Photonic Crystals: Molding the Flow of Light - Ab-Initio Research

305 Pages·2008·20.78 MB·English

November13,2007 Time: 06:25pm prelims.tex
Photonic Crystals
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Photonic Crystals
Molding the Flow of Light
Second Edition
John D. Joannopoulos
Steven G. Johnson
Joshua N. Winn
Robert D. Meade
PRINCETON UNIVERSITY PRESS • PRINCETON AND OXFORD
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Copyright(cid:1)c 2008byPrincetonUniversityPress
PublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,
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IntheUnitedKingdom:PrincetonUniversityPress,3MarketPlace,
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AllRightsReserved
LibraryofCongressCataloging-in-PublicationData
Joannopoulos,J.D.(JohnD.),1947-
Photoniccrystals:moldingtheflowoflight/JohnD.Joannopoulos...[etal.].
p.cm.
Includesbibliographicalreferencesandindex.
ISBN:978-0-691-12456-8(acid-freepaper)
1.Photons.2.Crystaloptics.I.Joannopoulos,J.D.(JohnD.),1947-II.Title.
QC793.5.P427J632008
(cid:1)
548.9–dc22 2007061025
BritishLibraryCataloging-in-PublicationDataisavailable
ThisbookhasbeencomposedinPalatino
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To Kyriaki and G. G. G.
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ToseeaWorldinaGrainofSand,
AndaHeaveninaWildFlower,
HoldInfinityinthepalmofyourhand
AndEternityinanhour.
—WilliamBlake,AuguriesofInnocence(1803)
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CONTENTS
PrefacetotheSecondEdition xiii
PrefacetotheFirstEdition xv
1 Introduction 1
ControllingthePropertiesofMaterials 1
PhotonicCrystals 2
AnOverviewoftheText 3
2 Electromagnetism in Mixed Dielectric Media 6
TheMacroscopicMaxwellEquations 6
ElectromagnetismasanEigenvalueProblem 10
GeneralPropertiesoftheHarmonicModes 12
ElectromagneticEnergyandtheVariationalPrinciple 14
Magneticvs.ElectricFields 16
TheEffectofSmallPerturbations 17
ScalingPropertiesoftheMaxwellEquations 20
Discretevs.ContinuousFrequencyRanges 21
ElectrodynamicsandQuantumMechanicsCompared 22
FurtherReading 24
3 Symmetries and Solid-State Electromagnetism 25
UsingSymmetriestoClassifyElectromagneticModes 25
ContinuousTranslationalSymmetry 27
Indexguiding 30
DiscreteTranslationalSymmetry 32
PhotonicBandStructures 35
RotationalSymmetryandtheIrreducibleBrillouinZone 36
MirrorSymmetryandtheSeparationofModes 37
Time-ReversalInvariance 39
Bloch-WavePropagationVelocity 40
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viii CONTENTS
Electrodynamicsvs.QuantumMechanicsAgain 42
FurtherReading 43
4 The Multilayer Film: A One-Dimensional Photonic
Crystal 44
TheMultilayerFilm 44
ThePhysicalOriginofPhotonicBandGaps 46
TheSizeoftheBandGap 49
EvanescentModesinPhotonicBandGaps 52
Off-AxisPropagation 54
LocalizedModesatDefects 58
SurfaceStates 60
OmnidirectionalMultilayerMirrrors 61
FurtherReading 65
5 Two-Dimensional Photonic Crystals 66
Two-DimensionalBlochStates 66
ASquareLatticeofDielectricColumns 68
ASquareLatticeofDielectricVeins 72
ACompleteBandGapforAllPolarizations 74
Out-of-PlanePropagation 75
LocalizationofLightbyPointDefects 78
Pointdefectsinalargergap 83
LinearDefectsandWaveguides 86
SurfaceStates 89
FurtherReading 92
6 Three-Dimensional Photonic Crystals 94
Three-DimensionalLattices 94
CrystalswithCompleteBandGaps 96
Spheresinadiamondlattice 97
Yablonovite 99
Thewoodpilecrystal 100
Inverseopals 103
Astackoftwo-dimensionalcrystals 105
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CONTENTS ix
LocalizationataPointDefect 109
ExperimentaldefectmodesinYablonovite 113
LocalizationataLinearDefect 114
LocalizationattheSurface 116
FurtherReading 121
7 Periodic Dielectric Waveguides 122
Overview 122
ATwo-DimensionalModel 123
PeriodicDielectricWaveguidesinThreeDimensions 127
SymmetryandPolarization 127
PointDefectsinPeriodicDielectricWaveguides 130
QualityFactorsofLossyCavities 131
FurtherReading 134
8 Photonic-Crystal Slabs 135
RodandHoleSlabs 135
PolarizationandSlabThickness 137
LinearDefectsinSlabs 139
Reduced-radiusrods 139
Removedholes 142
Substrates,dispersion,andloss 144
PointDefectsinSlabs 147
MechanismsforHighQwithIncompleteGaps 149
Delocalization 149
Cancellation 151
FurtherReading 155
9 Photonic-Crystal Fibers 156
MechanismsofConfinement 156
Index-GuidingPhotonic-CrystalFibers 158
Endlesslysingle-modefibers 161
ThescalarlimitandLPmodes 163
Enhancementofnonlineareffects 166
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