1 represents its ensemble. The magnitude and
the phase of the laser field fluctuate with the normal and tangential parts of the incoherent
optical field, which are essentially the noise sources. Evidently, the non-monochromaticity
of the laser field is originated from spontaneous emission.

Figure 2.1 Phasor model of spontaneous emission
As discussed before, it is the phase noise of lasers that mostly broadens the power spectrum,
namely the lineshape, of the laser field, of which the full width half maximum (FWHM), i.e.
the laser linewidth, was first derived by Schawlow and Townes [22], and is now well known
as the S-T linewidth:

Wsp
∆υ ST = .
4π N p

(2.5)

2.1.2 Coupling between intensity noise and frequency noise
The real linewidth of semiconductor lasers is typically larger than the S-T linewidth because
in semiconductor lasers, the intensity noise is coupled to the phase noise, causing additional
broadening of the lasers’ power spectrum, of which the mechanism is shown schematically
in Fig. 2.2. The laser intensity noise perturbs the stimulated emission rate and induces
fluctuations of the inverted electron number. Therefore, the gain, proportional to the inverted
electron number, also gets perturbed, causing the fluctuations of the refractive index of the
lasing mode because of their interconnection described by Kramers-Kronig relations. The
drift of the mode index leads to the drift of the lasing frequency, i.e. additional phase noise
and a more broadened optical spectrum.

Figure 2.2 Coupling between laser intensity noise and frequency noise
This coupling mechanism is known as linewidth enhancement, whose effect on the laser
linewidth can be expressed as
∆=
υH

Wsp
4π N p

(1 + α 2 ),

(2.6)

where α is the linewidth enhancement factor and was first introduced by Charles Henry
[23]. Its value can be calculated using
α=

∂χ r ∂N e
∂χ i ∂N e

(2.7)

where χ r and χ i are the real and imaginary parts of the optical susceptibility, respectively
and N e represents the electron number. The linewidth enhancement factor describes the
magnitude of the coupling between laser intensity noise and phase noise, whose value is
typically between two and ten in semiconductor lasers.
2.1.3 Direct current modulation of semiconductor lasers
In addition to laser linewidth, laser frequency noise PSD is also a widely used measure for
laser coherence. Before officially introducing it, in this section, we are going to talk about
direct current modulation of semiconductor lasers, which is closely related to laser frequency
noise PSD.
The direct current modulation process can be described with the following equations:
dN
− − A( N − N tr ) P
dt eV τ
dP
= A( N − N tr ) PΓ a − ,
dt
τp

(2.8)

where N and P represent the electron and photon number density, respectively. e is the
electron charge and V is the total volume of the laser. τ and τ p represent the electron and
photon lifetime. A is the coefficient for stimulated emission and Γ a is the mode confinement
factor in the active region. I is the injected current.
We consider small signal modulation here, i.e. small perturbations around a steady state, and
plug the attempted solution
I I 0 + i1eiωt
N N 0 + n1eiωt
P= P0 + p1e

(2.9)

iω t

into (2.8), where I 0 , N 0 and P0 are the current, the electron and photon number density of
the steady state while i1 , n1 and p1 represent the modulated parts. ω is the modulation
frequency. After some algebra, we obtain the modulation response

i1 AP0 Γ a eV
P1 = − 2
ω − iω τ − iω AP0 − AP0 τ p

10
(2.10)

This is a typical second order filter. Depending on the relation between the electron and
photon lifetime, the modulation response functions can be dramatically different, as shown
in Fig. 2.3. If the photon lifetime is much shorter than the electron lifetime, which is the case
for conventional III-V DFB lasers, the corresponding modulation response is peaked at the
so-called relaxation resonance frequency, which is defined below. On the contrary, if the
photon lifetime becomes comparable to the electron lifetime, the modulation response is
damped and straightly rolls off beyond the relaxation resonance frequency. Such difference
affects the semiconductor lasers’ coherence significantly, which will be explained later.
The relaxation resonance frequency is defined as
ωR =

AP0

τp

1 1
− ( + AP0 ) 2 ,
2 τ

(2.11)

indicating how fast the laser can be modulated directly. It is worth pointing out that we did
not take the parasitic capacitance of the materials into account. Hence, with regard to the
practical modulation bandwidth of semiconductor lasers, the relaxation resonance frequency
is the upper bound.

11

Figure 2.3 Normalized direct current modulation response of semiconductor lasers
2.1.4 Laser frequency noise PSD
Single-sided laser frequency noise PSD is defined as
+∞

S ∆υ ( f )= 2 ∫ < ϕ (t )ϕ (t + τ ) >e − i 2π f τ dτ ,
−∞

(2.12)

where <> denotes the time or ensemble average and ϕ (t ) is the frequency noise. τ and f
represents the time delay and the frequency, respectively. Unlike laser lineshape, laser
frequency noise PSD does not contain any explicit information on the optical field.
The frequency noise PSD of semiconductor lasers can be expressed as
∆υ ST

{1 + α 2 H ( f )}
∆υ ST ∆υ ST 2
α H ( f ),

S=
∆υ ( f )

(2.13)

where H ( f ) represents the normalized direct current modulation response. The frequency
noise PSD can be decomposed into two terms. The first term, which is a constant,

12
corresponds to the frequency noise generated by spontaneous emission while the second
term, as a function of the linewidth enhancement factor, is a direct consequence of the
coupling between laser intensity and frequency noise, which involves the process of
modulating the electron number as manifested by the direct current modulation response. Far
below and above the relaxation resonance frequency, the frequency noise PSD is white at the
levels of ∆υ H π and ∆υST π , respectively. Around the relaxation resonance frequency, the
frequency noise PSD can be either peaked or damped, depending on the relation between the
electron and photon lifetime, as shown in Fig. 2.4.
So far, we have introduced two measures for laser coherence. Here comes a natural question:
which one shall we use for our applications? Eventually, we would like to predict the lasers’
performance in the coherent optical communication systems based on their phase coherence.
Therefore, it is more straightforward and meaningful to use laser frequency noise PSD as the
measure, to which the phase noise in the coherent communication systems is related in a
simple way
+∞

σ ϕ2 = 4∫ S ∆υ ( f )

sin 2 (π f τ 0 )
df ,
f2

(2.14)

where τ 0 is the symbol duration time and σ ϕ2 represents the variance of the phase noise in
the communication system. You may also ask ‘is it possible that we can relate the lineshape
to the frequency noise PSD so that the phase noise can be expressed as a function of the
linewidth’. The answer to that question is, unfortunately, generally no. There is one special
case in which those two measures can be used interchangeably and that is the laser frequency
noise PSD being white [24]. Practically, due to the technical noise from current,
environment, temperature controller and so on, the frequency noise PSD of semiconductor
lasers is never white.
However, as both measures can be utilized reasonably to characterize laser coherence, they
must be related to each other in some way. Such a subject will be discussed in detail in

13
Chapter 5, where a general relation between laser frequency noise PSD and lineshape is
derived.

Figure 2.4 Frequency noise PSD of semiconductor lasers when (a) photon lifetime <<
electron lifetime and (b) photon lifetime ~ electron lifetime
2.2 High-coherence Si/III-V lasers
In the remainder, we will apply the theories to designing the high-coherence Si/III-V lasers.
After that, we will present the fabrication process and the properties of the Si/III-V lasers.
2.2.1 Reduce quantum noise with mode engineering
To enhance the coherence of semiconductor lasers, we shall suppress the spontaneous
emission rate

 
πq ω
|< V | e ⋅ x | C >|2 g (ω ) | u (r ) |2 .
Wsp=

14
(2.15)

It can be accomplished by engineering the laser structure to reduce the mode confinement
| u (r ) |2 inside quantum wells. However, it inevitably leads to the reduction of the stimulated

emission rate, the gain of semiconductor lasers
Wst=

 
π q 2ω
|< V | e ⋅ x | C >|2 N p g (ω ) | u (r ) |2 .

(2.16)

If the gain gets reduced significantly while the loss maintains, the threshold of the lasers
would surge. To overcome such a problem, the loss of the lasers must be decreased by the
same amount. It can be achieved by storing the optical energy pulled out of the gain materials,
which are lossy due to heavy doping, in other materials with ultra-low loss. This mode
engineering approach is not new. As a matter of fact, it is exactly why ECLs are very
coherent. In that case, the optical energy is moved out of the lossy III-V materials and stored
in the low-loss external cavities made of air or silica. The disadvantages of the external
cavities have been discussed in chapter 1. What we intend to achieve here is effectively to
replace the external cavities with low-loss silicon resonators, which can be heterogeneously
integrated with III-V materials.
Besides, a large amount of photons can be stored in the low-loss silicon resonators. Thus, the
S-T linewidth, which is proportional to the ratio between the spontaneous emission rate and
the stored photon number, can be substantially reduced.
2.2.2 Hybrid Si/III-V lasers
The very first hybrid Si/III-V Fabry-Perot (FP) laser was demonstrated by John Bower’s
group at university of California, Santa Barbara (UCSB) [25]. The newly developed wafer
bonding technology enables the heterogeneous integration, which allows us to fabricate the
Si/III-V lasers with CMOS-compatible wafer-scale processing.

15
The structure of the high-coherence Si/III-V laser is shown in Fig. 2.5, with the III-V die
on top of the silicon-on-insulator (SOI) substrate. The detailed layer structure of the III-V
dies can be found elsewhere [26]. N-contact layers (n-doped InP) are bonded to the silicon
substrate while P-contact layers (p-doped InP) are etched to form the mesa structure, defining
the current path. A layer of silicon dioxide is deposited on top of the P-contact layers,
preventing current leakage, on which a small window is opened for the electrical contact.
The current is injected through the center piece of the mesa, to which the optical mode is
evanescently coupled.
The lasing mode is mostly confined in the silicon rather than the III-V materials, of which
the intensity profile is shown in Fig. 2.5. A thin layer of silicon dioxide, i.e. the spacer, is
placed between the III-V materials and the silicon substrate, whose thickness can be adjusted
during the fabrication process in order to tune the mode confinement factor in the quantum
wells and therefore the phase coherence of the lasers. Theoretically, the Si/III-V lasers with
thicker spacer are more coherent. However, the reckless increase of the spacer thickness may
lead to a penalty on the threshold. As discussed in the previous section, in order to maintain
the laser threshold, we need to make sure the gain and the loss get reduced by the same factor,
which can only be achieved if the loss of the optical energy in the low-loss materials is
negligible. However, as we move more and more optical energy into the silicon, to the point
when the total loss in the silicon becomes comparable to the total loss in the III-V materials,
the decrease of the gain would exceed the decrease of the loss, resulting in the increase of
the laser threshold. In our experiments, the spacer thickness is kept below 100 nm.
The detailed fabrication process of the Si/III-V lasers can be found elsewhere [26-29]. Here,
we simply show the flow chart in Fig. 2.6 (a) and briefly talk about each step, giving you
some sense of how hybrid Si/III-V lasers are fabricated. The same fabrication techniques can
be applied to other hybrid platforms.
First, the silicon resonators are fabricated with e-beam lithography followed by two-step
plasma etching. A thin layer of chrome is used as the hard mask for the second etching to

16
avoid the aspect ratio effect. An SEM image of a typical silicon resonator is shown in Fig.
2.6 (b).
Second, the III-V dies are wafer-bonded onto the silicon substrates with their original
substrates removed afterwards using chemicals. The surface of the silicon resonators and the
III-V dies must stay extremely clean for the success of wafer-bonding. At this point, we have
achieved the heterogenous integration, of which an optical image is shown in Fig. 2.6 (c).

Figure 2.5 Structure and mode profile of Si/III-V lasers. The red dash line indicates that the
lasing mode is evanescently coupled to the quantum wells
Third, the mesa structure is defined on the remaining III-V materials with multi-step
photolithography and wet etching. Afterwards, a layer of silicon dioxide is deposited using
chemical vapor deposition (CVD). A window is then opened on the silicon dioxide layer for
metal contacts.

17
At last, metal contacts are deposited onto the mesa. Rapid thermal annealing (RTA) is
often applied to the chips for good ohmic contacts. The final laser chips are shown in Fig.
2.6 (d). There are hundreds of laser devices on a single chip. After lapping and cleaving, we
can measure the properties of individual devices, which will be presented in the following
sections.

18

19

Figure 2.6 (a) Flow chart of laser fabrication, (b) SEM image of the silicon resonator, (c)
Optical image of the laser chip after wafer-bonding and (d) Optical image of the final laser
chip
2.2.3 Laser characterization: power and spectrum
The power-current curves under various temperature and the optical spectrum of the hybrid
Si/III-V laser are shown in Fig. 2.7 (a) and (b), respectively. The laser has a threshold of
roughly 60 mA, more than 3 mW output power under room temperature and a side mode
suppression ratio (SMSR) over 50 dB. The maximum current that can be pumped into the
laser is about 160 mA, beyond which the laser output power drops because of thermal effects.
Compared to commercial III-V DFB lasers, the efficiency of the Si/III-V laser is low. This
is probably because the quality of the quantum wells gets degraded during the wafer bonding
process.

20

Figure 2.7 (a) LIV curves under various temperature and (b) optical spectra of Si/III-V
lasers
2.2.4 Laser characterization: relaxation resonance frequency and alpha parameter
We have introduced the concepts of the alpha parameter and the relaxation resonance
frequency in section 2.1.2 and 2.1.3, respectively, and discussed what roles they play in laser
frequency noise PSD in section 2.1.4. Those two critical parameters of the Si/III-V lasers can
be obtained by measuring the lasers’ direct current modulation responses including both the
intensity and frequency modulation responses. The relaxation resonance frequency is the
modulation bandwidth and the alpha parameter, representing the coupling strength between

21
laser intensity and frequency noises, can be obtained by taking the ratio between the
frequency and intensity modulation depths [30].
The measurement setup is shown in Fig. 2.8. The laser’s intensity and frequency modulation
responses are measured with the first and second optoelectronic loops, respectively. The
network analyzer produces small electrical modulation signals and measures the response.
In the frequency modulation response measurement, a Mach-Zehnder interferometer (MZI)
is utilized as the frequency discriminator, with the laser locked to its quadrature point using
an electrical feedback circuit.

Figure 2.8 Measurement setups for laser modulation response
The Si/III-V laser’s modulation responses are displayed in Fig. 2.9. Both the intensity and
frequency modulation responses start to roll off at the relaxation resonance frequency, which
is around 1 GHz. The ratio between the frequency and intensity modulation depths,
indicating the coupling between laser intensity and frequency noise, is shown in the inset in
Fig. 2.9. At relatively low frequencies, thermal effects are dominant as the thermo-optic
coefficient of silicon is quite large. At high frequencies, thermal effects, due to their slow
dynamics, become negligible and the coupling is purely due to carrier effects, i.e. linewidth

22
enhancement. The ratio curve in the inset approaches to a constant at high frequencies,
which is the alpha parameter with a value of 2.57 in this case.
In addition to laser frequency noise PSD, the coupling between laser intensity and frequency
noise plays an important role in lasers’ feedback sensitivity. We will come back to the ratio
curve in Chapter 4, where the feedback sensitivity of the Si/III-V laser is investigated.

Figure 2.9 Modulation responses and alpha parameters of Si/III-V lasers
2.2.5 Laser characterization: frequency noise PSD
Finally, it comes to examining the coherence of the Si/III-V lasers. The setup for measuring
laser frequency noise PSD is shown in Fig. 2.10. An MZI with a free spectral range (FSR)
of roughly 1.5 GHz is used as the frequency discriminator. The laser is locked to its
quadrature point with the same electrical feedback circuit used for frequency modulation
response measurement. Balanced photodetectors are used to minimize the effects of the
intensity noise on the measurement. The laser frequency noise PSD can be derived based on
the PSD of the output of the balanced photodetectors [26, 31-33].

23

Figure 2.10 Measure setup for laser frequency noise PSD. RFSA: radio frequency spectrum
analyzer
The results are shown in Fig. 2.11. Due to the response bandwidth of the MZI, we can only
measure the frequency noise PSD below the relaxation resonance frequency. The measured
frequency noise PSD corresponds to a ∆υ H of 5.4 KHz. Using the alpha parameter obtained
in the previous section, the S-T linewidth ∆υST is calculated to be about 0.7 KHz.
For comparison, the frequency noise PSD of a typical commercial III-V DFB laser is
displayed in Fig. 2.12. The ∆υ H of the III-V DFB laser is on the order of MHz and the
relaxation resonance frequency is around 10 GHz. Using equation (2.13) and assuming a
modulation frequency of 20 GHz, the Si/III-V lasers generate at least an order of magnitude
less phase noise than the commercial III-V DFB lasers in the coherent optical
communications.
It is important to point out that the frequency noise around the relaxation resonance frequency
of the III-V DFB laser contributes significantly to the phase noise due to its large magnitude
and high bandwidth. Hence, the high coherence of the Si/III-V laser truly means low quantum
noise, a small relaxation resonance frequency and a damped current modulation response, all
of which are direct consequences of a large photon lifetime.

24

Figure 2.11 Frequency noise PSD of the Si/III-V laser

Figure 2.12 Frequency noise PSD of a commercial III-V DFB laser

25
2.3 Conclusions
In this chapter, we have discussed how to design and fabricate high-coherence Si/III-V lasers
and characterized their properties. With the merits of possessing both monolithic structure
and high phase coherence, the hybrid Si/III-V lasers have great potential to be the light
sources in the upcoming coherent optical communication systems.

26
Chapter 3

COHRERENT OPTICAL COMMUNICATION
Coherent optical communication, as discussed in chapter 1, is considered as the indispensable
solution to the ever-increasing demands for the data rate. Unlike traditional incoherent optical
communications, they employ more complex modulation formats, leading to the fact that
most electronic and photonic components in the coherent optical communication networks,
such as modulators, demodulators and signal processing modules, are much different from
their conventional counterparts. Here, we will give an overview of how information is
encoded, decoded and processed in the coherent optical communications. Afterwards, the
performance of the high-coherence Si/III-V lasers in the coherent optical communication
system will be presented in comparison to the performance of a conventional III-V DFB laser
and a commercial ECL.
3.1 Fundamentals of coherent optical communications
A coherent optical communication link is shown schematically in Fig. 3.1, where a
transmitter and a receiver are connected to each other with an optical fiber.
The transmitter consists of a laser as the light source and a dual-polarization IQ modulator
for polarization division multiplexing (PDM). To fully use the capacity of optical fibers,
different information can be encoded in the polarization as well as laser intensity and phase,
by splitting the laser light into two beams, modulating them separately, rotating the
polarization of one laser light by 90 degrees and eventually combining them together. Those
are exactly the functions of IQ modulators.
In the receiver, lights with orthogonal polarizations are separated and then demodulated in a
dual-polarization IQ demodulator, where the electro-optical conversion takes place. The
obtained electrical signals must be processed digitally for the encoded information to be
correctly retrieved, where multiple algorithms are applied for signal processing.

27
The details on how the IQ modulators and demodulators are physically constructed will
be revealed in the following sections, which can help us understand how information is
encoded and decoded in the coherent optical communications.

Figure 3.1 A coherent optical communication link
3.1.1 Quadrature amplitude modulation
The schematic structure of the IQ modulators is shown in Fig. 3.2 (a). Each lane in the figure
represents a waveguide. The refractive index of a waveguide, which is flanked by two
electrodes, can be tuned by applying different voltages, making such a structure a phase
modulator. Two phase modulators connected by two 50/50 couplers and sharing the same
ground constitute a Mach-Zehnder modulator (MZM), which is used for intensity
modulation.
The IQ modulator works as follows. The laser field is equally split into two at the input. The
two optical fields, known as in-phase and quadrature components, travel along two different

28
paths, where their intensity and phase are modulated independently, and eventually are
combined at the output
Eout (t )
Ein (t )

uQ (t )
u (t )
π ),
cos( I π ) + i
cos(
2Vπ
2Vπ

In Phase

(3.1)

Quadrature

where Ein (t ) and Eout (t ) represent the input and output optical fields. uI (t ) and uQ (t ) are the
digitalized voltage signals applied to the MZMs, modulating the intensity of the in-phase and
quadrature components, respectively. Vπ , a key parameter of the MZM, denotes the voltage
at which the phase difference between the two phase modulators is π .
This type of modulation is known as QAM, where both the amplitude and the phase of the
light are modulated. To better illustrate that, an optical waveform of QAM is shown in Fig.
3.2 (b) as an example. The entire waveform consists of a sequence of optical pulses, each
satisfying equation (3.1) and having independent amplitude and phase. The red and green
arrows point to the places where the intensity and the phase of the pulses, due to modulation,
are different. In the literature, we refer to each optical pulse as a symbol, i.e. the smallest unit
carrying the information.
Conventionally, we use constellation diagrams, as shown in Fig. 3.2 (c), to represent the
ensemble of the symbols, meaning that each symbol is mapped to a certain constellation in
the diagram. We set the magnitudes of the in-phase and quadrature components as the two
Cartesian coordinates. Hence, each symbol can be mapped to a certain point in that twodimensional space, thus becoming a constellation. The amplitude and the phase of the symbol
are now represented by the norm and the phase of its corresponding constellation. The set of
all the constellations forms the constellation diagram. Each constellation diagram
corresponds to a unique modulation format.
To encode the information, we map a sequence of bits to a certain constellation. If there are
in total M = 2N constellations, then each constellation represents a N-bit sequence. In other
words, each symbol carries N bits of information. A quadrature-amplitude modulation

29
scheme with M constellations is referred to as M-QAM. In our experiments, both 16-QAM
and 64-QAM are employed, whose constellation diagrams can be found in Fig. 3.2 (c).

30

Figure 3.2 (a) An optical waveform of QAM, (b) Structure of an IQ modulator and (c)
Constellation diagrams of QAM

31
3.1.2 Demodulation and detection
In the modulation process, mixing occurs between beams with orthogonal polarizations and
between their in-phase and quadrature components. Demodulation is the reverse process of
modulation, where different components get separated before the detection.
The structure of the IQ demodulators is shown schematically in Fig. 3.3 (a). A polarization
beam splitter (PBS) is placed at the input to separate the optical fields with orthogonal
polarizations. Each optical field and the light from a local oscillator (LO), a high-coherence
tunable ECL in our case, are then hybridized in a 90 degree optical hybrid, which has two
inputs and four outputs. Each output is composed of the two inputs with unique phase offsets,
as shown in Fig. 3.3 (b). The phase offsets of two adjacent outputs differ by 90 degrees,
which the name ‘90 degree optical hybrid’ implies.
In the detection process, two balanced photodetectors are used, each detecting two outputs
of the four, whose phase offsets differ by 180 degrees, as shown in Fig. 3.3 (b). Assuming
E1 (t ) and E2 (t ) are the LO and the signal, respectively, which can be expressed as
E1 (t ) = eiω0t
E2 (t ) = a (t )ei{ω0t + b (t )} ,

(3.2)

where a(t ) and b(t ) represent the intensity and phase modulations, respectively, then the
electrical signal from the upper balanced photodetector is
Re[a=
(t )ei{b (t ) +ϕ } ] a (t ) cos{b(t ) + ϕ},

(3.3)

where the ‘Re’ function takes the real part of a complex number and ϕ is a constant
associated with the real structure of the 90 degree hybrid. It is equal to the in-phase
component when ϕ vanishes. The signal from the lower balanced photodetector is
Re[ia=
(t )ei{b (t ) +ϕ } ] a (t ) sin{b(t ) + ϕ},

(3.4)

32
which is the quadrature component when ϕ vanishes. Hence, we have successfully
separated the in-phase and quadrature components.
At this point, we have not retrieved the correct information yet as ϕ is still unknown.
Besides, the previous analysis is valid only in ideal situations. Practically, different types of
noise and the imperfection of the communication systems can distort the signals
significantly. To extract the information correctly, the detected electrical signals need to be
first digitalized by the analog to digital converter (ADC) and then processed digitally with
multiple algorithms.

Figure 3.3 (a) Structure of coherent receivers (b) Demodulation

33
3.1.3 Digital signal processing (DSP)
The goal of DSP is to process the data in the electrical domain in order to mitigate
impairments, both linear and nonlinear, deterministic and random. Generally speaking, there
are two types of problems to be addressed in the DSP. The first one is the distortion of the
detected signals, which usually arises from non-ideal communication channels and imperfect
optoelectronic devices. For example, the polarization of the beams rotates while propagating
in the single-mode optical fibers, causing crosstalk between signals encoded in the beams
with orthogonal polarizations; the beating between the optical fields and the LOs is not
strictly homodyne, leaving unwanted radio-frequency (RF) waves as the phase noise; the
frequency response function of the electronics, such as amplifiers, is not flat within the
modulation bandwidth, distorting the electrical pulses. Those problems should be resolved
to get a decent signal to noise ratio.
The second type of problems is about the unknown initial phase of the signals. There is a
variety of sources contributing to that initial phase, for example, ϕ in the previous analysis,
which comes from the 90 degree hybrid. In addition, both the laser carrying the information
and the LO have unknown initial phases, which are inherited by the electrical signals through
the beating process. The arbitrary initial phase must be unwrapped or no phase information
would be decoded correctly.
Our DSP module comprises seven functional blocks, as shown in Fig. 3.4. Each functional
block represents an algorithm performing a certain task. The first functional block resamples
the data, preparing the signals for the following processing. The next four functional blocks
deal with the first type of problems. Polarization recovery deals with the polarization rotation
of light in optical fibers, eliminating the crosstalk between the two channels with orthogonal
polarizations. Dispersion compensation, just as the name implies, mitigates the effects of
fiber dispersion. Frequency offset recovery finds out the beating frequency between the
signal and the LO and compensates for its effects in the phase. Equalization deals with the
non-flat frequency responses of the electronics.

34

Figure 3.4 Digital signal processing module
Among those effects mentioned above, polarization rotation, dispersion and non-flat
electronic response are naturally linear responses of the communication system, meaning
that they can be mitigated by finding out the linear response function and applying its inverse
function to the signals, which is exactly what these algorithms do. The frequency offset arises
from the beating between the signal and the LO, a nonlinear process. The beating frequency
can be figured out using Fourier transform. Its effect on the phase information would be
subtracted digitally.
The sixth functional block, carrier phase recovery, is implemented to recover the unknown
initial phase. As a matter of fact, it does more than that. If we treat the phase noise as a part
of the unknow phase, the algorithm can be programmed adaptively not only to capture the
initial phase, which is a constant, but also to predict the dynamic behaviors of the phase noise.
Hence, after applying such an algorithm, the ultimate phase noise in the signals could be
smaller than, but still related to, the value in equation (2.13). Plenty of phase recovery
algorithms have been developed such as the one based on the Kalman filter, Viterbi-Viterbi
(VV) algorithm and blind phase search (BPS) [34-36]. The latter two will be used in our
experiments.
The goal of all the signal processing discussed so far is not eliminating all the errors but
bringing the bit error rate (BER) down below a certain threshold so that the remaining errors
can be corrected systematically. Usually, redundant bits, which are constructed following

35
certain rules, are encoded along with the information. Those rules impose strict relations
between the information and the redundancy so that any error violating the rules can be
detected and then corrected. After error correction, which is the last functional block in the
DSP, the retrieved signal will be truly error-free and the information can be successfully
decoded.
3.1.4 System performance
Typically, we characterize lasers’ system performance by measuring the BER as a function
of optical signal to noise ratio (OSNR), which is defined to be the ratio between the laser
output power and the power of optical white noise in a given bandwidth, typically 12.5 GHz.
When the OSNR is small, the dominant noise in the system is the intensity noise and
therefore the BER becomes slightly dependent on the phase noise or the laser coherence. On
the contrary, when the OSNR is large and the effects of the intensity noise can be neglected,
the level of the phase noise solely determines the BER. In other words, the BER reaches its
lower limit and stays constant at very high OSNR. Such a limit can only be lowered by
decreasing the phase noise in the communication system, for example, using lasers with
higher phase coherence.
The BER-OSNR curves under various levels of phase noise are depicted schematically in
Fig. 3.5. Under the condition where there is no phase noise, the BER decreases rapidly as the
OSNR increases, leading to a ‘waterfall’ curve (blue curve in Fig. 3.5). As the phase noise
increases, the BER-OSNR curves become increasingly flat in the high OSNR region, where
the BER reaches its lower limit.

36

Figure 3.5 BER as a function of OSNR and phase noise. Black arrows indicate the direction
in which the phase noise increases
3.2 Si/III-V lasers as the light sources
In the section, we will describe the use of the hybrid Si/III-V lasers as the light sources to
conduct coherent optical communications. An ECL and a conventional III-V DFB laser, both
of which are commercially available, are also tested for comparison.
3.2.1 Back-to-Back coherent communications
We start with Back-to-Back (BTB) coherent optical communications. Back-to-Back means
the output of the transmitter is connected to the input of the receiver with a very short optical
fiber. In other words, the effects of communication channels such as dispersion and
polarization rotation are negligible in this case.
The whole measurement setup is shown schematically in Fig. 3.6. The laser lights are loaded
with 20 GBaud 16-QAM or 20 GBaud 64-QAM data signals, which are generated using an
arbitrary waveform generator (AWG) operating at 92 GSa/s. The polarization of the light is
adjusted with a polarization controller to minimize the insertion loss at the input of the IQ

37
modulator. An optical white noise source serves as the source of the intensity noise and a
variable optical attenuator (VOA) is inserted into the communication link to tune the OSNR.
The optical signals are coherently received with a tunable ECL as the LO. The decoded
information is processed offline and the BER, as a function of the OSNR, is measured by
error counting. As we want to measure the raw BER, there is no error correction in the DSP.

Figure 3.6 Measurement setup for coherent optical communications
3.2.2 Si/III-V laser vs III-V DFB laser vs external cavity laser
The frequency noise PSD of all three lasers used in the experiment is shown in Fig. 3.7. The
conventional III-V DFB laser is much noisier than our Si/III-V laser and the ECL. The
difference between the Si/III-V laser and the ECL is, however, marginal, with the ECL being
slightly more coherent.

38
We have mentioned before in section 3.1.3 that phase recovery algorithms can reduce the
phase noise in the communication systems and therefore modify the lasers’ system
performance to some extent, which will be demonstrated later. In our experiments, two types
of phase recovery algorithms are used, namely VV and BPS. Comparing these two, BPS is
more powerful and able to reduce the phase noise further than VV but requires more
computing resources.

Figure 3.7 Frequency noise PSD of lasers used in the experiments
The 16-QAM results are shown in Fig. 3.8 (a). There is no significant difference between the
Si/III-V laser and the ECL. The BER of those two lasers decreases sharply as the OSNR
increases with no sign of reaching the lower bound, meaning that the level of the phase noise
in the communication systems is quite low. Besides, different phase recovery algorithms do
not lead to different system performance in those two cases.
In contrast, the BER of the III-V DFB laser with VV approaches to a constant at high OSNR,
where the system performance is limited by the phase noise. With BPS, the BER does
decrease monotonically as the OSNR increases as BPS helps to further reduce the phase

39
noise in the system but the III-V DFB laser’s performance is still a little bit worse than the
other two lasers at high OSNR, indicating slightly larger phase noise in the system.
The constellation diagrams in Fig. 3.8 (b) confirm our descriptions. The phase noise is
negligible in all cases except one, the conventional III-V DFB laser with VV, where the shear
deformation of the constellations indicates the existence of non-negligible phase noise.
The magenta dash line in Fig. 3.8 (a) represents the threshold of implementing hard-decision
forward error correction (FEC), meaning that if the BER drops below the threshold, all the
errors can be corrected using standard error correction methods with 7% overhead [37]. Such
a condition can be met in all cases of 16-QAM. However, with VV, additional OSNR penalty
of roughly 4 dB must be paid for the III-V DFB laser. With BPS, the III-V DFB laser
performs as ‘good’ as the other two. But there are still downsides, which will be discussed
later.

40

Figure 3.8 20 GBaud 16-QAM (a) system performance and (b) Constellation diagrams
Why those two phase recovery algorithms have significantly different impacts on the
conventional III-V DFB laser but not on the Si/III-V laser or the ECL can be understood in
the following way. Because of the high phase coherence of the Si/III-V laser and the ECL,
the corresponding phase noise in the system is so small that as long as the phase recovery
algorithm can successfully recover the constant initial phase, the performance would be
good. Hence, using VV or BPS does not lead to much different system performance. For the

41
conventional III-V DFB laser, its much lower coherence results in much larger phase noise
in the system. Therefore, with VV, which does not track the phase noise very closely, large
phase noise still remains in the system while more powerful algorithms like BPS can help to
suppress the phase noise a lot, leading to a dramatical improvement. That is exactly why we
see the conventional III-V DFB laser performs so differently with those two algorithms.
At this point, one may wonder since phase recovery algorithms like BPS are so powerful,
why do we need algorithms like VV or even high-coherence lasers for coherent optical
communications? The answer to the question is twofold. First, the capability of phase
recovery algorithms is limited. For example, the 64-QAM results are shown in Fig. 3.9,
where BPS is used with all three lasers. Unlike 16-QAM, the performance of the III-V DFB
laser cannot meet the condition of implementing hard-decision FEC in this case because BPS
cannot reduce the phase noise to the level that 64-QAM can tolerate. Apparently, the
effectiveness of phase recovery algorithms depends on both the laser coherence and the
modulation format.
Second, as mentioned before, powerful algorithms like BPS require a great deal of computing
resources, which inevitably increases the power consumption and the latency [38, 39], both
of which are unfavorable in practical coherent communication networks. Hence,
economically, monolithic high-coherence semiconductor lasers and simple phase recovery
algorithms are the best combination for coherent optical communications, for example, the
hybrid Si/III-V laser and VV for BTB 20GBaud 16-QAM.

42

Figure 3.9 20 GBaud 64-QAM system performance
3.2.3 ZR coherent communications
In real-world applications, we conduct fiber optical communications within certain distances,
where effects like dispersion, polarization rotation and fiber nonlinearity all come into play.
Here, we investigate the lasers’ performance in ZR coherent communications. ZR is a
terminology for 80 km, which is approximately the range of metropolitan communications.
The experimental setup is also shown in Fig. 3.6, where a short fiber connecting the
transmitter to the receiver is replaced by an 80-km-long optical fiber and an erbium-doped
optical amplifier (EDFA), which is used to compensate for the propagation loss.
The linear responses of the communication channel, including dispersion and polarization
rotation, can be easily compensated by DSP, as discussed earlier. However, compensation
for fiber nonlinearity remains challenging. Among all the types of fiber nonlinearity, we are
mainly concerned about the Kerr nonlinearity. It induces intensity-dependent refractive
index, which means intensity modulation and pulse broadening due to dispersion can result
in unwanted phase modulation and thus a new source of phase noise, which is irrelevant to
the laser coherence but dependent on the power. The BER in ZR coherent communications
becomes dependent not only on the OSNR but also on the launch power at the input of the

43
fibers [40, 41]. Therefore, to achieve the best system performance, i.e. the lowest BER,
the launch power into the fiber should be optimized.
The Si/III-V laser and the ECL are tested in ZR coherent optical communications, whose
performance of 16-QAM and 64-QAM is shown in Fig. 3.10 (a) and (c), respectively. The
two lasers still possess similar performance. The dependence of the BER on the launch power
is shown in Fig. 3.10 (b) and (d), where the optimized launch power used for communication
experiments corresponds to the lowest BER. Throughout the experiments, BPS is used for
phase recovery because of nonlinearity-induced phase noise. Compared to BTB
communications, there is degradation of the system performance, which can be mostly
attributed to fiber nonlinearity. However, both lasers can still work with hard-decision FEC
in both 16-QAM and 64-QAM.

44

45

Figure 3.10 ZR communication system performance (a) 16-QAM (b) power optimization
for 16-QAM (c) 64-QAM (d) power optimization for 64-QAM

46
3.3 Conclusions
In this chapter, we have investigated the system performance of three different lasers, namely
the ECL, the conventional III-V DFB laser and our high-coherence Si/III-V laser. As a result,
the Si/III-V laser’s performance is comparable to the ECL’s and much better than the
conventional III-V DFB laser’s. Hence, the hybrid Si/III-V lasers, with their monolithic
structure and high phase coherence, are very promising light sources for future coherent
optical communication networks.

47
Chapter 4

FEEDBACK SENSITIVITY OF SEMICONDUCTOR LASERS
The historical studies on optical feedback’s effects on semiconductor lasers can be dated
back to 1980s. The properties of semiconductor lasers can be improved with very little optical
feedback [42-44] while a slightly higher level of optical feedback can degrade semiconductor
lasers, rendering them useless. In practical situations, the level of optical feedback varies
from one scenario to another and cannot be precisely controlled. Conventionally, optical
isolators are packaged with every semiconductor laser to mitigate optical feedback.
However, as the field is moving rapidly towards photonic integration, optical isolators, which
used to be the solution, now become the obstacle since they cannot be fabricated on chip,
thwarting the integration between semiconductor lasers and other photonic devices.
Consequently, we shall resolve the issue of optical feedback with a novel solution, which
facilitates photonic integration. An appealing solution that we come up with is to develop
monolithic semiconductor lasers with intrinsic insensitivity to optical feedback, which
requires the lasers to be equipped with high-Q resonators to block a significant amount of
optical feedback from entering. The hybrid Si/III-V lasers, with their high-Q resonators
originally designed for high coherence, are expected to be very robust against optical
feedback. Hence, the same lasers that we develop for coherent optical communication are
now strong contenders to be the integrated light sources.
This chapter is organized as follows. In the first half of this chapter, we are going to establish
the theories on how coherent and incoherent optical feedback affects laser frequency noise
PSD, respectively. In the second half of this chapter, the feedback sensitivity of the Si/III-V
laser is examined experimentally in comparison to a conventional III-V DFB laser without
optical isolators. The results illustrate that the Si/III-V laser is capable of preserving its phase
coherence under much larger optical feedback than the III-V DFB laser and functioning
properly in the isolator-free coherent optical communications under conditions where the

48
performance of the III-V DFB laser degrades dramatically. In addition, we will verify the
theories based on the experimental results.
4.1 Coherent optical feedback and incoherent optical feedback
Optical feedback can be classified into two categories, namely coherent and incoherent
optical feedback, as shown in Fig. 4.1. Coherent optical feedback, such as reflection from an
external mirror, is explicitly correlated with the laser output while incoherent optical
feedback, like amplified spontaneous emission (ASE), originates in a different and
independent light source, such as an optical amplifier, and thus is uncorrelated with the laser
output.

Figure 4.1 Optical feedback
In semiconductor lasers, spontaneous emission is the single noise source, which the intensity
and phase noises arise from. The intensity noise is then coupled to the phase noise through

49
the mechanism of linewidth enhancement. The noise source and the coupling mechanism
together determine the frequency noise PSD of semiconductor lasers, which has been
discussed in chapter 2. By introducing optical feedback into the laser system, either the noise
source or the coupling between laser intensity and phase noises changes, resulting in the
modification of the laser frequency noise PSD and eventually affecting the lasers’
performance in coherent optical communications.
4.2 Coherent optical feedback effects on laser coherence
In this section, we analyze how coherent optical feedback modifies laser coherence, of which
a simple model is shown schematically in Fig. 4.2. The noise source in this case is still
spontaneous emission in the laser active region as external mirrors or equivalent are passive
devices. However, due to the correlation between the coherent optical feedback and the laser
internal field, additional coupling channels between the laser intensity and phase noises are
created. The dynamic equations of laser noises under coherent optical feedback can be
written as [45]
I(t ) = {G (t ) − γ p }I (t ) + FI (t ) +

κ rext cos(ϕ ) I (t − τ ) − A0κ rext sin(ϕ ){Φ (t − τ ) − Φ (t )}

(4.1)

and
=
(t ) α {G (t ) − γ p } + FΦ (t ) +

κ rext cos(ϕ ){Φ (t − τ ) − Φ (t )} + κ rext sin(ϕ ){I (t − τ ) − I (t )} A0 ,

(4.2)

where I (t ) and Φ(t ) represent laser intensity noise and phase noise, respectively. τ is the
round-trip delay time of the optical feedback. rext is the mirror refractivity and ϕ is the
additional phase shift from the external mirror. A0 is the amplitude of the laser field in the
cavity and κ is the coupling rate of the optical feedback back into the laser resonator. FI (t )
and FΦ (t ) are Langevin noise terms corresponding to spontaneous emission. G (t ) represents
the intensity-dependent gain (gain-saturation) and α is the linewidth enhancement factor.

50

Figure 4.2 Schematic diagram of coherent optical feedback
Notice that we do not take the dynamics of the electron number, which is directly related to
the gain, into account. As a matter of fact, we treat its response to be instantaneous in order
to simplify the gain saturation process. Such a trick is valid for the dynamics below the
relaxation resonance frequency.
Equation (4.1) and (4.2) are written in two colors, where the black part is the intrinsic
dynamics of the laser noises while the red part represents the additional couplings created by
coherent optical feedback. The coupling mechanisms without and with coherent optical
feedback are shown schematically in Fig. 4.3 (a) and (b), respectively. Under coherent optical
feedback, the intensity and phase noises are coupled to each other, which will fundamentally
change the laser frequency noise PSD.

51

Figure 4.3 Noise coupling (a) w/o coherent optical feedback and (b) w/ coherent optical
feedback
We perform Fourier transformation of these two equations in the frequency domain and, after
some algebra, obtain
S ∆υ (Ω)
S ∆υ − feedback (Ω) =
eiΩτ − 1 2
| 1 + κ rextτ 1 + α 2
iΩτ

(4.3)

where S∆υ − feedback (Ω) and S∆υ (Ω) are the laser frequency noise PSD with and without coherent
optical feedback and Ω is the angular frequency. Mathematically, the effect of coherent
optical feedback on the laser frequency noise PSD appears in the denominator of equation
(4.3), whose magnitude can be quantified by the following parameter:
C κ rextτ 1 + α 2 .

(4.4)

Our definition matches Petermann’s [46, 47], where a special case of an FP laser was dealt
with. The denominator also possesses a very interesting feature, i.e. a periodic term, which
means the denominator approaches the local minimums periodically in the frequency
domain. If the C-parameter is much larger than unity, the denominator at the local minimums
can be much smaller than unity, leading to spikes in the laser frequency noise PSD.

52
Those spikes can be viewed equvalently as side modes, the rising of which eventually
drives single-mode lasers into multi-mode region. If we keep increasing the level of coherent
optical feedback, at some point, the side modes will be strong enough to compete with the
original lasing mode, causing the lasers to be unstable. This phenomenon is referred to as
coherence collapse, where the lasers’ behavior is totally chaotic and coherence is
dramatically degraded [48-52].
Based on the previous definition of the C-parameter, it is impossible to characterize lasers’
sensitivity to coherent optical feedback in any absolute sense because the effects depend on
not only the feedback level but also the distance between the laser and the external reflection
point, which varies from one scenario to another. However, in any given situation, the
difference between any two lasers’ feedback sensitivity is the same as the ratio between the
corresponding C-parameters is only dependent on the intrinsic parameters of the lasers.
4.3 Incoherent optical feedback effects on laser coherence
Incoherent optical feedback, originated from an independent light source, naturally serves as
a new noise source. Because it is uncorrelated to the laser output, it does not create new
coupling channels and the additional noise induced in the laser resonators is pure intensity
noise. Hence, the power of the incoherent optical feedback solely determines the degree of
the modification of the laser coherence and we can characterize the lasers’ sensitivity to
incoherent optical feedback in an absolute sense.
Here, we would like to study in particular how the ASE noise from semiconductor optical
amplifiers (SOAs) modifies laser coherence, as shown schematically in Fig. 4.4, because, in
practical applications, SOAs can be integrated with semiconductor lasers and other photonic
devices in order to boost the output power and compensate for large insertion loss from the
passive devices [53, 54]. The difference from coherent optical feedback is that the ASE noise
possesses a wide optical spectrum (roughly white optical noise in C-band) and therefore can
interact with multiple modes rather than just the lasing mode.

53

Figure 4.4 Schematic diagram of incoherent optical feedback
We should not be confused about the difference between the ASE noise as the incoherent
optical feedback and the optical white noise added into the coherent optical communication
system in chapter 3. The former one affects the laser’s properties, for example phase
coherence, so that the system performance gets altered. The latter one is directly related to
OSNR, on which the system performance depends, but does not have any impacts on the
laser itself. Those two noise sources, in fact, can coexist in a communication system, which
will be shown in our measurement setup for lasers’ sensitivity to incoherent optical feedback.
To study how the ASE noise affects the laser frequency noise PSD, we can still write down
the dynamic equations of the laser noises and do the analysis in the same way as we deal
with coherent optical feedback. Such analysis, however, is quite tedious and frankly
unnecessary. We can simply treat the ASE noise as equivalent to spontaneous emission,
generating intensity noise in the lasers, as shown in Fig. 4.5. The induced intensity noise is
coupled to the laser frequency noise through the mechanism of linewidth enhancement as
well, leading to the degradation of the laser coherence. Since the ASE-induced intensity noise
is white noise whose PSD is proportional to the feedback power, the laser frequency noise

54
PSD under incoherent optical feedback should remain white and increases linearly with
the ASE power fed back.

Figure 4.5 Noise coupling (a) w/o incoherent optical feedback and (b) w/ incoherent optical
feedback
4.4 Lasers’ sensitivity to optical feedback
Conventional III-V DFB lasers, the main light sources in today’s optical networks, are quite
sensitive to optical feedback. Even a small amount of optical feedback can cause dramatic
degradation of their performance, thwarting large-scale photonic integration. As fabricating
optical isolators on chip remains extremely challenging despite some progress, replacing
conventional III-V DFB lasers with monolithic semiconductor lasers with intrinsic
insensitivity to optical feedback becomes a much more intriguing approach.
To enhance the lasers’ robustness, preventing the optical feedback from entering the laser
resonator is the key, which can be achieved by employing mirrors with the reflectivity
approaching to unity. However, such an approach cannot be applied to conventional III-V

55
DFB lasers as it will reduce dramatically the output power, rendering the III-V DFB lasers
useless. To resolve such a problem, it is necessary for semiconductor lasers to have
resonators with very low internal loss so that much stronger optical field can be built inside
to compensate for the reduction of the output coupling in order to get the same level of laser
output power.
As discussed in Chapter 2, the Si/III-V lasers are designed in a way that most of the optical
energy is stored in the low-loss silicon rather than high-loss III-V materials. The mode
engineering approach increases the lasers’ intrinsic quality factor by several orders of
magnitude, which allows us to use high-Q resonators without sacrificing the output power.
The high-Q resonators can block a significant amount of optical feedback and thus we expect
the Si/III-V lasers to be much more insensitive to optical feedback than conventional III-V
DFB lasers, which will be validated later.
4.5 Laser frequency noise PSD under coherent optical feedback
In this section, we are going to investigate experimentally the lasers’ capability of preserving
their phase coherence under coherent optical feedback. The measurement setup is shown in
Fig. 4.6, where the red arrows represent the propagation of the coherent optical feedback.
The coherent optical feedback loop is constructed by coupling part of the laser output back
into the laser cavity via the optical circulator, emulating mirror reflection. A booster optical
amplifier (BOA) and a VOA are inserted into the optical feedback loop in order to control
the feedback level. The power fed back is calibrated using a high-precision photodetector,
which is then converted into the effective reflectivity to be the feedback level. An optical
isolator is placed in front of the frequency noise PSD measurement system to avoid any
unwanted optical feedback. Finally, the frequency noise PSDs of the lasers are measured
under various levels of optical feedback.

56

Figure 4.6 Measurement setup for laser frequency noise PSD under coherent optical
feedback
The results are shown in Fig. 4.7 (a) and (b). The conventional III-V DFB laser is extremely
sensitive to coherent optical feedback. As the feedback level of -50 dB, the RF oscillations,
i.e. the side modes, start to emerge. With the increase of the feedback power, the side modes
get stronger. On the contrary, the frequency noise PSD of the Si/III-V laser is barely changed
up to a feedback level of -31 dB. Beyond that level, the frequency noise PSD at relatively
low frequencies increases significantly, which deviates completely from the theory presented
in the section 4.2 and will be explained later. The increase of the frequency noise PSD at
relatively low frequency won’t jeopardize the system performance severely because of its
small bandwidth and therefore very limited contribution to the phase noise, as indicated by
equation (2.9).

57

Figure 4.7 Frequency noise PSD of (a) the III-V laser and (b) the Si/III-V laser under
various levels of coherent optical feedback
To determine why the frequency noise PSD of the Si/III-V laser under coherent optical
feedback differs significantly from the theory, we shall revisit the dynamic equations in
section 4.2. In the original theory, we treat linewidth enhancement as the only intrinsic

58
coupling mechanism between laser frequency noise and intensity noise while ignoring
others such as thermal effects, which are severe in the Si/III-V lasers [33, 55- 56]. As a matter
of fact, the alpha parameter in equation (4.2) should be replaced by a frequency-dependent
response function, which takes all the coupling mechanisms into account, to make the
original theory more rigorous. The exclusion of other coupling mechanisms could be the
reason why the frequency noise PSD of the Si/III-V laser under coherent optical feedback
deviates from the theory.
We have obtained the coupling curve between the intensity noise and the phase noise of the
Si/III-V laser, which is initially presented in Fig. 2.8 and now reproduced in Fig. 4.8. The
coupling strength is much larger at low frequencies due to thermal effects. If that is indeed
responsible for the bizarre frequency noise PSD of the Si/III-V laser under coherent optical
feedback, then the increase of the frequency noise PSD should take place only within the
bandwidth of the thermal effects. By comparing Fig. 4.7 to 4.8, we confirm that indeed both
the coupling strength and the frequency noise PSD increase rapidly as the frequency
decreases in the identical frequency range, i.e. below 100 MHz, which validates the
explanation that large thermal effects cause the rising of the laser frequency noise PSD at
low frequencies.
This behavior is not observed in the III-V DFB laser is because the thermal impedance of the
conventional III-V DFB laser, which is well packaged, is quite small and therefore the
thermal effects are negligible. Hence, what we have observed from the III-V DFB laser is
purely due to the carrier effect, i.e. linewidth enhancement, and agrees with the original
theory.
Our Si/III-V laser tested in the experiments is unpackaged, leading to poor thermal
management. We do expect its robustness to be improved with better packaging, for
example, with flip-chip bonding [57]. Nevertheless, its frequency noise PSD at high
frequencies staying unaffected indicates its superb insensitivity to coherent optical feedback.
Our experimental results illustrate that the Si/III-V laser is more stable against coherent
optical feedback than the conventional III-V DFB laser by at least 19 dB. As argued before,

59
lasers’ system performance should not be degraded severely by the increase of the
frequency noise PSD at low frequencies. Therefore, we do expect the difference between the
two lasers’ system performance would be larger than 19 dB, which will be demonstrated
later in the chapter.

Figure 4.8 Coupling between intensity noise and phase noise
4.6 Laser frequency noise PSD under incoherent optical feedback
Here, we study the impacts of incoherent optical feedback on laser coherence. Previously,
we used a very simple model to predict the consequences, which will be validated here.
The measurement setup is shown in Fig. 4.9. The output of the BOA, serving as the ASE
noise source, is injected directly into the laser cavity via the optical circulator. The laser
frequency noise PSD is measured under various ASE power.

60

Figure 4.9 Measurement setup for laser frequency noise PSD under incoherent optical
feedback
The ASE noise possesses a wide optical spectrum in C-band, as shown in Fig. 4.10 (a). It
interacts with multiple optical modes and induces additional intensity noise in all those
modes, which is clearly manifested by the increase of power in all the non-lasing modes in
Fig. 4.10 (b) and (c).

61

Figure 4.10 (a) ASE noise spectrum and optical spectra of (b) the hybrid Si/III-V laser and
(c) the III-V DFB laser with ASE noise injected

62
The measurement results are shown in Fig. 4.11 (a) and (b). The frequency noise PSD of
both lasers remains white under incoherent optical feedback, which agrees with our theory.
The laser linewidth, interpreted by the white noise floor, is plotted as a function of the
injected ASE power in Fig. 4.11 (c). The red lines are linear regression, which fit the data
very well. Hence, the prediction that the laser frequency noise PSD increases linearly with
the injected ASE power has been verified.
The major difference between the Si/III-V laser and the conventional III-V DFB laser lies at
the slopes of those two red lines. The slope extracted for the III-V laser is 32 MHz/mW while
only 0.2 MHz/mW for the Si/III-V laser, which is two orders of magnitude smaller. This
result shows the Si/III-V laser is much more insensitive to incoherent optical feedback than
the conventional III-V DFB laser by two orders of magnitude.

63

Figure 4.11 Frequency noise PSD of (a) the III-V laser and (b) Si/III-V laser w/ and w/o the
existence of incoherent optical feedback and (c) the corresponding linewidth as a function
of ASE power

64
So far, we only have indirect evidence to support our theory. To directly validate the
theory, we measure the intensity noise PSD under incoherent optical feedback to see whether
the increments of laser intensity and frequency noises match with each other. In this
experiment, only the III-V DFB laser is used, of which the intensity noise around the
relaxation resonance frequency can be accurately measured, as shown in Fig. 4.12 (a).
The results are shown in Fig. 4.12 (b). The level of the intensity or frequency noise PSD of
the III-V DFB laser under no incoherent optical feedback is set as the reference point. The
increment of the laser noise is characterized by the ratio between the level of noise under the
optical feedback and the reference point. There exists a very good match between the
increments of the intensity noise PSD and the frequency noise PSD, which confirms our
explanation that the ASE-induced intensity noise is coupled to the laser frequency noise via
linewidth enhancement, leading to the broadening of the laser lineshape. Our theory, in spite
of being very simple, describes accurately the effects of incoherent optical feedback on laser
coherence.

65

Figure 4.12 (a) Intensity noise PSD of the III-V DFB laser at various injected ASE power
and (b) the increment of laser intensity noise and laser frequency noise, respectively
To summarize, our Si/III-V laser is much more robust against coherent and incoherent optical
feedback than the III-V DFB laser. Particularly, the Si/III-V laser is capable of preserving its
phase coherence under much larger optical feedback, which is critical for isolator-free

66
coherent optical communications. In the rest of this chapter, we are going to investigate
the feedback sensitivity of the lasers in the coherent optical communication systems.
4.7 System performance under coherent optical feedback
We begin with examining the lasers’ system performance under coherent optical feedback.
The measurement setup is shown schematically in Fig. 4.13. The coherent optical feedback
loop is constructed in the same way as in Fig. 4.6. The semiconductor lasers, subject to a
variable-controlled coherent optical feedback, are used as the light sources to carry data
signals. We characterize the system performance by measuring the BER-OSNR curves at
various levels of coherent optical feedback.

Figure 4.13 Measurement setup for coherent optical feedback
The modulation formats for the hybrid Si/III-V laser and the III-V DFB laser are chosen to
be 20 GBaud 16-QAM and 20 GBaud quadrature phase shift keying (QPSK), respectively,
given their intrinsic coherence. The results are shown in Fig. 4.14 (a) and (b). The III-V DFB

67
laser is very sensitive to coherent optical feedback. The BER-OSNR curves of the III-V
DFB laser start to shift upwards at a feedback level of -45.5 dB, indicating a degradation of
the system performance. Beyond -41.5 dB, the coherent communication system is driven into
chaos, where the phase information is completely washed out, as revealed by the
constellation diagrams in Fig. 4.15. Hence, at a feedback level of -41.5 dB or beyond, it is
impossible to conduct coherent optical communications successfully with the conventional
III-V DFB laser.

Figure 4.14 System performance of (a) the Si/III-V laser and (b) the III-V DFB laser under
coherent optical feedback

68

Figure 4.15 Constellation diagrams of the III-V DFB laser (a) w/o optical feedback and (b)
with the feedback level beyond -41 dB
On the contrary, the BER-OSNR curves of the Si/III-V laser stay almost unchanged by
coherent optical feedback. Even at the feedback level of -18.3 dB, the largest feedback level
that can be achieved in the experiments, there is no obvious degradation of its system
performance. Based on the data, the Si/III-V laser is more robust against coherent optical
feedback than the conventional III-V DFB laser by at least 27.2 dB. For the record,
commercial optical isolators typically provide optical isolation between 25 dB and 30 dB,
which suggests that, in terms of sensitivity to coherent optical feedback, the Si/III-V laser is
as stable as the commercial III-V DFB laser packaged with an optical isolator.
4.8 System performance under incoherent optical feedback
In this section, we investigate how incoherent optical feedback affects semiconductor lasers’
system performance. The incoherent optical feedback loop is constructed in the same way as
in Fig. 4.9 and the whole measurement setup is shown in Fig. 4.16. In a manner similar to
the previous method of data collection, we measure the BER-OSNR curves under various
ASE power fed back.

69

Figure 4.16 Measurement setup for incoherent optical feedback
The results are shown in Fig. 4.17 (a) and (b). The BER-OSNR curves of the Si/III-V laser
are barely affected by incoherent optical feedback. However, those of the III-V DFB laser
keep shifting upwards with the increase of the feedback power, demonstrating the
degradation of its system performance. The constellation diagrams of the III-V DFB laser in
Fig. 4.18 clearly illustrates the increase of the phase noise in the communication system.
However, this kind of degradation, which gradually deepens as the feedback power increases,
is quite different from what we have observed under coherent optical feedback. Previously,
across a certain level of coherent optical feedback, -41 dB in our case, the communication
system experiences a sharp transition from being functional to being dysfunctional.

70

Figure 4.17 System performance of (a) the Si/III-V laser and (b) the III-V DFB laser under
incoherent optical feedback

71

Figure 4.18 Constellation diagrams of the III-V DFB laser (a) w/o optical feedback and (b)
with the ASE power of 0.7 mW
4.9 OSNR penalty due to optical feedback
A more straightforward tool to use for comparing the system performance under different
situations would be the OSNR penalty, which is defined as the increase of the OSNR relative
to that of the reference, in this case the OSNR under the condition without optical feedback,
at a fixed BER, in our case 10-3. The results are shown in Fig. 4.19 (a) and (b). As we can
see, the OSNR penalty of the Si/III-V laser is quite small, namely less than 1 dB in all cases,
indicating its robustness against optical feedback. While for the conventional III-V DFB
laser, coherent optical feedback at -46.6 dB can cause an OSNR penalty of 2 dB. The OSNR
penalty approaches infinity at the feedback level beyond -41.5 dB because of the chaotic
system performance. Besides, incoherent optical feedback can cause a maximum OSNR
penalty of 2.5 dB. From the OSNR penalty data, it is obvious that the degradation patterns
of the conventional III-V DFB laser are different under coherent and incoherent optical
feedback. The former one possesses a much sharper transition than the latter one.
Once again, the results show that the Si/III-V laser can indeed function without severe
degradation in the isolator-free coherent optical communication system, a precondition to its
usage in photonic integrated circuits.

72

Figure 4.19 Power penalty due to (a) coherent and (b) incoherent optical feedback
4.10 Conclusions
In this chapter, we have investigated the sensitivity of the Si/III-V laser and the conventional
III-V DFB laser to both coherent and incoherent optical feedback, respectively. Unlike the
conventional III-V DFB laser, the Si/III-V laser, due to its built-in high-Q resonator, can

73
preserve its phase coherence under much higher levels of optical feedback, leading to its
more stable system performance in an isolator-free environment. The superiority of the
Si/III-V laser to the conventional III-V DFB laser lies at not only the phase coherence but
also the robustness against optical feedback, making them stunningly suitable to be the
integrated light sources. Our work will have great impacts on how the semiconductor lasers
of the next generation will be made.

74
Chapter 5

A GENERAL RELATION BETWEEN LASER FREQUENCY NOISE
PSD AND LINESHAPE
There are two means of characterizing laser coherence. The first one is laser frequency noise
PSD, which has been used by us in all the experiments. We prefer using it because of its
close relation to the phase noise in coherent optical communications (see equation (2.13)).
The second one is laser lineshape, the PSD of the laser field, of which the FWHM is known
as the laser linewidth, for example, the S-T linewidth introduced in chapter 2.
In the current literature, the two measures are very often used interchangeably as a premise
to characterize laser coherence. This will be shown to be wrong in what follows. In this
chapter, we will show how those two are related to each other in general.
We are not the first group addressing the issue. Previous approaches are limited to numerical
computation or analysis on special cases [58-62], which do not provide physical insights.
Here, we derive a general relation, which we refer to as the Central Relation, between the
frequency noise PSD and the lineshape of laser light, which turns out to be surprisingly
simple. The Central Relation affords new insights into laser coherence, including how it can
be engineered with optical filtering.
5.1 Derivation of the general relation
The electric field of laser light can be expressed as
E = E0 ei{ω0t +ψ (t )} ,

(5.1)

where ψ (t ) represents the phase fluctuations due to random or deterministic modulation,
whose average value vanishes. E0 is the amplitude and ω0 is the angular frequency of the
light. The lineshape function (single-sided spectrum) of the laser light is represented by the
PSD of the laser field, which is the Fourier transform of the correlation function of the field

75
+∞

S=
2 ∫ e − iωτ < E * (t ) E (t + τ ) >dτ ,
E (ω )
−∞

(5.2)

where <> represents the time average.
The correlation function can be calculated as [60, 63]

< E * (t ) E (t=
+ τ ) > E02 eiω0τ < ei{ψ (t +τ ) −ψ (t )} >
− [ <{ψ ( t +τ ) −ψ ( t )}2 > ]

= E02 eiω0τ e 2
2 iω0τ

=E e

−2

+∞

∫0 S∆υ ( f )

sin 2 (π f τ )
f2

(5.3)
df

Since intensity fluctuations are strongly damped due to gain saturation, E02 is taken as a
constant.
+∞

S ∆υ ( f ) 2 ∫ e − i 2π f τ < ψ (t )ψ (t + τ ) > dτ
−∞

(5.4)

is the single-sided frequency noise PSD. The central frequency of lineshape is just ω0 .
We define a new function η (υ ) by means of the relation

1 2πυ +ω0
S E (ω )d ω= {1 − η (υ )}E02 .
πυ
2π

(5.5)

Notice that if we integrate over the whole laser lineshape function, we get the total power of
the laser light, namely

1 +∞+ω0
S E (ω )d ω = E02 ,
−∞+
2π

(5.6)

76
so that the function η (υ ) is equal to the total power contained outside the integrated
frequency range of width 4πυ straddling the central laser frequency ω0 . The function η (υ )
can be expressed as
η (υ )

1 1 −2πυ +ω0
1 +∞+ω0
S E (ω )d ω}
2π ∫2πυ +ω0
E02 2π ∫−∞+ω0

(5.7)

and it vanishes as υ approaches infinity.
The use of (5.2) and (5.3) in (5.5) leads to
+∞

−2 ∫ S∆υ ( f )
+∞
1 2πυ +ω0
i (ω0 −ω )τ
πυ
−∞
2π

sin 2 (π f τ )
f2

df

dτ = 1 − η (υ ).

(5.8)

Integrating over the angular frequency ω leads to

+∞

2υ ∫ sinc(2πτυ )e
−∞

−2

+∞

∫0 S∆υ ( f )

sin 2 (π f τ )
f2

df

dτ = 1 − η (υ ).

(5.9)

We use the following mathematical relations to deal with sinc functions:
sinc(2πτυ ) W (2πτυ ) as υ → ∞
2π f
2π f
sinc(
) W(
) as υ → ∞,
4υ
4υ

(5.10)

where W ( x) is equal to 1 when | x |≤ π 2 and vanishes otherwise. The upper equation is valid
as both 2υ sinc(2πτυ ) and 2υW (2πτυ ) are asymptotically identical to δ (τ ) function. The lower
equation is simply the Fourier transform of the upper one.
Using the definition of W ( x) we can limit the range of integration in (5.9) to −
which allows us to rewrite it as

≤τ ≤ ,
4υ
4υ

77

2υ ∫ 4υ1 e

−2

+∞

∫0 S∆υ ( f )

sin 2 (π f τ )
f2

df

dτ = 1 − η (υ ).

df

dτ = 1 − η (υ ).

4υ

Since the integrand is an even function of τ
4υ

4υ ∫ e

−2

+∞

∫0 S∆υ ( f )

sin 2 (π f τ )
f2

(5.11)

For sufficiently large υ , the time variable τ in (5.11) becomes small over the entire integral
range so that we can Taylor-expand the exponential part and keep only the leading term
4υ

+∞

4υ ∫ {1 − 2 ∫ S ∆υ ( f )

sin 2 (π f τ )
df }dτ =
1 − η (υ ).
(5.12)
f2

Integrating over τ first and get the following formula

+∞

S ∆υ ( f )
πf
η (υ ).
{1 − sinc(
)}df =
2υ

(5.13)

The second term on the left side in equation (5.13) contains a sinc function and using the
relation (5.10), we take the lower limit of integration at π f

+∞

∫υ

2υ

=π

S ∆υ ( f )
df = η (υ ).
f2

(5.14)

The physical meaning of (5.14) is more apparent in a form, which results from a
differentiation of both sides with respect to υ

S ∆υ (υ )

{S E (ω0 + 2πυ ) + S E (ω0 − 2πυ )},
E02

where the differential form of η (υ ) can be derived from equation (5.7).

(5.15)

Equation (5.15) constitutes a general relation between the frequency noise PSD S ∆υ (υ )

78

and the lineshape function S E (ω ) of the laser light. We will refer to it as the Central Relation.
It shows that at high frequencies there is a one-to-one correspondence between the frequency
noise and the lineshape function. Empirically, frequencies which are more than ten times the
linewidth can be considered as sufficiently high for the Central Relation to apply; such a rule
of thumb is confirmed by the experiments described in the following sections. Notice that
we have made no assumptions regarding the physical origin of the frequency noise.
It is worth pointing out that the left side of equation (5.15) is essentially the phase noise PSD
of the laser. The meaning of equation (5.15) can be interpreted as following. The frequency
noise at high base band frequency affects the lineshape at the same frequency offset with
respect to the optical central frequency. If the lineshape is symmetrical about the central
frequency, which is true for laser lineshape, then any feature in the phase noise PSD at high
frequency will appear identically in the lineshape and vice versa.
5.2 Validation of the Central Relation
To illustrate the validity of the Central Relation, both the frequency noise PSD and lineshape
of a single laser have been measured. The measurement setups are shown in Fig. 5.1. The
frequency noise PSD is measured as before. The laser’s lineshape is obtained by beating the
laser field with the field of a narrow-linewidth fiber laser and measuring the power spectrum
of the beat signal.

79

Figure 5.1 Measurement setups for (a) frequency noise power spectral density and (b)
lineshape. PC: polarization controller; RFSA: radio frequency spectrum analyzer. A
narrow-linewidth fiber laser is used as the reference laser
The laser’s frequency noise is shown in Fig. 5.2(a). There exists some jitter at tens of
megahertz in the spectrum, which comes from the controlling circuit of the laser. The
lineshape of the laser is displayed in Fig. 5.2(b) and it contains two bumps, which are
symmetrical about the central frequency. To show that the frequency noise PSD and the
lineshape indeed obey the Ceneral Relation (5.15), we first calculate the phase noise PSD,
namely the left side of equation (5.15), based on the measured frequency noise PSD and then
match it with the lineshape, as is shown in Fig. 5.2(b).
The jitter in the phase noise PSD is located at the same frequency as the bumps in the
lineshape with respect to the central frequency. In addition, the bump reproduces the
envelope of the jitter in the phase noise PSD. Because of the measurement resolution of the
spectrum analyzer, we are unable to observe the individual lines in the lineshape. The general
relation describes exactly the match between the frequency noise PSD and the optical
lineshape and therefore we show experimentally the validity of the Central Relation.

80

Figure 5.2 (a) Frequency noise PSD of the laser (b) Corresponding phase noise PSD and
lineshape of the laser
5.3 Insights into the Central Relation
Equation (5.15), i.e. the Central Relation, illustrates the fundamental relation between laser
frequency noise PSD and lineshape. What can we learn from such a relation? How do we
apply such a relation? In this section, we are going to discuss some corollaries of the Central
Relation along with the experimental proof.

81
5.3.1 Optical filtering of laser frequency noise PSD
The Central Relation (5.15) is valid for any laser light and can be used as a guide to customtailor the frequency noise PSD by optical filtering.
Consider the case where the laser light passes through a generalized filter, whose
transmission is the function H (| ω − ω0 |) , which is centered at the same frequency as the
laser. It is assumed to be symmetric about the central frequency. The filter possesses unity
transmission near ω0 and has negligible effects on the total power of the light. The output
lineshape function is changed from S E (ω ) to

S E′ (ω ) S E (ω ) H (| ω − ω0 |).

(5.16)

The Central Relation (6.15) also applies to the light exiting the filter, which leads to

S ∆′ υ (υ )

{S E′ (ω0 + 2πυ ) + S E′ (ω0 − 2πυ )},
E02

(5.17)

where S ∆υ ′ (υ ) represents the frequency noise PSD of the light modified by the filter. From
equation (5.15), (5.16) and (5.17), it follows that

S ∆′ υ (υ ) = S ∆υ (υ ) H (2πυ ),

(5.18)

where S ∆υ (υ ) is the original frequency noise PSD of the laser. Equation (5.18) indicates that
the frequency noise PSD at a base band frequency υ is modified by the same transmission
function of the filter at an optical frequency ω0 ± 2πυ . This equation indicates that the
frequency noise at some high baseband frequency υ can be controlled by optically filtering
the tail of lineshape at the frequency offset υ from the center. By correctly designing the
transmission spectrum of the filter, the frequency noise can be tailored correspondingly.

82
Equation (5.18) appears alarmingly simple but consider the fact that demonstrates a
tailoring of, for example, a microwaves spectrum near υ by optical filtering at frequencies

ω0 ± 2πυ , which are orders of magnitude larger. To demonstrate the significance of equation
(5.18) and further illustrate the validity of (5.15), we pass the laser output field through an
MZI with the FSR of 203 MHz, as shown in Fig. 5.3. The laser frequency is tuned to match
one of the maximum-transmission frequencies of the MZI, which is schematically shown in
Fig. 5.4. Notice that the Lorentzian linewidth of the laser is much smaller than the FSR, and
therefore the laser power is preserved after transmission. However, equation (5.18) predicts
that the frequency noise PSD should be modified by the transmission function of the MZI.

Figure 5.3 Measurement setup for the frequency noise PSD of laser output modified by the
MZI with the free spectral range of 203 MHz
The measured frequency noise PSD, along with the intrinsic one, is shown in Fig. 5.5(a),
which is modified dramatically by the MZI. To confirm the validity of equation (5.18), we
take the ratio between those two frequency spectra, which is plotted in Fig. 5.5(b). The
function is indeed the transmission spectrum of the MZI, which is sinusoid with an FSR of
203 MHz.
Being able to control laser frequency noise in any chosen frequency region is of great
importance for technologies and applications which employ phase modulation of lasers
and/or coherent detection. The corresponding phase noise of the system in general can be
estimated with

83

∫ τ S υ ( f ) df ,

(5.19)

where T is the total acquisition time of the signal and 1 T is usually very small; τ
represents the time interval between two successive samplings and therefore 1 τ is the
sampling or modulation frequency. 1 τ is typically orders of magnitude larger than 1 T and
varies from one application to another. For example, in high-speed coherent optical
communications, the modulation frequency can be as high as tens of GHz. However, for
applications such as phase-sensitive LIDAR and imaging, a sampling frequency on the order
of tens of MHz may be enough. S ∆υ ( f ) represents the frequency noise PSD of laser light.

Figure 5.4 Schematic plot of the laser lineshape and transmission spectrum of the MZI; the
laser frequency aligned to maximum transmission frequency of the MZI
In order to reduce the phase noise in the system, it is crucial to suppress the laser frequency
noise PSD at frequencies close to the sampling or modulation frequency, namely

S ∆υ ( f ) |

f

(5.20)

84
because it occupies the largest bandwidth and thus contributes mostly to the phase noise.
Therefore, optical filtering offers a brand-new way of engineering the laser frequency noise
PSD in any desired bandwidth to reduce the phase noise in the systems.

Figure 5.5 (a) Frequency noise PSD of the laser and laser passing through the MZI (b)
Ratio between the two frequency noise PSDs

85
5.3.2 Is laser linewidth a good measure for laser coherence
In our previous experiments, it makes sense to use laser frequency noise PSD as the measure
for laser coherence because of its straightforward relation to the phase noise in the coherent
optical communications. However, we have never judged whether laser linewidth, the other
common measure for laser coherence, is a good measure. In this section, we are going to
answer that question.
The following is the logic. First, the phase noise in coherent optical communications is
mostly relevant to the frequency noise PSD at high frequencies, indicated by equation (2.13).
Second, the Central Relation reveals that the frequency noise PSD at high frequencies is only
related to the tail of the optical lineshape. Hence, the laser linewidth, a characteristic of the
body of the optical lineshape, is in general independent on the frequency noise PSD at high
frequencies and therefore not a good measure for laser coherence in coherent optical
communications.
To prove the conclusion, we examine three different lasers, two of which are the hybrid
Si/III-V laser and the III-V DFB laser used before. The last one is the III-V DFB laser under
very little coherent optical feedback, where the laser remains single-mode. The coherent
optical feedback loop is constructed the same as before. We are going to measure their
frequency noise PSD, optical lineshape and performance in the coherent optical
communications.
The frequency noise PSDs of the lasers are shown in Fig. 5.6 and 5.7. The frequency noise
PSD of the III-V DFB laser at low frequencies is significantly reduced by very little coherent
optical feedback while at high frequencies, the RF oscillations are pretty weak. The optical
lineshapes are shown in Fig. 5.8. Evidently, little coherent optical feedback can help to
suppress the linewidth of the III-V DFB laser dramatically, making it as ‘coherent’ as the
Si/III-V laser if laser linewidth is used as the measure for laser coherence [64-68]. The results
validate our argument that laser linewidth is irrelevant to laser frequency noise PSD at high
frequencies.

86

Figure 5.6 Frequency noise PSD of the Si/III-V laser

Figure 5.7 Frequency noise PSD of the III-V DFB laser w/o and w/ small coherent optical
feedback

87

Figure 5.8 Optical lineshape of the three lasers
The three lasers are then tested in the coherent optical communication system. The results on
20 GBaud 16-QAM, shown in Fig. 5.9, indicate that the narrow linewidth of the III-V DFB
laser under very little coherent optical feedback is useless as there is no obvious improvement
of the laser’s system performance. The Si/III-V laser is superior due to its ultra-low frequency

88
noise PSD at high frequencies. Such results confirm our conclusion that in general, laser
linewidth is not a good measure for laser coherence when it comes to coherent optical
communications.

Figure 5.9 System performance of the three lasers
5.4 Conclusions
In this chapter, we have derived a general relation, the Central Relation, between laser
frequency noise PSD and lineshape. Predicted by the Central Relation and demonstrated
experimentally, laser frequency noise PSD can be optically filtered, which offers us a new
way of controlling laser phase coherence. Finally, we prove experimentally that laser
linewidth is not a good measure for laser coherence in coherent optical communications,
another prediction by the Central Relation.

89

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