Fiber Optical Parametric Amplifiers, Oscillators and Related Devices

377 Pages·2007·5.7 MB·English

by  Michel E. Marhic

FiberOpticalParametricAmplifiers,OscillatorsandRelatedDevices
Fiberopticalparametricamplifiers(OPAs)showgreatpotentialforapplicationsinhigh-
speedopticalcommunicationsystems.Thisisthefirstbooktoprovidecomprehensive
coverageofthetheoryandpracticeofOPAsandrelateddevices,includingfiberoptical
parametricoscillators(OPOs).
Followinganintroductiontothefield,thetheoryandtechniquesbehindalltypesof
fiber OPA are covered, starting from first principles. Topics include scalar and vector
OPA theory, the nonlinear Schro¨dinger equation, OPO theory, and the quantum noise
figure of fiber OPAs. The challenges of making fiber OPAs practical for a number of
applicationsarediscussed,andasurveyofthestateoftheartinfeasibilitydemonstrations
andperformanceevaluationsisprovided.ThecapabilitiesandlimitationsofOPAsare
presented,asarethepotentialapplicationsforbothOPAsandOPOsandtheprospects
forfuturedevelopmentsinthefield.Thetheoreticaltoolsdevelopedinthistextcanalso
beappliedtootherareasofnonlinearoptics.
Thisbookshouldprovideavaluableresourceforresearchers,advancedpractitioners,
andgraduatestudentsinoptoelectronics.
Michel E. Marhic is Chair Professor at the Institute of Advanced Telecommu-
nications at the University of Wales, Swansea. He was awarded a Ph.D. in Electrical
EngineeringfromtheUniversityofCalifornia,LosAngeles,in1974.Hehasheldsev-
eralpositionsintheacademicworldintheUSovertheyears.Heistheco-founderof
Holicon,HolographicIndustries,andOPALLaboratories.AseniormemberoftheIEEE
andamemberofOSA,hehastakenouteightpatentsandauthoredorco-authoredabout
300publications.Hisrecentresearchinterestsincludeopticalcommunicationsystems
andnonlinearopticalineractionsinfibers.

Fiber Optical Parametric
Amplifiers, Oscillators and
Related Devices
MICHEL E. MARHIC
UniversityofWales,Swansea
cambridge university press
Cambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,Sa˜oPaulo
CambridgeUniversityPress
TheEdinburghBuilding,CambridgeCB28RU,UK
PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork
www.cambridge.org
Informationonthistitle:www.cambridge.org/9780521861021
(cid:2)C CambridgeUniversityPress2008
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithout
thewrittenpermissionofCambridgeUniversityPress.
Firstpublished2008
PrintedintheUnitedKingdomattheUniversityPress,Cambridge
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary
ISBN 978-0-521-86102-1hardback
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accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto
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Contents
Acknowledgments page ix
1 Introduction 1
References 7
2 Propertiesofsingle-modeopticalfibers 9
2.1 Modeprofile 9
2.2 Loss 10
2.3 Propagationconstantanddispersion 10
2.4 Longitudinalfluctuationsofthezero-dispersionwavelength 14
2.5 Temperaturedependenceofthezero-dispersionwavelength 14
2.6 Fiberbirefringence 15
2.7 Nonlinearities 17
2.8 TypesoffiberusedforOPAwork 21
References 27
3 ScalarOPAtheory 31
3.1 Introduction 31
3.2 TypesoffiberOPA 31
3.3 DerivationoftheOPAequationsandγ 35
3.4 Scalinglaws 40
3.5 Solutionofthetwo-pumpOPAequations 42
3.6 Theoryforone-pumpOPA 60
3.7 Caseofnodispersionwithloss 69
3.8 SolutionsfordegenerateOPAs 70
3.9 Conclusion 75
References 75
4 VectorOPAtheory 78
4.1 Introduction 78
4.2 Isotropicfibers 78
4.3 Fiberswithconstantbirefringence 93
vi Contents
4.4 Fiberswithrandombirefringence 98
4.5 Conclusion 107
References 108
5 Theopticalgainspectrum 110
5.1 Introduction 110
5.2 Theeffectofpumppowerongainbandwidth 110
5.3 Theeffectoffiberdispersiononthegainspectrum 111
5.4 OPAswithsimilargainspectra 120
5.5 EquivalentgainspectraforOPAsusingpumpswithdifferentSOPs 123
5.6 Saturatedgainspectra 125
5.7 Fiberswithlongitudinaldispersionvariations 134
5.8 Fiberswithconstantlinearbirefringence 140
5.9 Few-modefibers 143
References 144
6 ThenonlinearSchro¨dingerequation 146
6.1 Introduction 146
6.2 DerivationoftheNLSEforanisotropicfiber 147
6.3 DerivationoftheNLSEforabirefringentfiber 148
6.4 AnalyticsolutionsofthescalarNLSE 151
6.5 IncludingtheRamangainintheNLSE 156
6.6 NumericalsolutionsoftheNLSEbythesplit-stepFouriermethod 157
6.7 ApplicationsoftheSSFMtofiberswithlongitudinalvariations 162
6.8 SourcesofSSFMsoftware 166
6.9 Conclusion 167
References 167
7 Pulsed-pumpOPAs 169
7.1 Introduction 169
7.2 Thequasi-CWregime 169
7.3 Thesplit-stepFouriermethod 172
7.4 Importantpulseshapes 173
7.5 Examplesofpulsed-pumpOPAs 178
7.6 Conclusion 185
References 185
8 OPOtheory 187
8.1 Introduction 187
8.2 FiberOPOtheory 188
8.3 Conclusion 192
References 193
Contents vii
9 QuantumnoisefigureoffiberOPAs 194
9.1 Introduction 194
9.2 Quantum-mechanicalderivationoftheOPAequations 195
9.3 Noisefigureofnon-degeneratefiberOPAs 200
9.4 Wavelengthexchange 203
9.5 NoisefigureofdegeneratefiberOPAs 205
9.6 EffectofRamangainonOPAnoisefigure 206
9.7 Conclusion 209
References 209
10 Pumprequirements 211
10.1 Introduction 211
10.2 Pumppowerrequirements 211
10.3 Polarizationconsiderations 213
10.4 Pumpamplitudefluctuations(pumpRIN) 213
10.5 Pumpphaseorfrequencyfluctuations 219
10.6 Conclusion 223
References 223
11 Performanceresults 226
11.1 Introduction 226
11.2 Pulseddevices 226
11.3 CWdevices 233
References 245
12 PotentialapplicationsoffiberOPAsandOPOs 249
12.1 Introduction 249
12.2 OPAsinopticalcommunication 249
12.3 OPAsinhigh-powerwavelengthconversion 273
12.4 OPOs 275
References 275
13 NonlinearcrosstalkinfiberOPAs 281
13.1 Introduction 281
13.2 Four-wavemixing 281
13.3 Cross-gainmodulation 292
13.4 Coherentcrosstalk 298
13.5 Cross-phasemodulation 299
13.6 Conclusion 300
References 301
viii Contents
14 Distributedparametricamplification 303
14.1 Introduction 303
14.2 DPAexperimentin75kmofDSF 304
14.3 PossibleextensionsofDPA 309
14.4 Conclusion 311
References 312
15 Prospectsforfuturedevelopments 315
15.1 Introduction 315
15.2 Fibers 315
15.3 Pumps 319
15.4 SBSsuppression 320
15.5 Integratedoptics 322
15.6 Pumpresonators 324
15.7 Discreteordistributedparametricamplification? 326
15.8 Conclusion 329
References 329
Appendices
A.1 GeneraltheoremsforsolvingtypicalOPA 333
A.2 TheWKBapproximation 340
A.3 Jacobianellipticfunctionsolutions 344
A.4 Solutionoffourcoupledequationsforthesix-wavemodel 355
A.5 Summaryofusefulequations 358
Index 361
Acknowledgments
ThanksareduetoK.K.-Y.Wong,J.Nielsen,M.JamshidifarandP.Vossforproofreading
partsofthemanuscript.IwouldalsoliketothankG.Kalogerakis,J.M.ChavezBoggio,
T.Torounidis,K.K.-Y.Wong,andP.Vossforprovidingsomeofthefigures.