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Modeling 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 [email protected]. 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