Table Of ContentMicrocavitySemiconductorLasers
Microcavity Semiconductor Lasers
Principles, Design, and Applications
Yong-zhen Huang
Yue-de Yang
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v
Contents
Preface xi
1 Introduction 1
1.1 Whispering-Gallery-ModeMicrocavities 1
1.2 ApplicationsofWhispering-Gallery-ModeMicrocavities 2
1.3 Ultra-HighQWhispering-Gallery-ModeMicrocavities 5
1.4 ModeQFactorsforSemiconductorMicrolasers 6
1.4.1 OutputEfficiencyandModeQFactor 6
1.4.2 MeasurementofModeQFactor 7
1.5 BookOverview 10
References 11
2 MultilayerDielectricSlabWaveguides 13
2.1 Introduction 13
2.2 TEandTMModesinSlabWaveguides 14
2.3 ModesinSymmetricThree-LayerSlabWaveguides 15
2.3.1 TEModesinThree-LayerSlabWaveguides 15
2.3.2 TMModesinThree-LayerSlabWaveguides 17
2.3.3 GuidedandRadiationModes 17
2.4 EigenvalueEquationsforMultilayerSlabComplexWaveguides 18
2.4.1 EigenvalueEquationforTEModes 19
2.4.2 EigenvalueEquationforTMModes 21
2.4.3 PhaseShiftofTotalInternalReflection 21
2.5 EigenvalueEquationsforOne-DimensionalMultilayerWaveguides 22
2.5.1 EigenvalueEquationforVertical-CavitySurface-EmittingLasers 22
2.5.2 ResonanceConditionfortheFabry–PerotCavity 24
2.5.3 ModeSelectionforDistributedFeedbackLasers 26
2.6 ModeGainandOpticalConfinementFactor 28
2.6.1 OpticalConfinementFactorBasedonPowerFlow 28
2.6.2 ModeGainforTEModes 29
2.6.3 ModeGainforTMModes 30
vi Contents
2.7 NumericalResultsofOpticalConfinementFactors 31
2.7.1 Edge-EmittingSemiconductorLasers 31
2.7.2 Si-on-SiO SlabWaveguide 32
2
2.7.3 Vertical-CavitySurface-EmittingLasers 33
2.8 EffectiveIndexMethod 35
References 36
3 FDTDMethodandPadéApproximation 37
3.1 Introduction 37
3.2 BasicPrincipleofFDTDMethod 38
3.2.1 Maxwell’sEquation 38
3.2.2 2DFDTDMethodinCartesianCoordinateSystem 38
3.2.3 3DFDTDMethodinCartesianCoordinateSystem 41
3.2.4 3DFDTDMethodinCylindricalCoordinateSystem 43
3.2.5 NumericalStabilityCondition 45
3.2.6 AbsorptionBoundaryCondition 46
3.2.7 FDTDSimulationofMicrocavities 48
3.3 PadéApproximationforTime-DomainSignalProcessing 50
3.3.1 PadéApproximationwithBaker’sAlgorithm 50
3.3.2 CalculationofIntensitySpectraforOscillators 52
3.4 ExamplesofFDTDTechniqueandPadéApproximation 53
3.4.1 SimulationforCoupledMicrodisks 53
3.4.2 SimulationforMicroringChannelDropFilters 54
3.4.3 LightDelaySimulationforCoupledMicroringResonators 57
3.4.4 CalculationofPropagationLossinPhotonicCrystalWaveguides 59
3.5 Summary 62
References 62
4 DeformedandChaoticMicrocavityLasers 65
4.1 Introduction 65
4.2 NondeformedCircularMicrodiskLasers 65
4.2.1 Whispering-GalleryModesinCircularMicrodisks 65
4.2.2 CircularMicrodiskSemiconductorLasers 70
4.3 DeformedMicrocavityLaserswithDiscontinuousBoundary 70
4.3.1 MicrodiskLaserswithaLocalBoundaryDefect 70
4.3.2 Spiral-ShapedMicrocavityLasers 72
4.3.3 Waveguide-ConnectedSpiralMicrocavityLasers 75
4.4 ChaoticMicrocavityLaserswithSmoothlyDeformedBoundary 75
4.4.1 Quadrupolar-ShapedMicrocavityLaserswithDirectionalEmission 76
4.4.2 LimaçonMicrocavityLaserswithUnidirectionalEmission 79
4.4.3 Wavelength-ScaleMicrocavityLaserswithUnidirectionalEmission 82
4.4.4 Waveguide-CoupledChaoticMicrocavityLasers 86
4.5 Summary 87
References 88
Contents vii
5 UnidirectionalEmissionMicrodiskLasers 91
5.1 Introduction 91
5.2 ModeCouplinginWaveguide-ConnectedMicrodisks 92
5.2.1 Whispering-GalleryModesinCircularMicrodisks 92
5.2.2 ModeCouplinginWaveguide-ConnectedMicrodisks 94
5.3 Waveguide-ConnectedUnidirectionalEmissionMicrodiskLasers 100
5.3.1 LasingCharacteristicsofUnidirectionalEmissionMicrodiskLasers 100
5.3.2 DirectModulationCharacteristicsofUnidirectionalEmissionMicrodisk
Lasers 103
5.4 UnidirectionalEmissionMicroringLasers 107
5.5 UnidirectionalEmissionHybridDeformed-MicroringLasers 111
5.6 Wide-AngleEmissionandMultiportMicrodiskLasers 113
5.6.1 Wide-AngleEmission-DeformedMicrodiskLasers 113
5.6.2 MultiportOutputMicrodiskLasers 117
5.7 Summary 119
References 119
6 Equilateral-Triangle-ResonatorMicrolasers 123
6.1 Introduction 123
6.2 ModeAnalysisBasedontheETRSymmetry 123
6.2.1 WaveEquationsforTEandTMModes 123
6.2.2 TransverseModesbyUnfoldingLightRayintheETR 124
6.2.3 EvanescentFieldsinExternalRegions 125
6.2.4 EigenvalueEquation 127
6.3 Mode-FieldDistributions 128
6.3.1 ModeDegeneracyandClassify 128
6.3.2 ComparisonsofAnalyticalSolutionswithSimulatedResults 129
6.3.3 SizeLimitforETR 129
6.4 Far-FieldEmissionandWaveguide-OutputCoupling 131
6.4.1 ModeQ-FactorCalculatedbyFar-FieldEmission 131
6.4.2 OutputCouplingbyConnectingaWaveguide 133
6.5 ModeAnalysisUsingReflectedPhaseShiftofPlaneWave 135
6.5.1 ModeAnalysisUsingModeLightRayApproximation 135
6.5.2 ComparisonofModeQFactors 138
6.5.3 EffectofMetalLayeronModeConfinement 139
6.6 ModeCharacteristicsofETRMicrolasers 140
6.6.1 DeviceFabrication 140
6.6.2 LasingCharacteristics 142
6.7 Summary 145
References 145
7 SquareMicrocavityLasers 147
7.1 Introduction 147
7.2 AnalyticalSolutionofConfinedModes 148
7.3 SymmetryAnalysisandModeCoupling 150
viii Contents
7.4 ModeAnalysisforHighQModes 154
7.5 Waveguide-CoupledSquareMicrocavities 157
7.6 Directional-EmissionSquareSemiconductorLasers 163
7.7 Dual-ModeLasingSquareLaserswithaTunableInterval 165
7.8 ApplicationofDual-ModeSquareMicrolasers 168
7.9 LasingSpectraControlledbyOutputWaveguides 171
7.10 Circular-SideSquareMicrocavityLasers 174
7.11 Summary 180
References 181
8 HexagonalMicrocavityLasersandPolygonal
Microcavities 185
8.1 Introduction 185
8.2 ModeCharacteristicsofRegularPolygonalMicrocavities 186
8.2.1 SymmetryAnalysesBasedonGroupTheory 186
8.2.2 NumericalSimulationsofWGMsinRegularPolygonal
Microcavities 190
8.2.3 Circular-SidePolygonalMicrocavities 193
8.3 WGMSinHexagonalMicrocavities 197
8.3.1 PeriodicOrbitsinHexagonalMicrocavities 197
8.3.2 SymmetryAnalysesandModeCoupling 200
8.3.3 NumericalSimulationofWGMsinHexagonalMicrocavities 201
8.3.4 WGMsinWavelength-ScaleHexagonalMicrocavities 203
8.4 UnidirectionalEmissionHexagonalMicrocavityLasers 205
8.4.1 Waveguide-CoupledHexagonalMicrocavityLasers 206
8.4.2 Circular-SideHexagonalMicrocavityLasers 209
8.5 OctagonalResonatorMicrolasers 211
8.6 Summary 214
References 215
9 VerticalLossfor3DMicrocavities 219
9.1 Introduction 219
9.2 NumericalMethodfortheSimulationof3DMicrocavities 220
9.2.1 EffectiveIndexMethod 220
9.2.2 S-MatrixMethod 222
9.3 ControlofVerticalRadiationLossforCircularMicrocavities 225
9.3.1 ModeCouplingandVerticalRadiationLoss 225
9.3.2 SemiconductorMicrocylinderLaserswiththeSizesLimitedbyVertical
RadiationLoss 230
9.3.3 CancelationofVerticalRadiationLossbyDestructiveInterference 236
9.4 VericalRadiationLossforPolygonalMicrocavities 245
9.4.1 3DEquilateral-TriangularMicrocavitywithWeakVertical
Waveguiding 245
9.4.2 3DSquareMicrocavitywithWeakVerticalWaveguiding 246
9.5 Summary 247
References 249
Contents ix
10 NonlinearDynamicsforMicrocavityLasers 251
10.1 Introduction 251
10.2 RateEquationModelwithOpticalInjection 253
10.3 DynamicalStatesofRateEquationswithOpticalInjection 255
10.4 SmallSignalAnalysisofRateEquations 261
10.5 ExperimentsofOpticalInjectionMicrodiskLasers 263
10.5.1 NonlinearDynamicsUnderOpticalInjection 263
10.5.2 ComparisonBetweenExperimentandSimulatedResults 268
10.5.3 ModulationBandwidthEnhancementUnderOpticalInjection 269
10.6 MicrowaveGenerationinMicrolaserwithOpticalInjection 271
10.7 IntegratedTwin-MicrolaserwithMutuallyOpticalInjection 275
10.8 DiscussionandConclusion 276
References 278
11 Hybrid-CavityLasers 283
11.1 Introduction 283
11.2 ReflectivityofaWGMResonator 284
11.3 ModeQ-FactorEnhancementforHybridModes 286
11.4 HybridMode-FieldDistributions 288
11.5 FabricationofHybridLasers 290
11.6 Q-FactorEnhancementandLasingCharacteristics 292
11.7 RobustSingle-ModeOperation 295
11.8 OpticalBistabilityforHSRLS 297
11.9 All-OpticalSwitching 302
11.10 All-OpticalLogicGates 306
11.11 HybridSquare/Rhombus-RectangularLasers(HSRRLS) 309
11.12 Summary 312
References 314
Index 317
xi
Preface
As typical whispering-gallery microcavities, microdisks, and microrings have
been studied for applications in integrated optics over a half century. The study
of semiconductor microdisk lasers has become a distinct subject of optoelectron-
ics, and deformed microdisk lasers have attracted great attention for realizing
directional emission microlasers. In addition to circular microcavities, polygonal
microcavitiescanalsosupporthighQ-confinedmodesthatrelyonthetotalinternal
reflection,similartowhispering-gallerymodesinmicrodisks.Wehaveinvestigated
microcavity lasers for the past two decades, mainly focusing on mode analysis,
design,processingtechnique,photonicintegration,andapplicationsofmicrocavity
lasers. This book summarizes the research on semiconductor microcavity lasers
based on whispering-gallery modes. Although there are several books on optical
microcavities, this book provides unique descriptions of directional emission
microcavity lasers by directly connecting an output waveguide, mode behaviors
based on group theory for polygonal microcavities, and hybrid-cavity lasers with
integratedmicrocavityandwaveguide.
The book is organized into 11 chapters: introduction emphasized on mode Q
factor, multilayer optical waveguides, FDTD method and Padé approximation,
deformed and chaos microdisk lasers, unidirectional emission microdisk lasers,
equilateral triangle resonator microlasers, square microcavity lasers, hexagonal
microcavity lasers and polygonal microcavities, vertical loss for 3D microcavities,
nonlineardynamicsformicrocavitylasers,andhybrid-cavitylasers.
WewanttothankHuang’sstudents,especiallyDr.Wei-HuaGuo,atInstituteof
Semiconductors;theirworkshavecontributedtomainpartsofthisbook.
Yong-zhenHuang
Yue-deYang
StateKeyLabofIntegratedOptoelectronics
InstituteofSemiconductors
ChineseAcademyofSciencesandCollegeof
Beijing,China MaterialsSciencesandOptoelectronicTechnology
November2020 UniversityofChineseAcademyofSciences
1
1
Introduction
1.1 Whispering-Gallery-Mode Microcavities
Optical resonant cavities, composed of two or more mirrors, are essential part of
ordinarylasersandhavebeenutilizedinalmostallbranchesofmodernopticsand
photonics.Opticalenergyisrecirculatedinsidethecavitiesduetothereflectionon
themirrors,andonebasicpropertyoftheopticalcavitiesisthequality(Q)factor
relatedtothemodelifetimefordescribingthelight-confiningability.Modevolume
(V) is another important parameter of an optical cavity and a small V is of great
importance for realizing a compact-size integrated device. A suitable parameter,
finesse, which is defined as the ratio of the free spectral range to the resonance
linewidth, takes both the mode Q factor and the resonator size into account. For
certain applications, high-finesse microcavity with a large value of Q/V, which is
alsorelatedtotheelectromagneticfieldenhancementfactorofanopticalcavity,is
veryimportant.Comparedwithconventionallasers,microcavitylaserswithalarge
Q/V can promise lower lasing threshold. Moreover, light–matter interactions can
begreatlyenhancedbystoringopticalenergyinasmallmodevolume[1,2].The
ability to concentrate light is important to both fundamental science studies and
practicaldeviceapplications[3],suchasstrong-couplingcavityquantumelectrody-
namics, enhancement and suppression of spontaneous emission, high-sensitivity
sensors,low-thresholdlightsources,andcompactopticaladd-dropfiltersinoptical
communication.
ToobtainhighQmodesinopticalcavitieswithasmallV,ahighreflectivitycloseto
unityisnecessary,whichcanberealizedbyutilizingaperiodicstructuretoconstruct
a photonic forbidden band, such as that in vertical-cavity surface-emitting lasers
andphotoniccrystalmicrocavities,orsimplybytotalinternalreflection(TIR)atthe
dielectricboundarywithahigh-lowrefractiveindexcontrastinwhispering-gallery
(WG)-mode optical microcavities [4]. The idea of WG mode was born out of the
observation of acoustical phenomenon in [5] where sound waves were efficiently
reflectedwithminimaldiffractionandstruckthewallagainatthesameangleand
therebytraveledalongthegallerysurface.Similarly,classicalelectromagneticwaves
can undergo reflection,refraction,and diffractionlike the sound waves whenthe
wavelengthsofthewavesaresmallerthanthebendingradiusofareflectionmirror.
Amongvariouskindsofopticalmicrocavities,WG-modemicrocavitieswithsimple
MicrocavitySemiconductorLasers:Principles,Design,andApplications,FirstEdition.
Yong-zhenHuangandYue-deYang.
©2021WILEY-VCHGmbH.Published2021byWILEY-VCHGmbH.
