Principles of Electromagnetic Waves and Materials

448 Pages·2013·10.564 MB·English

by  Kalluri, Dikshitulu K.

KALLURI
Digital and Wireless Communications
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Principles of Electromagnetic Waves and Materials is a condensed
m
version of Dikshitulu K. Kalluri’s previously published textbook, Electromagnetic
Waves, Materials, and Computation with MATLAB®. This book focuses on lower-
a
level courses, primarily senior undergraduate and graduate students in elec-
g
tromagnetic waves and materials courses. It takes an integrative approach to
n
the subject of electromagnetics by supplementing quintessential “old-school”
information and methods with the appropriate amount of material on plasmas e
for exposing the students to the broad area of Plasmonics and by striking t
a balance between theoretical and practical aspects. i
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W
The book begins with a discussion of the electromagnetics of bounded simple
media and introduces the equations in the time domain, the time-harmonic
equations, wave propagation solutions, and their applications are obtained a
for one-dimensional, two-dimensional, and then three-dimensional problems. v
It then covers the electromagnetics of complex media and brings out the e
dominant effect of each kind of complexity. The following chapters bring the
s
system approach to relating the kind of complexity resultant dominant effect
as an input-output description of a system element. The book then provides a
appendices for most chapters and pedagogical tools such as homework prob- n
lems, 15-minute quizzes, and take-home examinations. d

A highlight of this textbook, compared to similar texts on electromagnetics M
suitable for senior undergraduate/first year graduate students, is the inclusion
of an appropriate amount of material on the topic of Electromagnetics and a
Plasmas. This topic has a resurgence of interest because of new applications t
in (1) High Electron Mobility Transistors (HEMT) (2) Plasma Wave Electronics, e
and (3) the broad area of Plasmonics and Metamaterials. This is just one of r
the many features in this text that give students the foundation they need to i
a
specialize in the many technological areas for which electromagnetics is a base.
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K20643
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Principles of
Electromagnetic
Waves and Materials

Principles of
Electromagnetic
Waves and Materials
DIKSHITULU K. KALLURI
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2013 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
Version Date: 20130515
International Standard Book Number-13: 978-1-4665-9373-2 (eBook - PDF)
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Contents
Preface ..............................................................................................................................................xi
Acknowledgments .....................................................................................................................xvii
Author ..........................................................................................................................................xix
Selected List of Symbols .............................................................................................................xxi
List of Book Sources ..................................................................................................................xxiii
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 .......................................19
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 ......................................................................................27
2.9 Electromagnetic Wave Polarization..........................................................................29
2.10 Arbitrary Direction of Propagation ..........................................................................30
2.11 Wave Reflection ...........................................................................................................31
2.12 Incidence of p Wave: Parallel-Polarized ...................................................................32
2.13 Incidence of s Wave: Perpendicular-Polarized .......................................................34
2.14 Critical Angle and Surface Wave ..............................................................................35
2.15 One-Dimensional Cylindrical Wave and Bessel Functions ..................................37
References ...............................................................................................................................43
3 Two-Dimensional Problems and Waveguides ...............................................................45
3.1 Two-Dimensional Solutions in Cartesian Coordinates .........................................45
3.2 TM Modes in a Rectangular Waveguide ..............................................................47
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3.3 TE Modes in a Rectangular Waveguide ...............................................................50
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3.4 Dominant Mode in a Rectangular Waveguide: TE Mode...................................52
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3.5 Power Flow in a Waveguide: TE Mode ..................................................................53
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vi Contents
3.6 Attenuation of TE Mode due to Imperfect Conductors and 
10
Dielectric Medium ......................................................................................................53
3.7 Cylindrical Waveguide: TM Modes .........................................................................54
3.8 Cylindrical Waveguide: TE Modes ...........................................................................55
3.9 Sector Waveguide ........................................................................................................56
3.10 Dielectric Cylindrical Waveguide—Optical Fiber .................................................57
References ...............................................................................................................................60
4 Three-Dimensional Solutions ...........................................................................................61
4.1 Rectangular Cavity with PEC Boundaries: TM Modes .........................................61
4.2 Rectangular Cavity with PEC Boundaries: TE Modes ..........................................62
4.3 Q of a Cavity ................................................................................................................63
Reference .................................................................................................................................64
5 Spherical Waves and Applications ....................................................................................65
5.1 Half-Integral Bessel Functions ..................................................................................65
5.2 Solutions of Scalar Helmholtz Equation ..................................................................66
5.3 Vector Helmholtz Equation .......................................................................................68
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5.4 TM Modes ...................................................................................................................69
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5.5 TE Modes .....................................................................................................................70
5.6 Spherical Cavity ..........................................................................................................71
6 Laplace Equation: Static and Low-Frequency Approximations ..................................75
6.1 One-Dimensional Solutions ......................................................................................76
6.2 Two-Dimensional Solutions ......................................................................................76
6.2.1 Cartesian Coordinates ...................................................................................76
6.2.2 Circular Cylindrical Coordinates ................................................................82
6.3 Three-Dimensional Solution .....................................................................................87
6.3.1 Cartesian Coordinates ...................................................................................87
6.3.2 Cylindrical Coordinates ................................................................................88
6.3.3 Spherical Coordinates ...................................................................................88
References ...............................................................................................................................91
7 Miscellaneous Topics on Waves ........................................................................................93
7.1 Group Velocity v ........................................................................................................93
g
7.2 Green’s Function ..........................................................................................................94
7.3 Network Formulation .................................................................................................98
7.3.1 ABCD Parameters ..........................................................................................98
7.3.2 S Parameters .................................................................................................101
7.4 Stop Bands of a Periodic Media ..............................................................................103
7.5 Radiation ....................................................................................................................106
7.5.1 Hertzian Dipole ............................................................................................109
7.5.2 Half-Wave Dipole .........................................................................................110
7.5.3 Dipoles of Arbitrary Length .......................................................................112
7.5.4 Shaping the Radiation Pattern ...................................................................112
7.5.5 Antenna Problem as a Boundary Value Problem....................................113
7.5.6 Traveling Wave Antenna and Cerenkov Radiation ................................113
7.5.7 Small Circular Loop Antenna ....................................................................114
7.5.8 Other Practical Radiating Systems ............................................................115
Contents vii
7.6 Scattering ....................................................................................................................115
7.6.1 Cylindrical Wave Transformations ...........................................................116
7.6.2 Calculation of Current Induced on the Cylinder ....................................116
7.6.3 Scattering Width ..........................................................................................118
7.7 Diffraction ..................................................................................................................119
7.7.1 Magnetic Current and Electric Vector Potential ......................................119
7.7.2 Far-Zone Fields and Radiation Intensity ..................................................122
7.7.3 Elemental Plane Wave Source and Radiation Intensity .........................123
7.7.4 Diffraction by the Circular Hole ................................................................124
References .............................................................................................................................126
Part II Electromagnetic Equations of Complex Media
8 Electromagnetic Modeling of Complex Materials .......................................................129
8.1 Volume of Electric Dipoles .......................................................................................129
8.2 Frequency-Dependent Dielectric Constant ...........................................................132
8.3 Modeling of Metals ...................................................................................................134
8.4 Plasma Medium ........................................................................................................135
8.5 Polarizability of Dielectrics .....................................................................................137
8.6 Mixing Formula ........................................................................................................141
8.7 Good Conductors and Semiconductors .................................................................142
8.8 Perfect Conductors and Superconductors .............................................................144
8.9 Magnetic Materials ...................................................................................................151
8.10 Chiral Medium ..........................................................................................................156
8.11 Plasmonics and Metamaterials ...............................................................................160
References .............................................................................................................................160
9 Waves in Isotropic Cold Plasma: Dispersive Medium ...............................................161
9.1 Basic Equations ..........................................................................................................161
9.2 Dielectric–Dielectric Spatial Boundary .................................................................165
9.3 Reflection by a Plasma Half-Space .........................................................................168
9.4 Reflection by a Plasma Slab .....................................................................................169
9.5 Tunneling of Power through a Plasma Slab ..........................................................174
9.6 Inhomogeneous Slab Problem.................................................................................177
9.7 Periodic Layers of Plasma ........................................................................................178
9.8 Surface Waves ............................................................................................................182
9.9 Transient Response of a Plasma Half-Space .........................................................186
9.9.1 Isotropic Plasma Half-Space s Wave .........................................................186
9.9.2 Impulse Response of Several Other Cases
Including Plasma Slab .................................................................................188
9.10 Solitons .......................................................................................................................188
References .............................................................................................................................188
10 Spatial Dispersion and Warm Plasma ............................................................................191
10.1 Waves in a Compressible Gas ..................................................................................191
10.2 Waves in Warm Plasma ............................................................................................193
10.3 Constitutive Relation for a Lossy Warm Plasma ..................................................197
10.4 Dielectric Model of Warm Loss-Free Plasma ........................................................199
viii Contents
10.5 Conductor Model of Warm Lossy Plasma .............................................................200
10.6 Spatial Dispersion and Nonlocal Metal Optics ....................................................201
10.7 Technical Definition of Plasma State ......................................................................202
10.7.1 Temperate plasma ........................................................................................202
10.7.2 Debye Length, Collective Behavior, and
Overall Charge Neutrality ..........................................................................202
10.7.3 Unneutralized Plasma .................................................................................203
References .............................................................................................................................203
11 Wave in Anisotropic Media and Magnetoplasma .......................................................205
11.1 Introduction ...............................................................................................................205
11.2 Basic Field Equations for a Cold Anisotropic Plasma Medium .........................205
11.3 One-Dimensional Equations: Longitudinal Propagation and
L and R Waves ...........................................................................................................206
11.4 One-Dimensional Equations: Transverse Propagation: O Wave........................211
11.5 One-Dimensional Solution: Transverse Propagation: X Wave ...........................211
11.6 Dielectric Tensor of a Lossy Magnetoplasma Medium .......................................216
11.7 Periodic Layers of Magnetoplasma ........................................................................217
11.8 Surface Magnetoplasmons .......................................................................................217
11.9 Surface Magnetoplasmons in Periodic Media ......................................................218
11.10 Permeability Tensor ..................................................................................................218
References .............................................................................................................................218
12 Optical Waves in Anisotropic Crystals ..........................................................................221
12.1 Wave Propagation in a Biaxial Crystal along the Principal Axes ......................221
12.2 Propagation in an Arbitrary Direction ..................................................................223
12.3 Propagation in an Arbitrary Direction: Uniaxial Crystal ...................................225
12.4 k-Surface .....................................................................................................................226
12.5 Group Velocity as a Function of Polar Angle ........................................................228
12.6 Reflection by an Anisotropic Half-Space ...............................................................231
References .............................................................................................................................232
Part III Appendices
Appendix 1A: Vector Formulas and Coordinate Systems ..............................................235
Appendix 1B: Retarded Potentials and Review of Potentials for the Static Cases .....245
Appendix 1C: Poynting Theorem ........................................................................................253
Appendix 1D: Low-Frequency Approximation of Maxwell’s Equations R, L, C,
and Memristor M ................................................................................................................255
Appendix 2A: AC Resistance of a Round Wire When the Skin Depth δ Is
Comparable to the Radius a of the Wire ........................................................................261
Appendix 2B: Transmission Lines: Power Calculation ...................................................265
Appendix 2C: Introduction to the Smith Chart ................................................................269
Appendix 2D: Nonuniform Transmission Lines .............................................................289
Contents ix
Appendix 4A: Calculation of Losses in a Good Conductor at High
Frequencies: Surface Resistance R ................................................................................297
S
Appendix 6A: On Restricted Fourier Series Expansion .................................................299
Appendix 7A: Two- and Three-Dimensional Green’s Functions ..................................303
Appendix 8A: Wave Propagation in Chiral Media ..........................................................317
Appendix 8B: Left-Handed Materials and Transmission Line Analogies ..................319
Appendix 9A: Backscatter from a Plasma Plume due to Excitation of
Surface Waves ..............................................................................................................333
Appendix 10A: Thin Film Reflection Properties of a Warm Isotropic Plasma
Slab between Two Half-Space Dielectric Media ..........................................................345
Appendix 10B: First-Order Coupled Differential Equations for Waves
in Inhomogeneous Warm Magnetoplasmas .................................................................367
Appendix 10C: Waveguide Modes of a Warm Drifting Uniaxial Electron Plasma ....371
Appendix 11A: Faraday Rotation versus Natural Rotation ............................................377
Appendix 11B: Ferrites and Permeability Tensor ............................................................381
Part IV Chapter Problems
Problems ......................................................................................................................................387