ELECTROMAGNETIC WAVE PROPAGATION, RADIATION, AND SCATTERING IEEEPress 445HoesLane Piscataway,NJ08854 IEEEPressEditorialBoard TariqSamad,EditorinChief GiancarloFortino XiaoouLi RayPerez DmitryGoldgof AndreasMolisch LindaShafer DonHeirman SaeidNahavandi MohammadShahidehpour EkramHossain JeffreyNanzer ZidongWang KennethMoore,DirectorofIEEEBookandInformationServices(BIS) ELECTROMAGNETIC WAVE PROPAGATION, RADIATION, AND SCATTERING From Fundamentals to Applications Second Edition AKIRA ISHIMARU UniversityofWashington,Seattle,WA,USA IEEE Antennas and Propagation Society, Sponsor TheIEEEPressSeriesonElectromagneticWaveTheory AndreasC.Cangellaris,SeriesEditor Copyright©2017byTheInstituteofElectricalandElectronicsEngineers,Inc.Allrightsreserved. PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey. PublishedsimultaneouslyinCanada. 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ISBN:978-1-118-09881-3 PrintedintheUnitedStatesofAmerica. 10 9 8 7 6 5 4 3 2 1 To YUKO and Emily,Ben,Joyce,Gene,Aaron,Eric,Andrew,Karen,Jim, Grace,Patty,Chad,Katie,Will,Jane,Chuck,John CONTENTS ABOUT THE AUTHOR xix PREFACE xxi PREFACE TO THE FIRST EDITION xxv ACKNOWLEDGMENTS xxvii PARTI FUNDAMENTALS 1 1 INTRODUCTION 3 2 FUNDAMENTALFIELDEQUATIONS 7 2.1 Maxwell’sEquations / 7 2.2 Time-HarmonicCase / 10 2.3 ConstitutiveRelations / 11 2.4 BoundaryConditions / 15 2.5 EnergyRelationsandPoynting’sTheorem / 18 2.6 VectorandScalarPotentials / 22 2.7 ElectricHertzVector / 24 2.8 DualityPrincipleandSymmetryofMaxwell’sEquations / 25 2.9 MagneticHertzVector / 26 2.10 UniquenessTheorem / 27 vii viii CONTENTS 2.11 ReciprocityTheorem / 28 2.12 AcousticWaves / 30 Problems / 33 3 WAVESININHOMOGENEOUSANDLAYEREDMEDIA 35 3.1 WaveEquationforaTime-HarmonicCase / 35 3.2 Time-HarmonicPlane-WavePropagationinHomogeneous Media / 36 3.3 Polarization / 37 3.4 Plane-WaveIncidenceonaPlaneBoundary:Perpendicular Polarization(sPolarization) / 39 3.5 ElectricFieldParalleltoaPlaneofIncidence:Parallel Polarization(pPolarization) / 43 3.6 FresnelFormula,Brewster’sAngle,andTotalReflection / 44 3.7 WavesinLayeredMedia / 47 3.8 AcousticReflectionandTransmissionfromaBoundary / 50 3.9 ComplexWaves / 51 3.10 TrappedSurfaceWave(SlowWave)andLeakyWave / 54 3.11 SurfaceWavesAlongaDielectricSlab / 57 3.12 ZenneckWavesandPlasmons / 63 3.13 WavesinInhomogeneousMedia / 66 3.14 WKBMethod / 68 3.15 BremmerSeries / 72 3.16 WKBSolutionfortheTurningPoint / 76 3.17 TrappedSurface-WaveModesinanInhomogeneousSlab / 77 3.18 MediumWithPrescribedProfile / 80 Problems / 81 4 WAVEGUIDESANDCAVITIES 85 4.1 UniformElectromagneticWaveguides / 85 4.2 TMModesorEModes / 86 4.3 TEModesorHModes / 87 4.4 EigenfunctionsandEigenvalues / 89 4.5 GeneralPropertiesofEigenfunctionsforClosedRegions / 91 4.6 k–βDiagramandPhaseandGroupVelocities / 95 4.7 RectangularWaveguides / 98 4.8 CylindricalWaveguides / 100 4.9 TEMModes / 104 CONTENTS ix 4.10 DispersionofaPulseinaWaveguide / 106 4.11 Step-IndexOpticalFibers / 109 4.12 DispersionofGraded-IndexFibers / 116 4.13 RadialandAzimuthalWaveguides / 117 4.14 CavityResonators / 120 4.15 WavesinSphericalStructures / 123 4.16 SphericalWaveguidesandCavities / 128 Problems / 133 5 GREEN’SFUNCTIONS 137 5.1 ElectricandMagneticDipolesinHomogeneousMedia / 137 5.2 ElectromagneticFieldsExcitedbyanElectricDipoleina HomogeneousMedium / 139 5.3 ElectromagneticFieldsExcitedbyaMagneticDipoleina HomogeneousMedium / 144 5.4 ScalarGreen’sFunctionforClosedRegionsandExpansionof Green’sFunctioninaSeriesofEigenfunctions / 145 5.5 Green’sFunctioninTermsofSolutionsoftheHomogeneous Equation / 150 5.6 FourierTransformMethod / 155 5.7 ExcitationofaRectangularWaveguide / 157 5.8 ExcitationofaConductingCylinder / 159 5.9 ExcitationofaConductingSphere / 163 Problems / 166 6 RADIATIONFROMAPERTURESANDBEAMWAVES 169 6.1 Huygens’PrincipleandExtinctionTheorem / 169 6.2 FieldsDuetotheSurfaceFieldDistribution / 173 6.3 KirchhoffApproximation / 176 6.4 FresnelandFraunhoferDiffraction / 178 6.5 FourierTransform(Spectral)Representation / 182 6.6 BeamWaves / 183 6.7 Goos–HanchenEffect / 187 6.8 Higher-OrderBeam-WaveModes / 191 6.9 VectorGreen’sTheorem,Stratton–ChuFormula,andFranz Formula / 194 6.10 EquivalenceTheorem / 197 6.11 KirchhoffApproximationforElectromagneticWaves / 198 Problems / 199 x CONTENTS 7 PERIODICSTRUCTURESANDCOUPLED-MODETHEORY 201 7.1 Floquet’sTheorem / 202 7.2 GuidedWavesAlongPeriodicStructures / 203 7.3 PeriodicLayers / 209 7.4 PlaneWaveIncidenceonaPeriodicStructure / 213 7.5 ScatteringfromPeriodicSurfacesBasedontheRayleigh Hypothesis / 219 7.6 Coupled-ModeTheory / 224 Problems / 229 8 DISPERSIONANDANISOTROPICMEDIA 233 8.1 DielectricMaterialandPolarizability / 233 8.2 DispersionofDielectricMaterial / 235 8.3 DispersionofConductorandIsotropicPlasma / 237 8.4 DebyeRelaxationEquationandDielectricConstant ofWater / 240 8.5 InterfacialPolarization / 240 8.6 MixingFormula / 241 8.7 DielectricConstantandPermeabilityforAnisotropic Media / 244 8.8 MagnetoionicTheoryforAnisotropicPlasma / 244 8.9 Plane-WavePropagationinAnisotropicMedia / 247 8.10 Plane-WavePropagationinMagnetoplasma / 248 8.11 PropagationAlongtheDCMagneticField / 249 8.12 FaradayRotation / 253 8.13 PropagationPerpendiculartotheDCMagneticField / 255 8.14 TheHeightoftheIonosphere / 256 8.15 GroupVelocityinAnisotropicMedium / 257 8.16 WarmPlasma / 259 8.17 WaveEquationsforWarmPlasma / 261 8.18 FerriteandtheDerivationofItsPermeabilityTensor / 263 8.19 Plane-WavePropagationinFerrite / 266 8.20 MicrowaveDevicesUsingFerrites / 267 8.21 LorentzReciprocityTheoremforAnisotropicMedia / 270 8.22 Bi-AnisotropicMediaandChiralMedia / 272 8.23 Superconductors,LondonEquation,andtheMeissner Effects / 276 8.24 Two-FluidModelofSuperconductorsatHighFrequencies / 278 Problems / 280