Table Of ContentTransformation Wave Physics
Transformation Wave Physics
Electromagnetics, Elastodynamics,
and Thermodynamics
edited by
Mohamed Farhat
Pai-Yen Chen
Sebastien Guenneau
Stefan Enoch
PAN STANFORD PUBLISHING
July27,2016 13:35 PSPBook-9inx6in 00-Mohamed-Farhat-Prelims
Publishedby
PanStanfordPublishingPte.Ltd.
PenthouseLevel,SuntecTower3
8TemasekBoulevard
Singapore038988
Email:[email protected]
Web:www.panstanford.com
BritishLibraryCataloguing-in-PublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
Transformation Wave Physics: Electromagnetics, Elastodynamics,
andThermodynamics
Copyright(cid:2)c 2016PanStanfordPublishingPte.Ltd.
Allrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinany
form or by any means, electronic or mechanical, including photocopying,
recordingoranyinformationstorageandretrievalsystemnowknownorto
beinvented,withoutwrittenpermissionfromthepublisher.
For photocopying of material in this volume, please pay a copying
fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive,
Danvers, MA 01923, USA. In this case permission to photocopy is not
requiredfromthepublisher.
ISBN978-981-4669-95-5(Hardcover)
ISBN978-981-4669-96-2(eBook)
PrintedintheUSA
July27,2016 13:35 PSPBook-9inx6in 00-Mohamed-Farhat-Prelims
Contents
Preface xiii
1 TransformationOptics 1
UlfLeonhardt
1.1 Introduction 1
1.2 Maxwell’sElectromagnetism 3
1.2.1 Maxwell’sEquations 3
1.2.2 TheMediumofaGeometry 5
1.2.3 TheGeometryofaMedium 7
1.3 SpatialTransformations 8
1.3.1 InvisibilityCloaking 8
1.3.2 TransformationMedia 11
1.3.3 PerfectImagingwithNegativeRefraction 12
1.4 CurvedSpace 14
1.4.1 Einstein’sUniverseandMaxwell’sFishEye 14
1.4.2 PerfectImagingwithPositiveRefraction 17
1.5 Space–TimeMedia 20
1.5.1 Space–TimeGeometries 20
1.5.2 MagnetoelectricMedia 20
1.5.3 MovingMedia 22
1.5.4 Space–TimeTransformations 23
2 ConformalMappinginTransformationOptics 29
KanYaoandYongminLiu
2.1 Introduction 29
2.2 TheBasicsofOpticalConformalMapping 32
2.3 TransformationOpticalDesignwithanAnalogy
Strategy 39
2.3.1 AnalogieswithFluidMechanics 40
July27,2016 13:35 PSPBook-9inx6in 00-Mohamed-Farhat-Prelims
vi Contents
2.3.1.1 Opticalsinks 41
2.3.1.2 Airfoilcarpetcloak 42
2.3.1.3 Magnuscarpetcloak 46
2.3.2 AnalogieswithElectrostatics 47
2.3.2.1 Chargelenses 48
2.3.2.2 Capacitorwaveguidebend 51
2.4 TransformationPlasmonics 52
2.4.1 TransformationOpticsforSPPs 52
2.4.1.1 CarpetcloakforSPPs 53
2.4.1.2 Plasmonicwaveguidingdevices 57
2.4.2 GRINPlasmonicLenses 59
2.4.3 TransformationOpticsforLSPs 62
2.5 ConformalMappinginAnisotropicDevices 66
2.5.1 DevicesfromStacked2DProfiles 66
2.5.1.1 Stereographicprojection 67
2.5.1.2 Collimatinglensesandsuperantennas 69
2.5.1.3 Geodesicwaveguidesfor
subwavelengthimaging 73
2.5.2 DevicesofAzimuthalInvariance 74
2.6 Outlook 77
3 QuasiconformalTransformationMediaandTheir
ElectrostaticAnalogy 89
JensenLi,FuLiu,ZhengChang,andGengkaiHu
3.1 Introduction 90
3.2 TransformationOpticswithAnisotropy
Minimization 91
3.2.1 MinimizingAnisotropy 91
3.2.2 ElectrostaticAnalogy 94
3.3 ExamplesofQuasiconformalTransformationMedia 98
3.3.1 AnAnalyticExample 98
3.3.2 QuasiconformalMapwithArbitraryShapeof
DeviceBoundaries 100
3.3.3 FromSlippingBoundarytoFixedBoundary 103
3.4 ExtensiontoAcousticandElasticWaves 104
3.4.1 AcousticCase 105
3.4.2 ElastodynamicCase 107
3.5 Conclusion 111
July27,2016 13:35 PSPBook-9inx6in 00-Mohamed-Farhat-Prelims
Contents vii
4 ControlofElectromagneticFluxinInhomogeneous
AnisotropicMedia 117
JieLuo,YunLai,andC.T.Chan
4.1 Introduction 118
4.2 InhomogeneousAnisotropicZero-IndexMedia 119
4.2.1 ScatteringsinHighlyAnisotropicMediaand
EMFluxRedistribution 121
4.2.2 RobustHighTransmission 126
4.2.3 ExamplesofEMFluxControl 128
4.2.4 EffectofAnisotropy 131
4.2.5 EffectofLossandFailureofEffectiveMedium
Theory 132
4.3 ApplicationsinWaveguides 135
4.3.1 WaveguideswithIrregularBoundaries 135
4.3.2 BendingWaveguides 140
4.3.3 BendingWaveguideswithIrregular
Boundaries 142
4.4 InhomogeneousAnisotropicHigh-IndexMedia 146
4.5 Summary 147
5 Transmission-LineMetamaterialsforSurface-to-Leaky-Wave
Transformation 157
Chung-TseMichaelWu,Pai-YenChen,andTatsuoItoh
5.1 Introduction 158
5.2 PrincipleofTransmission-LineMetamaterials 160
5.3 GuidedandRadiatedModesofCRLH-TLS 164
5.4 Free-SpaceScanningandAdaptiveCRLH-LWAS 167
5.4.1 1Dand2DBeamScanning 167
5.4.2 TunableLWA 169
5.4.3 ActiveCRLH-LWA 171
5.4.3.1 Cascadedamplifiers 171
5.4.3.2 Distributedamplifier-basedLWAs 171
5.4.3.3 Power-recyclingschemesfor
DA-basedCRLH-LWAs 173
5.5 HolographicAntennasBasedonMetasurfaces 180
5.5.1 IntroductiontoMetasurfaceTechnology 181
5.5.2 PrincipleandPracticeofHolographicAntennas 182
5.6 Conclusions 185
July27,2016 13:35 PSPBook-9inx6in 00-Mohamed-Farhat-Prelims
viii Contents
6 MetasurfacesforExtremeLightManipulationandWave
Control 191
NasimMohammadiEstakhriandAndreaAlu`
6.1 Introduction 191
6.2 MetasurfaceDesignandSynthesis 198
6.2.1 NanoresonatorsasOpticalPhaseElements 208
6.2.2 Tunability,FrequencyDispersion,andEffectof
Loss 213
6.2.3 PolarizationControlinOpticalLumped
Resonators 217
6.3 BeamFormingwithGradedMetasurfaces 219
6.3.1 OpticalReflectarraysandTransmitarrays 220
6.3.2 FlatLens 224
6.3.3 PolarizationBeamSplitter 226
6.4 OtherPotentialApplications 228
6.4.1 ConformalCloaking 229
6.4.2 BroadbandEnergyHarvesting 233
6.4.3 NanoscaleSignalProcessing 235
6.5 ConclusionsandOutlook 235
7 RF/OpticalScatteringManipulationUsingMetasurface
CoatingsandPlasmonicLoadings 243
ZhiHaoJiang,AnastasiosH.Panaretos,and
DouglasH.Werner
7.1 Introduction 244
7.2 MetasurfaceCoatingsforCloakingandIllusion 245
7.2.1 ScatteringfromanAnisotropic
Metasurface-CoatedCylinder 246
7.2.2 MetasurfaceCloakingbeyondtheQuasi-Static
Limit 250
7.2.2.1 Metasurfacecloakingfordielectric
cylinders 250
7.2.2.2 Metasurfacecloakingforconducting
cylinders 252
7.2.3 Angle-TolerantMetasurfaceIllusion 257
7.3 OpticalPlasmonicCore-ShellParticlesExhibiting
Zero-ImpedanceandZero-AdmittanceProperties 263
July27,2016 13:35 PSPBook-9inx6in 00-Mohamed-Farhat-Prelims
Contents ix
7.3.1 ElementsofRadiallyInhomogeneousSpherical
TransmissionLineTheory,andImpedance
CharacterizationofaCore-ShellParticle 265
7.3.2 Zero-ImpedanceandZero-Admittance
ConditionsontheSurfaceofaCore-Shell
Particle 267
7.3.3 MaterialInterpretationoftheCore-Shell’s
Response 269
7.4 TunableOpticalNanoantennaLoadedbyPlasmonic
Core-ShellParticles 271
7.4.1 NanodipoleGeometryandResponse 272
7.4.2 LoadingtheGapVolumewithaHomogeneous
DielectricSphere 276
7.4.3 LoadingtheGapVolumewithaPlasmonic
Core-ShellParticle 277
7.5 Conclusion 280
8 ExperimentsonCloakingforSurfaceWaterWaves 287
SebastienGuenneau,GuillaumeDupont,StefanEnoch,
andMohamedFarhat
8.1 Introduction 287
8.2 AcousticCloakingforLiquidSurfaceWaves 289
8.2.1 FromNavier–StokestoHelmholtz 289
8.2.2 TransformedHelmholtz’sEquationontheFree
Surface 292
8.2.2.1 Coordinatechangeforawaterwave
cloak 294
8.2.3 EffectiveAnisotropicShearViscositythrough
Homogenization 295
8.3 HomogenizationofHelmholtz’sEquation 297
8.3.1 NumericalAnalysisofLSWCloaking 302
8.3.2 ExperimentalMeasurementsofLSW
Cloaking 306
8.4 WaterWaveCloaksandInvisibilityCarpetsofan
ArbitraryShape 306
8.5 Conclusion 311
July27,2016 13:35 PSPBook-9inx6in 00-Mohamed-Farhat-Prelims
x Contents
9 CloakingforHeatandMassDiffusion 313
SebastienGuenneau,DavidPetiteau,MyriamZerrad,
ClaudeAmra,andTaniaM.Puvirajesinghe
9.1 Introduction 313
9.2 CoordinatesChangesasaMagicPotiontoControl
Convection-DiffusionPhenomena 316
9.3 InvisibilityCloak,Concentrator,andRotatorofan
ArbitraryShapeforDiffusionProcesses 319
9.3.1 DiffusionCloaks 319
9.3.2 DiffusionConcentratorsandRotators 322
9.3.3 Three-DimensionalCloakofaComplexShape
forDiffusionProcesses 325
9.4 MultilayeredCloakwithSimplifiedIsotropic
Parameters 326
9.4.1 Two-DimensionalMultilayeredThermalCloaks 327
9.4.2 Three-DimensionalMultilayeredThermal
Cloaks 327
9.5 InvisibilityCarpetforDiffusionProcesses:Mappinga
CurvedSurfaceonaFlatSurface 328
9.5.1 Two-DimensionalCarpets 330
9.5.2 Three-DimensionalCarpets 330
9.6 ConcludingRemarks 332
10 ExperimentsonCloakinginElectromagnetism,Mechanics,
andThermodynamics 335
MuamerKadic,RobertSchittny,TiemoBu¨ckmann,
andMartinWegener,
10.1 Introduction 335
10.1.1 TrueCloaks 336
10.1.2 RoleoftheEnvironment 337
10.1.3 DesignApproaches 338
10.2 FromTransformationstoMaterials 338
10.2.1 LaminateMetamaterials 341
10.3 Electromagnetism 344
10.3.1 OpticalCarpetCloaks 345
10.4 Mechanics 347
10.4.1 Flexural-WaveCloaks 349
10.4.2 Three-DimensionalElastostaticCloaks 352
