Table Of ContentModeling and Design Photonics
®
by Examples Using MATLAB
IOP Series in Emerging Technologies in Optics and Photonics
Series Editor
R Barry Johnson a Senior Research Professor at Alabama A&M
University, has been involved for over 50 years in lens design,
optical systems design, electro-optical systems engineering, and
photonics. He has been a faculty member at three academic
institutions engaged in optics education and research, employed
by a number of companies, and provided consulting services.
DrJohnsonisanIOPFellow,SPIEFellowandLifeMember,OSAFellow,andwas
the 1987 President of SPIE. He serves on the editorial board of Infrared Physics &
Technology and Advances in Optical Technologies. Dr Johnson has been awarded
manypatents,haspublishednumerouspapersandseveralbooksandbookchapters,
andwasawardedthe2012OSA/SPIEJosephWGoodmanBookWritingAwardfor
LensDesignFundamentals,SecondEdition.Heisaperennialco-chairoftheannual
SPIE Current Developments in Lens Design and Optical Engineering Conference.
Foreword
Untilthe1960s,thefieldofopticswasprimarilyconcentratedintheclassicalareasof
photography, cameras, binoculars, telescopes, spectrometers, colorimeters, radio-
meters,etc.Inthelate1960s,opticsbegantoblossomwiththeadventofnewtypesof
infrareddetectors,liquidcrystaldisplays(LCD),lightemittingdiodes(LED),charge
coupled devices (CCD), lasers, holography, fiber optics, new optical materials,
advances in optical and mechanical fabrication, new optical design programs, and
many more technologies.With thedevelopment ofthe LED,LCD, CCD and other
electo-optical devices, the term ‘photonics’ came into vogue in the 1980s to describe
thescienceofusinglightindevelopmentofnewtechnologiesandtheperformanceof
amyriadofapplications.Today,opticsandphotonicsaretrulypervasivethroughout
societyandnewtechnologiesarecontinuingtoemerge.Theobjectiveofthisseriesis
to provide students, researchers, and those who enjoy self-teaching with a wide-
ranging collection of books that each focus on a relevant topic in technologies and
applicationofopticsand photonics.Thesebookswill provideknowledgetoprepare
thereadertobebetterabletoparticipateintheseexcitingareasnowandinthefuture.
The title of this series is Emerging Technologies in Optics and Photonics where
‘emerging’ is taken to mean ‘coming into existence,’ ‘coming into maturity,’ and
‘coming into prominence.’ IOP Publishing and I hope that you find this Series of
significant value to you and your career.
Modeling and Design Photonics
®
by Examples Using MATLAB
Dan T Nguyen
Corning Research and Development Corporation, Corning, NY 14831, USA
IOP Publishing, Bristol, UK
ªIOPPublishingLtd2021
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem
ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording
orotherwise,withoutthepriorpermissionofthepublisher,orasexpresslypermittedbylawor
undertermsagreedwiththeappropriaterightsorganization.Multiplecopyingispermittedin
accordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgency,theCopyright
ClearanceCentreandotherreproductionrightsorganizations.
MATLABisaregisteredtrademarksofTheMathWorks,Inc.Seemathworks.com/trademarksfor
alistofadditionaltrademarks.
PermissiontomakeuseofIOPPublishingcontentotherthanassetoutabovemaybesought
atpermissions@ioppublishing.org.
DanTNguyenhasassertedhisrighttobeidentifiedastheauthorofthisworkinaccordancewith
sections77and78oftheCopyright,DesignsandPatentsAct1988.
ISBN 978-0-7503-2272-0(ebook)
ISBN 978-0-7503-2270-6(print)
ISBN 978-0-7503-2273-7(myPrint)
ISBN 978-0-7503-2271-3(mobi)
DOI 10.1088/978-0-7503-2272-0
Version:20210701
IOPebooks
BritishLibraryCataloguing-in-PublicationData:Acataloguerecordforthisbookisavailable
fromtheBritishLibrary.
PublishedbyIOPPublishing,whollyownedbyTheInstituteofPhysics,London
IOPPublishing,TempleCircus,TempleWay,Bristol,BS16HG,UK
USOffice:IOPPublishing,Inc.,190NorthIndependenceMallWest,Suite601,Philadelphia,
PA19106,USA
This book is dedicated to my parents.
Contents
Preface ix
Author biography xi
1 Introduction 1-1
1.1 Overview of the book 1-1
1.2 An instruction using MATLAB® programs 1-9
References 1-11
2 One-dimensional periodic and quasi-periodic photonics 2-1
crystal structures
2.1 1D photonics crystals and mathematics models 2-2
2.1.1 One-dimensional photonics crystals 2-2
2.1.2 Transfer matrix method 2-4
2.2 Linear transfer matrix method and modeling examples 2-6
2.2.1 Linear transfer matrix method formalism 2-6
2.2.2 Modeling example: 1D photonics band gap structures 2-9
2.2.3 Modeling example: distributed bragg reflector (DBR) fiber 2-16
laser—cavity design
2.2.4 Modeling example: distributed feedback fiber 2-25
laser—cavity design
2.2.5 Modeling example: quasi-periodic Fibonacci mirrors 2-33
2.3 Nonlinear transfer matrix method formalism 2-38
2.3.1 General equations 2-39
2.3.2 Modeling example: nonlinear defected PhC structures 2-42
References 2-59
3 Beam propagation method for modeling multimode 3-1
cladding-pumped fiber amplifiers
3.1 Modeling problems for multimode cladding-pumped fiber amplifiers 3-1
3.1.1 PREM modeling SM pumped fiber amplifiers 3-2
3.1.2 Problems of modeling MM pumped fiber amplifiers by PREM 3-9
3.2 Beam propagation method for modeling multimode cladding-pumped 3-12
fiber amplifiers
3.3 Modeling example: effective BPM modeling MM cladding-pumped 3-16
Yb-doped fiber amplifiers
vii
ModelingandDesignPhotonicsbyExamplesUsingMATLAB®
3.3.1 Example with MATLAB®: cladding-pumped YDFA 3-18
3.3.2 Explanation of program 3.1 3-25
3.4 Modeling example: effective BPM modeling of MM cladding-pumped 3-26
Yb–Er do-doped fiber amplifiers
3.4.1 Modeling 1480 nm-pumped Er-doped fiber amplifiers 3-27
3.4.2 Modeling 980 nm-pumped Er-doped fiber amplifiers 3-43
3.5 Modeling multimode cladding-pumped Yb–Er co-doped 3-48
fiber amplifiers
3.5.1 The model of 980 nm-pumped Yb–Er Co-doped 3-48
fiber amplifiers
3.5.2 Normalization and dimensionless notations 3-51
3.6 Modeling example: MM cladding-pumped Yb–Er Co-doped fiber 3-56
amplifiers
3.6.1 Programming example 3-59
3.7 Modeling MM cladding-pumped fiber amplifiers with ASEs 3-69
References 3-75
4 Modeling ultrafast mode-locked fiber lasers 4-1
4.1 A brief introduction to mode-locked lasers 4-2
4.2 General model of mode-locked fiber lasers 4-6
4.2.1 Saturable absorption 4-11
4.2.2 Material and waveguide dispersions 4-14
4.2.3 Nonlinear Schrödinger equation 4-17
4.2.4 Fourth-order Runge–Kutta in interaction picture method 4-21
4.3 Example of modeling mode-locked ring fiber lasers 4-25
4.4 Example of modeling linear cavity mode-locked fiber lasers 4-44
References 4-51
5 Chirped pulse fiber amplifiers 5-1
5.1 Background 5-1
5.2 Example: CPA system based on Tm-doped fiber lasers and amplifiers 5-3
5.2.1 Tm-doped fiber lasers and fiber amplifiers 5-4
5.2.2 All-fiber pulse stretcher 5-7
5.2.3 Third stage: cladding-pump Tm-doped fiber amplifiers in 5-22
2 μm-region
5.2.4 Effects of high order dispersion in pulse compression 5-25
References 5-34
viii
Preface
Over the past few decades, photonics has become a major field of science and
technology. Now covering a broad range of physics from silicon waveguides and
fiber lasers to photonics band-gap structures, and many other approaches of light
manipulation, it is evident that this discipline is undergoing a period of extremely
rapid progress.
As many physicists have entered this exciting field, they have driven the
development of photonics systems through their unique skill sets. For example,
theoretical physicists have played important roles not only for exploring new
concepts and new photonics systems, but also for modeling and designing these
new systems. These tasks require robust knowledge of fundamental theories of
physics, ability to manipulate equations, development of new models for various
systems, and the effective computation of these models. Nowadays, although most
computational modeling relies on supercomputing and sophisticated software, a
comprehensive understanding of physics remains critical for guiding research in
novel, exploratory systems.
Back in 2000, when I worked as a theoretical physicist, I was offered the
opportunity to model and design fiber amplifiers for applications in optical tele-
communication.Atfirst,Ididn’tthinkIcould takethejob;notonlydidInothave
any experience in the field, but I also didn’t think any theorist could effectively
develop real-world devices. When Professor Peyghambarian, the head of the
University of Arizona’s photonics division in the Optical Sciences Center, invited
severalofustoaprojectmeeting,Iwassurprisedtoseeactualtheoreticalphysicists
present, such as Professor N Bloembergen, a Nobel laureate in physics, and
Professor S Koch, a leading theorist in condensed matter physics, and others. The
event changed my thinking completely about working as a modeler in photonics.
From 2001 to 2016, I have experienced both highs and lows in the field of
photonics, both in the Optical Science Center and at NP Photonics, a research
companybasedinTucson,Arizona.However,asIdelveddeeperintomywork,the
more I enjoyed the process of modeling and design, especially in photonics. As a
theoristitisincredibletoseethatmanyobservedeffectsoflightmanipulationcanbe
predictedpreciselyfromsolutionsofMaxwell’sequationsestablishedmorethan160
years ago.Theoretical models can playa critical role in designing and optimizing a
photonicssystem,andItrulyappreciatetheroleofphysicaltheoriesinthecreation
of groundbreaking technology and discovery of novel systems.
This book was a product of my experience of modeling and design of photonics
after nearly 20 years working in academy and industry. It was initiated by Ms
Ashley Gasque from IOP Publishing (Institute of Physics, UK), who had patiently
convinced me to write this book. I know very well that there are a number of
excellent books on modeling and computational photonics. Several also include
computing programs that are very useful for students, scientists, and engineers.
However,becausephotonicsisaverybroadareaofscienceandtechnology,anditis
relatively new to many, these books have mostly focused on the introductory and
ix
