ELECTROMAGNETIC RADIATION, SCATTERING, AND DIFFRACTION IEEEPress 445HoesLane Piscataway,NJ08854 IEEEPressEditorialBoard EkramHossain,EditorinChief JónAtliBenediktsson XiaoouLi JeffreyReed AnjanBose LianYong DiomidisSpinellis DavidAlanGrier AndreasMolisch SarahSpurgeon ElyaB.Joffe SaeidNahavandi AhmetMuratTekalp ELECTROMAGNETIC RADIATION, SCATTERING, AND DIFFRACTION Prabhakar H. Pathak and Robert J. Burkholder TheIEEEPressSeriesonElectromagneticWaveTheory Copyright © 2022 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. 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Identifiers: LCCN 2021030662 (print) | LCCN 2021030663 (ebook) | ISBN 9781119810513 (cloth) | ISBN 9781119810520 (adobe pdf) | ISBN 9781119810537 (epub) Subjects: LCSH: Electromagnetic waves. | Electromagnetic waves– Scattering. | Electromagnetic waves– Diffraction. Classification: LCC QC661 .P38 2022 (print) | LCC QC661 (ebook) | DDC 539.2– dc23 LC record available at https://lccn.loc.gov/2021030662 LC ebook record available at https://lccn.loc.gov/2021030663 Cover Design: Wiley Set in 10/12pt STIXGeneral by Straive, Chennai, India 10 9 8 7 6 5 4 3 2 1 To Lakshman Das (Babaji) Vina Malti and Gita and to the memory of Nilima and my parents — P. H. P. Veronica and Adele and to the memory of my parents — R. J. B. CONTENTS About the Authors xvii Preface xix Acknowledgments xxiii 1 Maxwell’sEquations,ConstitutiveRelations,WaveEquation,andPolarization 1 1.1 Introductory Comments 1 1.2 Maxwell’s Equations 5 1.3 Constitutive Relations 10 1.4 Frequency Domain Fields 15 1.5 Kramers-Kronig Relationship 19 1.6 Vector and Scalar Wave Equations 21 1.6.1 Vector Wave Equations for EM Fields 21 1.6.2 Scalar Wave Equations for EM Fields 22 1.7 Separable Solutions of the Source-Free Wave Equation in Rectangular Coordinates and for Isotropic Homogeneous Media. Plane Waves 23 1.8 Polarization of Plane Waves, Poincaré Sphere, and Stokes Parameters 29 1.8.1 Polarization States 29 1.8.2 General Elliptical Polarization 32 1.8.3 Decomposition of a Polarization State into Circularly Polarized Components 36 1.8.4 Poincaré Sphere for Describing Polarization States 37 1.9 Phase and Group Velocity 40 1.10 Separable Solutions of the Source-Free Wave Equation in Cylindrical and Spherical Coordinates and for Isotropic Homogeneous Media 44 1.10.1 Source-Free Cylindrical Wave Solutions 44 1.10.2 Source-Free Spherical Wave Solutions 48 References 51 2 EM Boundary and Radiation Conditions 52 2.1 EM Field Behavior Across a Boundary Surface 52 2.2 Radiation Boundary Condition 60 2.3 Boundary Conditions at a Moving Interface 63 2.3.1 Nonrelativistic Moving Boundary Conditions 63 2.3.2 Derivation of the Nonrelativistic Field Transformations 66 2.3.3 EM Field Transformations Based on the Special Theory of Relativity 69 2.4 Constitutive Relations for a Moving Medium 84 References 85 3 Plane Wave Propagation in Planar Layered Media 87 3.1 Introduction 87 vii viii CONTENTS 3.2 Plane Wave Reflection from a Planar Boundary Between Two Different Media 87 3.2.1 Perpendicular Polarization Case 88 3.2.2 Parallel Polarization Case 93 3.2.3 Brewster Angle 𝜃 97 𝑏 3.2.4 Critical Angle 𝜃 100 𝑐 3.2.5 Plane Wave Incident on a Lossy Half Space 104 3.2.6 Doppler Shift for Wave Reflection from a Moving Mirror 110 3.3 Reflection and Transmission of a Plane Wave Incident on a Planar Stratified Isotropic Medium Using a Transmission Matrix Approach 112 3.4 Plane Waves in Anisotropic Homogeneous Media 119 3.5 State Space Formulation for Waves in Planar Anisotropic Layered Media 135 3.5.1 Development of State Space Based Field Equations 135 3.5.2 Reflection and Transmission of Plane Waves at the Interface Between Two Anisotropic Half Spaces 139 3.5.3 Transmission Type Matrix Analysis of Plane Waves in Multilayered Anisotropic Media 142 References 143 4 Plane Wave Spectral Representation for EM Fields 144 4.1 Introduction 144 4.2 PWS Development 144 References 155 5 Electromagnetic Potentials and Fields of Sources in Unbounded Regions 156 5.1 Introduction to Vector and Scalar Potentials 156 5.2 Construction of the Solution for 𝐴 160 5.3 Calculation of Fields from Potentials 165 5.4 Time Dependent Potentials for Sources and Fields in Unbounded Regions 176 5.5 Potentials and Fields of a Moving Point Charge 185 5.6 Cerenkov Radiation 192 5.7 Direct Calculation of Fields of Sources in Unbounded Regions Using a Dyadic Green’s Function 195 5.7.1 Fields of Sources in Unbounded, Isotropic, Homogeneous Media in Terms of a Closed Form Representation of Green’s Dyadic, 𝐺 195 0 5.7.2 On the Singular Nature of 𝐺0(𝑟|𝑟′) for Observation Points Within the Source Region 197 5.7.3 Representation of the Green’s Dyadic 𝐺 in Terms of an Integral in 0 the Wavenumber (𝑘) Space 201 5.7.4 Electromagnetic Radiation by a Source in a General Bianisotropic Medium Using a Green’s Dyadic 𝐺 in 𝑘-Space 208 𝑎 References 209 6 Electromagnetic Field Theorems and Related Topics 211 6.1 Conservation of Charge 211 6.2 Conservation of Power 212 6.3 Conservation of Momentum 218 6.4 Radiation Pressure 225