Principles of Electromagnetic Waves and Materials Second Edition Principles of Electromagnetic Waves and Materials Second Edition Dikshitulu K. Kalluri CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2018 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper International Standard Book Number-13: 978-1-4987-3329-8 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. 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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Names: Kalluri, Dikshitulu K., author. Title: Principles of electromagnetic waves and materials / Dikshitulu K. Kalluri. Description: Second edition. | Boca Raton : Taylor & Francis, CRC Press, 2018. | Includes bibliographical references and index. Identifiers: LCCN 2017015930| ISBN 9781498733298 (hardback) | ISBN 9781315272351 (ebook) Subjects: LCSH: Electromagnetism--Mathematical models. | Electromagnetic waves--Computer simulation. Classification: LCC QC760 .K363 2018 | DDC 537--dc23 LC record available at https://lccn.loc.gov/2017015930 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface ...........................................................................................................................................xiii Acknowledgments ........................................................................................................................xv Author ..........................................................................................................................................xvii Selected List of Symbols ..............................................................................................................xix List of Book Sources .....................................................................................................................xxi Part I Electromagnetics of Bounded Simple Media 1. Electromagnetics of Simple Media ......................................................................................3 1.1 Introduction ...................................................................................................................3 1.2 Simple Medium .............................................................................................................4 1.3 Time-Domain Electromagnetics ..................................................................................5 1.3.1 Radiation by an Impulse Current Source .....................................................7 1.4 Time-Harmonic Fields ..................................................................................................9 1.5 Quasistatic and Static Approximations ....................................................................11 1.6 Maxwell’s Equations in Integral Form and Circuit Parameters ...........................12 References ...............................................................................................................................16 2. Electromagnetics of Simple Media: One-Dimensional Solution ................................17 2.1 Uniform Plane Waves in Sourceless Medium (ρ = 0, J = 0) ..........................17 V source 2.2 Good Conductor Approximation .............................................................................18 2.3 Uniform Plane Wave in a Good Conductor: Skin Effect .......................................18 2.4 Boundary Conditions at the Interface of a Perfect Electric Conductor with a Dielectric ...........................................................................................................19 2.5 AC Resistance ..............................................................................................................20 2.6 AC Resistance of Round Wires..................................................................................22 2.7 Voltage and Current Harmonic Waves: Transmission Lines ................................23 2.8 Bounded Transmission Line ......................................................................................26 2.9 Electromagnetic Wave Polarization ..........................................................................28 2.10 Arbitrary Direction of Propagation ..........................................................................29 2.11 Wave Reflection ...........................................................................................................30 2.12 Incidence of p Wave: Parallel-Polarized ...................................................................31 2.13 Incidence of s Wave: Perpendicular-Polarized .......................................................33 2.14 Critical Angle and Surface Wave ..............................................................................33 2.15 One-Dimensional Cylindrical Wave and Bessel Functions ...................................36 References ...............................................................................................................................41 3. Two-Dimensional Problems and Waveguides ................................................................43 3.1 Two-Dimensional Solutions in Cartesian Coordinates ..........................................43 3.2 TM Modes in a Rectangular Waveguide ..............................................................45 mn 3.3 TE Modes in a Rectangular Waveguide ...............................................................48 mn 3.4 Dominant Mode in a Rectangular Waveguide: TE Mode ...................................49 10 3.5 Power Flow in a Waveguide: TE Mode .................................................................51 10 v vi Contents 3.6 Attenuation of TE Mode due to Imperfect Conductors 10 and Dielectric Medium ............................................................................................51 3.7 Cylindrical Waveguide: TM Modes .........................................................................52 3.8 Cylindrical Waveguide: TE Modes ...........................................................................53 3.9 Sector Waveguide ........................................................................................................54 3.10 Dielectric Cylindrical Waveguide: Optical Fiber ....................................................55 References ...............................................................................................................................58 4. Three-Dimensional Solutions ............................................................................................59 4.1 Rectangular Cavity with PEC Boundaries: TM Modes .........................................59 4.2 Rectangular Cavity with PEC Boundaries: TE Modes ..........................................60 4.3 Q of a Cavity ................................................................................................................61 Reference .................................................................................................................................62 5. Spherical Waves and Applications ....................................................................................63 5.1 Half-Integral Bessel Functions ..................................................................................63 5.2 Solutions of Scalar Helmholtz Equation ..................................................................64 5.3 Vector Helmholtz Equation .......................................................................................67 5.4 TMr Modes ...................................................................................................................68 5.5 TEr Modes .....................................................................................................................68 5.6 Spherical Cavity ..........................................................................................................69 6. Laplace Equation: Static and Low-Frequency Approximations ..................................73 6.1 One-Dimensional Solutions .......................................................................................74 6.2 Two-Dimensional Solutions ......................................................................................74 6.2.1 Cartesian Coordinates ...................................................................................74 6.2.2 Circular Cylindrical Coordinates ................................................................79 6.3 Three-Dimensional Solution ......................................................................................85 6.3.1 Cartesian Coordinates ...................................................................................85 6.3.2 Cylindrical Coordinates ................................................................................85 6.3.3 Spherical Coordinates ...................................................................................85 References ...............................................................................................................................89 7. Miscellaneous Topics on Waves .........................................................................................91 7.1 Group Velocity v ........................................................................................................91 g 7.2 Green’s Function .........................................................................................................92 7.3 Network Formulation .................................................................................................95 7.3.1 ABCD Parameters ..........................................................................................96 7.3.2 S Parameters ...................................................................................................99 7.4 Stop Bands of a Periodic Media ..............................................................................101 7.5 Radiation ....................................................................................................................104 7.5.1 Hertzian Dipole ............................................................................................106 7.5.2 Half-Wave Dipole ........................................................................................107 7.5.3 Dipoles of Arbitrary Length .......................................................................110 7.5.4 Shaping the Radiation Pattern ...................................................................110 7.5.5 Antenna Problem as a Boundary Value Problem ....................................110 7.5.6 Traveling Wave Antenna and Cerenkov Radiation ................................110 7.5.7 Small Circular Loop Antenna .....................................................................111 7.5.8 Other Practical Radiating Systems ............................................................113 Contents vii 7.6 Scattering ....................................................................................................................113 7.6.1 Cylindrical Wave Transformations ............................................................113 7.6.2 Calculation of Current Induced on the Cylinder ....................................114 7.6.3 Scattering Width ...........................................................................................115 7.7 Diffraction ..................................................................................................................117 7.7.1 Magnetic Current and Electric Vector Potential ......................................117 7.7.2 Far-Zone Fields and Radiation Intensity ..................................................119 7.7.3 Elemental Plane Wave Source and Radiation Intensity .........................120 7.7.4 Diffraction by the Circular Hole ................................................................121 References .............................................................................................................................123 Part II Electromagnetic Equations of Complex Media 8. Electromagnetic Modeling of Complex Materials .......................................................127 8.1 Volume of Electric Dipoles .......................................................................................127 8.2 Frequency-Dependent Dielectric Constant ...........................................................130 8.3 Modeling of Metals ...................................................................................................132 8.3.1 Case 1: ω < ν and ν2 ≪ wp2 (Low-Frequency Region) ................................132 8.3.2 Case 2: ν < ω < ω (Intermediate-Frequency Region) ..............................133 p 8.3.3 Case 3: ω > ω (High-Frequency Region) ..................................................133 p 8.4 Plasma Medium ........................................................................................................133 8.5 Polarizability of Dielectrics ......................................................................................135 8.6 Mixing Formula .........................................................................................................138 8.7 Good Conductors and Semiconductors .................................................................139 8.8 Perfect Conductors and Superconductors .............................................................141 8.9 Magnetic Materials ...................................................................................................148 8.10 Chiral Medium ..........................................................................................................153 8.11 Plasmonics and Metamaterials ...............................................................................156 References .............................................................................................................................157 9. Waves in Isotropic Cold Plasma: Dispersive Medium ................................................159 9.1 Basic Equations ..........................................................................................................159 9.2 Dielectric–Dielectric Spatial Boundary ..................................................................163 9.3 Reflection by a Plasma Half-Space .........................................................................166 9.4 Reflection by a Plasma Slab .....................................................................................167 9.5 Tunneling of Power through a Plasma Slab ..........................................................172 9.6 Inhomogeneous Slab Problem .................................................................................175 9.7 Periodic Layers of Plasma ........................................................................................175 9.8 Surface Waves ............................................................................................................180 9.9 Transient Response of a Plasma Half-Space ..........................................................183 9.9.1 Isotropic Plasma Half-Space s Wave .........................................................184 9.9.2 Impulse Response of Several Other Cases Including Plasma Slab .......185 9.10 Solitons .......................................................................................................................185 9.11 Perfect Dispersive Medium .....................................................................................185 References .............................................................................................................................185 10. Spatial Dispersion and Warm Plasma ............................................................................187 10.1 Waves in a Compressible Gas ..................................................................................187 10.2 Waves in Warm Plasma ............................................................................................189 viii Contents 10.3 Constitutive Relation for a Lossy Warm Plasma ..................................................193 10.4 Dielectric Model of Warm Loss-Free Plasma ........................................................195 10.5 Conductor Model of Warm Lossy Plasma .............................................................195 10.6 Spatial Dispersion and Nonlocal Metal Optics .....................................................196 10.7 Technical Definition of Plasma State ......................................................................197 10.7.1 Temperate Plasma ........................................................................................197 10.7.2 Debye Length, Collective Behavior, and Overall Charge Neutrality ...198 10.7.3 Unneutralized Plasma .................................................................................198 References .............................................................................................................................198 11. Wave in Anisotropic Media and Magnetoplasma ........................................................201 11.1 Introduction ...............................................................................................................201 11.2 Basic Field Equations for a Cold Anisotropic Plasma Medium .........................201 11.3 One-Dimensional Equations: Longitudinal Propagation and L and R Waves ...203 11.4 One-Dimensional Equations: Transverse Propagation—O Wave ......................207 11.5 One-Dimensional Solution: Transverse Propagation—X Wave .........................207 11.6 Dielectric Tensor of a Lossy Magnetoplasma Medium .......................................212 11.7 Periodic Layers of Magnetoplasma ........................................................................213 11.8 Surface Magnetoplasmons .......................................................................................213 11.9 Surface Magnetoplasmons in Periodic Media ......................................................213 11.10 Permeability Tensor ..................................................................................................213 11.11 Reflection by a Warm Magnetoplasma Slab ..........................................................214 References .............................................................................................................................214 12. Optical Waves in Anisotropic Crystals ...........................................................................215 12.1 Wave Propagation in a Biaxial Crystal along the Principal Axes .......................215 12.2 Propagation in an Arbitrary Direction ...................................................................217 12.3 Propagation in an Arbitrary Direction: Uniaxial Crystal ....................................219 12.4 k-Surface .....................................................................................................................220 12.5 Group Velocity as a Function of Polar Angle ........................................................221 12.6 Reflection by an Anisotropic Half-Space ...............................................................224 References .............................................................................................................................225 13. Time-Domain Solutions ....................................................................................................227 13.1 Introduction ...............................................................................................................227 13.2 Transients on Bounded Ideal Transmission Lines ................................................227 13.2.1 Step Response for Resistive Terminations ................................................228 13.2.2 Response to a Rectangular Pulse ...............................................................238 13.2.3 Response to a Pulse with a Rise Time and Fall Time ..............................239 13.2.4 Source with Rise Time: Response to Reactive Load Terminations .......239 13.2.5 Response to Nonlinear Terminations ........................................................241 13.2.6 Practical Applications of the Theory .........................................................243 13.3 Transients on Lossy Transmission Lines ................................................................243 13.3.1 Solution Using the Laplace Transform Technique ..................................244 13.3.1.1 Loss-Free Line ...............................................................................245 13.3.1.2 Distortionless Line .......................................................................245 13.3.1.3 Lossy Line ......................................................................................245 Contents ix 13.4 Direct Solution in Time Domain: Klein–Gordon Equation .................................247 13.4.1 Examples of Klein–Gordon Equation .......................................................247 13.5 Nonlinear Transmission Line Equations and KdV Equation .............................249 13.5.1 Korteweg-de-Vries (KdV) Equation and Its Solution .............................250 13.5.2 KdV Approximation of NLTL Equation ...................................................252 13.6 Charged Particle Dynamics .....................................................................................253 13.6.1 Introduction ..................................................................................................253 13.6.2 Kinematics .....................................................................................................254 13.6.3 Conservation of Particle Energy due to Stationary Electric and Magnetic Fields ............................................................................................256 13.6.4 Constant Electric and Magnetic Fields .....................................................256 13.6.4.1 Special Case of E = 0 ....................................................................257 13.6.5 Constant Gravitational Field and Magnetic Field ...................................259 13.6.6 Drift Velocity in Nonuniform B Field .......................................................260 13.6.7 Time-Varying Fields and Adiabatic Invariants ........................................261 13.6.8 Lagrange and Hamiltonian Formulations of Equations of Motion ......263 13.6.8.1 Hamiltonian Formulation ...........................................................264 13.6.8.2 Photon Ray Theory ......................................................................265 13.6.8.3 Space and Time Refraction Explained through Photon Theory..............................................................................268 13.7 Nuclear Electromagnetic Pulse and Time-Varying Conducting Medium ........270 13.8 Magnetohydrodynamics (MHD) ............................................................................274 13.8.1 Evolution of the B Field ..............................................................................274 13.9 Time-Varying Electromagnetic Medium................................................................276 13.9.1 Frequency Change due to a Temporal Discontinuity in the Medium Properties ......................................................................................276 13.9.2 Effect of Switching an Unbounded Isotropic Plasma Medium .............277 13.9.2.1 Sudden Creation of an Unbounded Plasma Medium .............280 13.9.3 Sudden Creation of a Plasma Slab .............................................................282 13.9.4 Time-Varying Magnetoplasma Medium ..................................................282 13.9.4.1 Basic Field Equations ...................................................................284 13.9.4.2 Characteristic Waves ....................................................................284 13.9.4.3 R-Wave Propagation ....................................................................285 13.9.4.4 Sudden Creation ...........................................................................286 13.9.4.5 Frequency-Shifting Characteristics of Various R Waves .........287 13.9.5 Modeling of Building Up Plasma versus Collapsing Plasma ...............288 13.9.5.1 Building Up Magnetoplasma .....................................................288 13.9.5.2 Collapsing Magnetoplasma ........................................................290 13.9.6 Applications ..................................................................................................291 13.9.6.1 Application: Frequency Transformer 10–1000 GHz ................291 13.9.7 Subcycle Time-Varying Medium ...............................................................292 13.9.8 Periodically Time-Varying Parameter, Mathieu Equation, and Parametric Resonance .................................................................................292 13.10 Statistical Mechanics and Boltzmann Equation ....................................................295 (cid:31) 13.10.1 Maxwell Distribution f and Kinetic Definition of Temperature T .....296 M 13.10.2 Boltzmann Equation ....................................................................................297 13.10.3 Boltzmann–Vlasov Equation ......................................................................298 13.10.4 Krook Model for Collisions ........................................................................298