Nonlinear optics

626 Pages·2020·3.836 MB·English

by  Boyd, Robert W

Nonlinear Optics

Nonlinear Optics
Fourth Edition
Robert W. Boyd
The Institute of Optics
University of Rochester
Rochester, NY, United States
Department of Physics
University of Ottawa
Ottawa, ON, Canada
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Contents
Prefacetothe FourthEdition..................................................... xv
Prefacetothe Third Edition ...................................................... xvii
Prefacetothe SecondEdition..................................................... xix
Prefacetothe FirstEdition ....................................................... xxi
Chapter 1:The NonlinearOptical Susceptibility .................................. 1
1.1 IntroductiontoNonlinearOptics.............................................. 1
1.2 DescriptionsofNonlinearOpticalProcesses ................................. 4
1.2.1 Second-HarmonicGeneration............................................ 4
1.2.2 Sum-andDifference-FrequencyGeneration ............................ 6
1.2.3 Sum-FrequencyGeneration .............................................. 7
1.2.4 Difference-FrequencyGeneration........................................ 8
1.2.5 OpticalParametricOscillation ........................................... 9
1.2.6 Third-OrderNonlinearOpticalProcesses ............................... 10
1.2.7 Third-HarmonicGeneration.............................................. 10
1.2.8 Intensity-DependentRefractiveIndex ................................... 11
1.2.9 Third-OrderInteractions(GeneralCase) ................................ 11
1.2.10 ParametricversusNonparametricProcesses............................. 13
1.2.11 SaturableAbsorption ..................................................... 14
1.2.12 Two-PhotonAbsorption .................................................. 15
1.2.13 StimulatedRamanScattering............................................. 16
1.3 FormalDefinitionoftheNonlinearSusceptibility............................ 16
1.4 NonlinearSusceptibilityofaClassicalAnharmonicOscillator ............. 20
1.4.1 NoncentrosymmetricMedia.............................................. 21
1.4.2 Miller’sRule .............................................................. 26
1.4.3 CentrosymmetricMedia.................................................. 27
vii
Contents
1.5 PropertiesoftheNonlinearSusceptibility .................................... 32
1.5.1 RealityoftheFields....................................................... 33
1.5.2 IntrinsicPermutationSymmetry ......................................... 34
1.5.3 SymmetriesforLosslessMedia.......................................... 34
1.5.4 FieldEnergyDensityforaNonlinearMedium.......................... 35
1.5.5 Kleinman’sSymmetry.................................................... 37
1.5.6 ContractedNotation....................................................... 38
1.5.7 EffectiveValueofd (d ) ................................................ 40
eff
1.5.8 SpatialSymmetryoftheNonlinearMedium ............................ 41
1.5.9 Influence of Spatial Symmetry on the Linear Optical Properties of a
MaterialMedium.......................................................... 41
1.5.10 Influence of Inversion Symmetry on the Second-Order Nonlinear
Response .................................................................. 42
1.5.11 InfluenceofSpatialSymmetryontheSecond-OrderSusceptibility ... 44
(2)
1.5.12 NumberofIndependentElementsofχ (ω ,ω ,ω ).................. 45
ijk 3 2 1
1.5.13 DistinctionbetweenNoncentrosymmetricandCubicCrystalClasses. 45
1.5.14 DistinctionbetweenNoncentrosymmetricandPolarCrystalClasses.. 50
1.5.15 InfluenceofSpatialSymmetryontheThird-OrderNonlinearResponse 50
1.6 Time-DomainDescriptionofOpticalNonlinearities......................... 50
1.7 Kramers–KronigRelationsinLinearandNonlinearOptics ................. 56
1.7.1 Kramers–KronigRelationsinLinearOptics ............................ 56
1.7.2 Kramers–KronigRelationsinNonlinearOptics......................... 59
Problems ............................................................................... 61
References ............................................................................. 63
Chapter 2:Wave-Equation DescriptionofNonlinearOptical Interactions ......... 65
2.1 TheWaveEquationforNonlinearOpticalMedia............................ 65
2.2 TheCoupled-WaveEquationsforSum-FrequencyGeneration.............. 70
2.2.1 Phase-MatchingConsiderations.......................................... 72
2.3 PhaseMatching ................................................................ 74
2.4 Quasi-Phase-Matching(QPM) ................................................ 79
2.5 TheManley–RoweRelations.................................................. 83
2.6 Sum-FrequencyGeneration.................................................... 86
2.7 Second-HarmonicGeneration................................................. 91
2.7.1 ApplicationsofSecond-HarmonicGeneration.......................... 98
2.8 Difference-FrequencyGenerationandParametricAmplification ........... 100
2.9 OpticalParametricOscillators................................................. 102
2.9.1 InfluenceofCavityModeStructureonOPOTuning ................... 105
2.10 NonlinearOpticalInteractionswithFocusedGaussianBeams.............. 109
2.10.1 ParaxialWaveEquation................................................... 109
2.10.2 GaussianBeams........................................................... 110
viii
Contents
2.10.3 HarmonicGenerationUsingFocusedGaussianBeams................. 112
2.11 NonlinearOpticsatanInterface............................................... 116
2.12 AdvancedPhaseMatchingMethods .......................................... 121
Problems ............................................................................... 130
References ............................................................................. 134
Chapter 3:Quantum-Mechanical Theoryofthe NonlinearOptical Susceptibility .. 137
3.1 Introduction .................................................................... 137
3.2 SchrödingerEquationCalculationoftheNonlinearOpticalSusceptibility. 138
3.2.1 EnergyEigenstates........................................................ 139
3.2.2 PerturbationSolutiontoSchrödinger’sEquation........................ 140
3.2.3 LinearSusceptibility...................................................... 142
3.2.4 Second-OrderSusceptibility.............................................. 144
3.2.5 Third-OrderSusceptibility................................................ 146
3.2.6 Third-HarmonicGenerationinAlkaliMetalVapors.................... 148
3.3 DensityMatrixFormulationofQuantumMechanics ........................ 151
3.3.1 Example:Two-LevelAtom............................................... 158
3.4 PerturbationSolutionoftheDensityMatrixEquationofMotion ........... 159
3.5 DensityMatrixCalculationoftheLinearSusceptibility..................... 161
3.5.1 LinearResponseTheory.................................................. 164
3.6 DensityMatrixCalculationoftheSecond-OrderSusceptibility............. 169
3.6.1 χ(2) intheLimitofNonresonantExcitation............................. 178
3.7 DensityMatrixCalculationoftheThird-OrderSusceptibility............... 179
3.8 ElectromagneticallyInducedTransparency................................... 184
3.9 Local-FieldEffectsintheNonlinearOptics .................................. 192
3.9.1 Local-FieldEffectsinLinearOptics..................................... 192
3.9.2 Local-FieldEffectsinNonlinearOptics ................................. 194
Problems ............................................................................... 198
References ............................................................................. 201
Chapter 4:The Intensity-Dependent Refractive Index............................. 203
4.1 DescriptionsoftheIntensity-DependentRefractiveIndex................... 203
4.2 TensorNatureoftheThird-OrderSusceptibility ............................. 209
4.2.1 PropagationthroughIsotropicNonlinearMedia ........................ 213
4.3 NonresonantElectronicNonlinearities........................................ 217
4.3.1 Classical,AnharmonicOscillatorModelofElectronicNonlinearities. 218
4.3.2 Quantum-MechanicalModelofNonresonantElectronicNonlinearities 218
4.3.3 χ(3) intheLow-FrequencyLimit ........................................ 222
4.4 NonlinearitiesDuetoMolecularOrientation................................. 223
4.4.1 TensorPropertiesofχ(3) fortheMolecularOrientationEffect......... 229
ix
Contents
4.5 ThermalNonlinearOpticalEffects............................................ 231
4.5.1 ThermalNonlinearitieswithContinuous-WaveLaserBeams.......... 233
4.5.2 ThermalNonlinearitieswithPulsedLaserBeams....................... 234
4.6 SemiconductorNonlinearities................................................. 235
4.6.1 NonlinearitiesResultingfromBand-to-BandTransitions............... 235
4.6.2 NonlinearitiesInvolvingVirtualTransitions............................. 241
4.7 ConcludingRemarks........................................................... 243
Problems ............................................................................... 245
References ............................................................................. 247
Chapter 5:MolecularOriginofthe NonlinearOpticalResponse .................. 249
5.1 NonlinearSusceptibilitiesCalculatedUsingTime-IndependentPerturbation
Theory .......................................................................... 249
5.1.1 HydrogenAtom........................................................... 250
5.1.2 GeneralExpressionfortheNonlinearSusceptibilityintheQuasi-Static
Limit....................................................................... 251
5.2 SemiempiricalModelsoftheNonlinearOpticalSusceptibility ............. 255
ModelofBoling,Glass,andOwyoung............................................... 256
5.3 NonlinearOpticalPropertiesofConjugatedPolymers....................... 257
5.4 Bond-ChargeModelofNonlinearOpticalProperties........................ 259
5.5 NonlinearOpticsofChiralMedia............................................. 264
5.6 NonlinearOpticsofLiquidCrystals .......................................... 266
Problems ............................................................................... 269
References ............................................................................. 269
Chapter 6:NonlinearOpticsinthe Two-LevelApproximation..................... 273
6.1 Introduction .................................................................... 273
6.2 DensityMatrixEquationsofMotionforaTwo-LevelAtom ................ 274
6.2.1 ClosedTwo-LevelAtom.................................................. 276
6.2.2 OpenTwo-LevelAtom ................................................... 279
6.2.3 Two-LevelAtomwithaNon-RadiativelyCoupledThirdLevel........ 279
6.3 Steady-StateResponseofaTwo-LevelAtomtoaMonochromaticField... 280
6.4 OpticalBlochEquations....................................................... 288
6.4.1 HarmonicOscillatorFormoftheDensityMatrixEquations ........... 291
6.4.2 Adiabatic-FollowingLimit ............................................... 293
6.5 RabiOscillationsandDressedAtomicStates ................................ 295
6.5.1 RabiSolutionoftheSchrödingerEquation.............................. 296
6.5.2 SolutionforanAtomInitiallyintheGroundState...................... 298
6.5.3 DressedStates............................................................. 302
6.5.4 InclusionofRelaxationPhenomena ..................................... 305
x