Table Of ContentYASUO KOKUBUN
46489 cvr mech.indd 1 7/18/12 9:25 AM
Lightwave
Engineering
OPTICAL SCIENCE AND ENGINEERING
Founding Editor
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University ofR ochester
Rochester, New York
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Lightwave
Engineering
Yasuo Kokubun
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Contents
ListofFigures................................................................................................ix
ListofTables.................................................................................................xv
Preface.........................................................................................................xvii
AuthorBiography.......................................................................................xxi
Part I Introduction
Chapter1 FundamentalsofOpticalPropagation........................................3
1.1 ParametersandUnitsUsedtoDescribeLight..................3
1.2 OpticalCoherence............................................................7
1.3 FundamentalEquationsoftheElectromagnetic
FieldsandPlaneWaves..................................................11
1.3.1 ElectromagneticWaveEquations......................11
1.3.2 PlaneWavePropagationConstant.....................13
1.3.3 PropagationVelocityandPowerFlow
DensityofaPlaneWave....................................17
1.4 ReflectionandRefractionofPlaneWaves.....................20
1.4.1 RefractiveIndexandSnell’sLaw......................20
1.4.2 AmplitudeReflectanceandPower
Reflectivity.........................................................23
1.4.3 ReflectionfromaMetalSurface........................33
1.4.4 TotalInternalReflection.....................................35
1.5 PolarizationandBirefringence.......................................40
1.6 PropagationofaPlaneWaveinaMediumwithGain
andAbsorptionLoss.......................................................44
1.7 WaveFrontandLightRays............................................47
Chapter2 FundamentalsofOpticalWaveguides......................................51
2.1 Free-SpaceWavesandGuidedWaves............................51
2.2 GuidedModeandEigenvalueEquations.......................52
2.3 EigenmodeandDispersionCurves.................................55
2.4 ElectromagneticDistributionandEigenmode
Expansion.......................................................................59
v
vi Contents
2.5 FundamentalPropertiesofMultimodeWaveguides.......67
2.6 TransmissionBandofMultimodeWaveguide................69
2.6.1 PhaseVelocityandGroupVelocity....................70
2.6.2 PulsePropagationandFrequencyResponse
inMultimodeWaveguides.................................73
Chapter3 PropagationofLightBeamsinFreeSpace..............................79
3.1 RepresentationofSphericalWavesandthe
DiffractionPhenomenon.................................................79
3.2 FresnelDiffractionandFraunhoferDiffraction..............85
3.3 FraunhoferDiffractionofaGaussianBeam...................87
3.4 WaveFrontTransformationEffectoftheLens..............94
3.5 FourierTransformwithLenses.....................................100
Chapter4 InterferenceandResonators...................................................103
4.1 PrincipleofTwo-BeamInterference.............................103
4.2 Resonators.....................................................................106
4.3 VariousInterferometers................................................114
4.4 DiffractionbyGratings.................................................119
4.5 MultilayerThinFilmInterference................................122
Part II Description of Light Propagation
through Electromagnetism
Chapter5 GuidedWaveOptics...............................................................131
5.1 GeneralConceptoftheGuidedModes........................134
5.1.1 WaveEquationsandBoundaryConditions.....134
5.1.2 ClassificationofEigenmodesand
PropagationConstants.....................................137
5.1.3 ElectromagneticFieldDistribution,
Near-FieldPattern,andSpotSize....................143
5.1.4 ModeOrthogonalityandEigenmode
Expansion.........................................................145
5.1.5 Far-FieldPatternandNumericalAperture.......148
5.1.6 OpticalConfinementFactor.............................149
5.1.7 Single-ModeConditionandModeNumber....154
5.2 FundamentalStructureandModeoftheOptical
Waveguide....................................................................155
5.2.1 Two-DimensionalSlabWaveguide..................155
5.2.2 Three-DimensionalWaveguides......................171
Contents vii
Chapter6 OpticalFibers.........................................................................179
6.1 OpticalFiberModes.....................................................181
6.1.1 EigenvalueEquationsofOpticalFibers..........181
6.1.2 WeaklyGuidingApproximation......................185
6.1.3 ClassificationofModes....................................185
6.1.4 LPModeandDispersionCurves.....................187
6.1.5 FundamentalModeandSingle-ModeFibers...189
6.1.6 PolarizationPropertiesofSingle-ModeFibers
andPolarization-MaintainingFiber.................193
6.1.7 DistributedIndexSingle-ModeFibers.............196
6.1.8 DistributedIndexMultimodeFibers................197
6.2 SignalPropagationinOpticalFiber.............................203
6.2.1 GroupDelayandDispersion............................203
6.2.2 DispersioninSingle-ModeOpticalFibers......211
6.2.3 TransmissionBandwidthofSingle-Mode
Fibers................................................................218
6.2.4 Dispersion-ShiftedFiberandDispersion
Compensation..................................................222
6.3 Transmission Characteristics of Distributed Index
MultimodeFibers..........................................................223
6.3.1 GroupDelayofMultimodeOpticalFibers......224
6.3.2 TransmissionCapacityofα-PowerProfile
Fibers................................................................225
6.4 OpticalFiberCommunication......................................228
Chapter7 PropagationandFocusingoftheBeam..................................235
7.1 GaussianBeam.............................................................235
7.2 PropagationoftheGaussianBeam...............................237
7.3 WaveCoefficientandMatrixFormalism......................239
7.4 PropagationofNon-GaussianBeam............................242
7.5 CalculationFormulaforSpotSize...............................244
7.6 RepresentationbyDiffractionIntegral.........................249
Chapter8 BasicOpticalWaveguideCircuit...........................................251
8.1 CouplingbyCascadeConnectionofOptical
Waveguides...................................................................251
8.1.1 GeneralFormulaforCouplingEfficiency.......251
8.1.2 MisalignmentLossCharacteristic
byGaussianApproximation.............................254
8.1.3 ConditionsfortheLowLossConnectionof
OpticalWaveguides.........................................257
viii Contents
8.2 OpticalCouplingbetweenParallelWaveguides...........259
8.3 MergingandBranchingofOpticalWaveguides...........263
8.3.1 MergingandBranchingofMultimode
Waveguides......................................................263
8.3.2 MergingandBranchingofSingle-Mode
Waveguides......................................................267
8.4 ResonatorsandEffectiveIndex....................................271
8.5 WaveguideBends.........................................................273
8.6 PolarizationCharacteristics..........................................277
8.7 Description of the Optical Circuit by Scattering
MatrixandTransmissionMatrix..................................280
8.8 AnalysisofanOpticalWaveguide,IncludingStruc-
tureChangesinPropagationAxisDirection................288
AppendixA FourierTransformFormulas..............................................293
AppendixB CharacteristicsoftheDeltaFunction.................................297
AppendixC DerivationofGreen’sTheorem..........................................299
AppendixD VectorAnalysisFormula....................................................301
AppendixE InfiniteIntegralofGaussianFunction................................303
AppendixF CylindricalFunctions.........................................................305
AppendixG Hermite–GaussianFunctions.............................................307
AppendixH DerivationoftheOrthogonalityoftheEigenmode............309
AppendixI LorentzReciprocityTheorem............................................313
AppendixJ WKBMethod.....................................................................315
AppendixK DerivationofthePetermann’sFormulafortheOptical
FiberSpotSize...................................................................317
AppendixL DerivationoftheCouplingModeEquation.......................319
AppendixM GeneralSolutionoftheCoupledModeEquation..............327
AppendixN PerturbationTheory............................................................333
Bibliography................................................................................................337
Index............................................................................................................341
List of Figures
1.1 Inputandoutputpoweroftheopticalcircuit..........................................4
1.2 Lossspectrumofopticalfiber.................................................................6
1.3 Temporalcoherenceofspontaneousemission........................................8
1.4 Temporalcoherenceoflaserlight...........................................................9
1.5 Spatialcoherenceofspontaneousemission..........................................10
1.6 Spatialcoherenceoflaserlight.............................................................11
1.7 Electromagneticfielddistributionoftheplanewave...........................15
1.8 Phasechangeduetoplanewavepropagation.......................................17
1.9 Refractionofaplanewave...................................................................21
1.10 Boundaryconditionsattheboundaryoftwomediawithdifferent
dielectricconstants................................................................................23
1.11 Reflectionandrefractionofaplanewaveattheboundariesoftwo
mediawithdifferentrefractiveindices.................................................25
1.12 Twointrinsicpolarizationsinthereflectionandrefractionofplane
waves....................................................................................................26
1.13 Reflectionandrefractionofabackwardtravelingplanewave............30
1.14 Changeinthecross-sectionalareaoftheenergyflowduringrefrac-
tionandreflection.................................................................................31
1.15 Reflectionoftheplanewaveonametalsurface..................................33
1.16 Phasechangesduringthereflectionoftheplanewaveatthesurface
ofaperfectconductor...........................................................................34
1.17 Dependenceofpowerreflectivityontheangleofincidence...............36
1.18 Dependenceontheangleofincidenceofthephasechangeofthe
electricfieldreflectioncoefficientduringtotalreflection.....................38
1.19 Thestandingwaveformedbytheincidentwaveandthereflected
wavewhenthepropagationvectorisresolvedintothenormalcom-
ponentandthetangentialcomponentoftheboundarysurface............39
1.20 Propagation of a plane wave inclined from the main polarization
axisofabirefringentmaterial...............................................................42
1.21 Changesassociatedwithpolarizationstatepropagationinbirefrin-
gentmaterials. ......................................................................................43
1.22 Amplificationandattenuationofaplanewaveinamediumwitha
complexrefractiveindex......................................................................45
1.23 Thewavefrontandthedirectionoftheray..........................................49
2.1 Cross-sectionalstructureofopticalslabwaveguideandaguided
wave......................................................................................................52
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