About the Authors xvii Preface xix Acknowledgments xxiii 1 Maxwell''s Equations, Constitutive Relations, Wave Equation, and Polarization 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 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 b 97 3.2.4 Critical Angle θ c 100 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 0 195 5.

7.2 On the Singular Nature of G 0 (r r ') for Observation Points Within the Source Region 197 5.7.3 Representation of the Green''s Dyadic G 0 in Terms of an Integral in the Wavenumber (k) Space 201 5.7.4 Electromagnetic Radiation by a Source in a General Bianisotropic Medium Using a Green''s Dyadic G a in k-Space 208 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 6.5 Duality Theorem 235 6.6 Reciprocity Theorems and Conservation of Reactions 242 6.6.1 The Lorentz Reciprocity Theorem 243 6.6.2 Reciprocity Theorem for Bianisotropic Media 249 6.

7 Uniqueness Theorem 251 6.8 Image Theorems 254 6.9 Equivalence Theorems 258 6.9.1 Volume Equivalence Theorem for EM Scattering 258 6.9.2 A Surface Equivalence Theorem for EM Scattering 260 6.9.

3 A Surface Equivalence Theorem for Antennas 270 6.10 Antenna Impedance 278 6.11 Antenna Equivalent Circuit 282 6.12 The Receiving Antenna Problem 282 6.13 Expressions for Antenna Mutual Coupling Based on Generalized Reciprocity Theorems 287 6.13.1 Circuit Form of the Reciprocity Theorem for Antenna Mutual Coupling 287 6.13.

2 A Mixed Circuit Field Form of a Generalized Reciprocity Theorem for Antenna Mutual Coupling 292 6.13.3 A Mutual Admittance Expression for Slot Antennas 294 6.13.4 Antenna Mutual Coupling, Reaction Concept, and Antenna Measurements 296 6.14 Relation Between Antenna and Scattering Problems 297 6.14.1 Exterior Radiation by a Slot Aperture Antenna Configuration 297 6.

14.2 Exterior Radiation by a Monopole Antenna Configuration 299 6.15 Radar Cross Section 308 6.16 Antenna Directive Gain 309 6.17 Field Decomposition Theorem 311 References 313 7 Modal Techniques for the Analysis of Guided Waves, Resonant Cavities, and Periodic Structures 314 7.1 On Modal Analysis of Some Guided Wave Problems 314 7.2 Classification of Modal Fields in Uniform Guiding Structures 314 7.2.

1 TEM z Guided waves 315 7.3 TM z Guided Waves 325 7.4 TE z Guided Waves 328 7.5 Modal Expansions in Closed Uniform Waveguides 330 7.5.1 TM z Modes 331 7.5.2 TE z Modes 332 7.

5.3 Orthogonality of Modes in Closed Perfectly Conducting Uniform Waveguides 334 7.6 Effect of Losses in Closed Guided Wave Structures 337 7.7 Source Excited Uniform Closed Perfectly Conducting Waveguides 338 7.8 An Analysis of Some Closed Metallic Waveguides 342 7.8.1 Modes in a Parallel Plate Waveguide 342 7.8.

2 Modes in a Rectangular Waveguide 350 7.8.3 Modes in a Circular Waveguide 358 7.8.4 Coaxial Waveguide 364 7.8.5 Obstacles and Discontinuities in Waveguides 366 7.8.

6 Modal Propagation Past a Slot in a Waveguide 379 7.9 Closed and Open Waveguides Containing Penetrable Materials and Coatings 383 7.9.1 Material-Loaded Closed PEC Waveguide 384 7.9.2 Material Slab Waveguide 388 7.9.3 Grounded Material Slab Waveguide 395 7.

9.4 The Goubau Line 395 7.9.5 Circular Cylindrical Optical Fiber Waveguides 398 7.10 Modal Analysis of Resonators 400 7.10.1 Rectangular Waveguide Cavity Resonator 402 7.10.

2 Circular Waveguide Cavity Resonator 406 7.10.3 Dielectric Resonators 408 7.11 Excitation of Resonant Cavities 409 7.12 Modal Analysis of Periodic Arrays 411 7.12.1 Floquet Modal Analysis of an Infinite Planar Periodic Array of Electric Current Sources 412 7.12.

2 Floquet Modal Analysis of an Infinite Planar Periodic Array of Current Sources Configured in a Skewed Grid 419 7.13 Higher-Order Floquet Modes and Associated Grating Lobe Circle Diagrams for Infinite Planar Periodic Arrays 422 7.13.1 Grating Lobe Circle Diagrams 422 7.14 On Waves Guided and Radiated by Periodic Structures 425 7.15 Scattering by a Planar Periodic Array 430 7.15.1 Analysis of the EM Plane Wave Scattering by an Infinite Periodic Slot Array in a Planar PEC Screen 432 7.

16 Finite 1-D and 2-D Periodic Array of Sources 437 7.16.1 Analysis of Finite 1-D Periodic Arrays for the Case of Uniform Source Distribution and Far Zone Observation 437 7.16.2 Analysis of Finite 2-D Periodic Arrays for the Case of Uniform Distribution and Far Zone Observation 444 7.16.3 Floquet Modal Representation for Near and Far Fields of 1-D Nonuniform Finite Periodic Array Distributions 446 7.16.

4 Floquet Modal Representation for Near and Far Fields of 2-D Nonuniform Planar Periodic Finite Array Distributions 449 References 451 8 Green''s Functions for the Analysis of One-Dimensional Source-Excited Wave Problems 453 8.1 Introduction to the Sturm-Liouville Form of Differential Equation for 1-D Wave Problems 453 8.2 Formulation of the Solution to the Sturm-Liouville Problem via the 1-D Green''s Function Approach 456 8.3 Conditions Under Which the Green''s Function Is Symmetric 463 8.4 Construction of the Green''s Function G(x x') 464 8.4.1 General Procedure to Obtain G(x x') 464 8.5 Alternative Simplified Construction of G(x x') Valid for the Symmetric Case 466 8.

6 On the Existence and Uniqueness of G(x x') 483 8.7 Eigenfunction Expansion Representation for G(x x') 483 8.8 Delta Function Completeness Relation and the Construction of Eigenfunctions from G( x x' ) = U (x) W 488 8.9 Explicit Representation of G(x x') Using Step Functions 519 References 520 9 Applications of One-Dimensional Green''s Function Approach for the Analysis of Single and Coupled Set of EM Source Excited Transmission Lines 522 9.1 Introduction 522 9.2 Analytical Formulation for a Single Transmission Line Made Up of Two Conductors 522 9.3 Wave Solution for the Two Conductor Lines When There.