Principles of Electromagnetic Waves and Materials, Second Edition

675 Pages·2018·21.513 MB·English

by  Dikshitulu K. Kalluri

Principles of Electromagnetic
Waves and Materials
Second Edition

Principles of Electromagnetic
Waves and Materials
Second Edition
Dikshitulu K. Kalluri
CRC Press
Taylor & Francis Group
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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
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and the CRC Press Web site at
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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