Light Propagation in Gain Media: Optical Amplifiers

286 Pages·2011·2.79 MB·English

by  Malin Premaratne

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LIGHT PROPAGATION IN GAIN MEDIA
Over the past two decades, optical amplifiers have become of key importance
in modern communications. In addition to this, the technology has applications
in cutting-edge research such as biophotonics and lab-on-a-chip devices. This
book provides a comprehensive treatment of the fundamental concepts, theory,
andanalyticaltechniquesbehindmodernopticalamplifiertechnology.
Thebookcoversallmajoropticalamplificationschemesinconventionalmateri-
als,includingtheRamanandparametricgainprocesses.Thefinalchapterisdevoted
toopticalgaininmetamaterials,atopicthathasbeenattractingconsiderableatten-
tion in recent years. The authors emphasize analytical insights to give a deeper,
moreintuitiveunderstandingofvariousamplificationschemes.Thebookassumes
backgroundknowledgeofelectricalengineeringorappliedphysics,includingexpo-
sure to electrodynamics and wave motion, and is ideal for graduate students and
researchersinphysics,optics,bio-optics,andcommunications.
MALIN PREMARATNE is Research Director and Associate Professor in the
Advanced Computing and Simulation Laboratory, Department of Electrical and
ComputerSystemsEngineering,MonashUniversity,Clayton,Australia.Heguides
the research program in theory, modeling, and simulation of light propagation in
guidedandscatteringmedia.
GOVIND P. AGRAWAL is Professor of Optics and Physics in the Institute of
Optics,UniversityofRochester,USA.Hiscurrentresearchinterestsincludeoptical
communications,nonlinearoptics,andlaserphysics.

LIGHT PROPAGATION IN GAIN
MEDIA
OpticalAmplifiers
MALIN PREMARATNE
MonashUniversity
Australia
GOVIND P. AGRAWAL
TheInstituteofOptics
UniversityofRochester
USA
CAMBRIDGEUNIVERSITYPRESS
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CambridgeUniversityPress
TheEdinburghBuilding,CambridgeCB28RU,UK
PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork
www.cambridge.org
Informationonthistitle:www.cambridge.org/9780521493482
©M.PremaratneandG.P.Agrawal2011
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithout
thewrittenpermissionofCambridgeUniversityPress.
Firstpublished2011
PrintedintheUnitedKingdomattheUniversityPress,Cambridge
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary
ISBN978-0-521-49348-2Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceor
accuracyofURLsforexternalorthird-partyinternetwebsitesreferredtoin
thispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis,
orwillremain,accurateorappropriate.
ForAnne,Sipra,Caroline,andClaire
–GovindP.Agrawal
ForErosha,Gehan,andSayumi
–MalinPremaratne

Contents
Preface pagexi
1 Introduction 1
1.1 Maxwell’sequations 2
1.2 Permittivityofisotropicmaterials 9
1.3 Dispersionrelations 12
1.4 Causalityanditsimplications 19
1.5 SimplesolutionsofMaxwell’sequations 22
References 26
2 Lightpropagationthroughdispersivedielectricslabs 28
2.1 Stateofpolarizationofopticalwaves 29
2.2 Impedanceandrefractiveindex 31
2.3 Fresnelequations 33
2.4 Propagationofopticalpulses 37
2.5 Finite-differencetime-domain(FDTD)method 42
2.6 Phaseandgroupvelocities 53
2.7 Pulsepropagationthroughadielectricslab 56
References 60
3 Interactionoflightwithgenericactivemedia 63
3.1 Reflectionoflightfromagainmedium 64
3.2 Surface-plasmonpolaritons 69
3.3 Gain-assistedmanagementofgroupvelocity 75
3.4 Gain-assisteddispersioncontrol 79
References 85
4 OpticalBlochequations 88
4.1 Thebraandketvectors 89
vii
viii Contents
4.2 Densityoperator 91
4.3 Density-matrixequationsfortwo-levelatoms 93
4.4 OpticalBlochequations 101
4.5 Maxwell–Blochequations 104
4.6 NumericalintegrationofMaxwell–Blochequations 107
References 111
5 Fiberamplifiers 113
5.1 Erbium-dopedfiberamplifiers 114
5.2 Amplifiergainanditsbandwidth 116
5.3 RateequationsforEDFAs 119
5.4 AmplificationunderCWconditions 122
5.5 Amplificationofpicosecondpulses 124
5.6 Autosolitonsandsimilaritons 131
5.7 Amplificationoffemtosecondpulses 138
References 140
6 Semiconductoropticalamplifiers 143
6.1 MaterialaspectsofSOAs 144
6.2 Carrierdensityandopticalgain 147
6.3 Picosecondpulseamplification 151
6.4 Femtosecondpulseamplification 164
References 171
7 Ramanamplifiers 173
7.1 Ramaneffect 174
7.2 Ramangainspectrumofopticalfibers 177
7.3 FiberRamanamplifiers 183
7.4 SiliconRamanamplifiers 188
References 205
8 Opticalparametricamplifiers 208
8.1 Physicsbehindparametricamplification 208
8.2 Phase-matchingcondition 211
8.3 Four-wavemixinginopticalfibers 212
8.4 Three-wavemixinginbirefringentcrystals 224
8.5 Phasematchinginbirefringentfibers 229
References 235
9 Gaininopticalmetamaterials 237
9.1 Classificationofmetamaterials 238
9.2 Schemesforlosscompensationinmetamaterials 241