Advanced Electromagnetics and Scattering Theory (eBook)

Foreword 5
Preface 7
Contents 9
Biographies of Contributors 14
Part I Electromagnetic Theory 16
1 Maxwell's Equations 17
1.1 Differential Form 17
1.2 Constitutive Relations 19
1.3 Integral Form 22
1.4 Boundary Relations 25
1.4.1 Derivation 25
1.4.2 Special Cases 29
1.4.3 Other Boundary Conditions 31
1.5 The Wave Equation 31
1.6 Electromagnetic Potentials 34
1.6.1 Lorenz's Potentials 34
1.6.2 Lorenz's Gauge 36
1.6.3 Gauge Transformation 37
1.6.4 Coulomb's Gauge 37
1.6.5 Hertz Potential 38
1.7 Energy Flow 39
1.7.1 Uniqueness Conditions 41
1.8 Time Harmonic Fields 42
1.9 Complex Poynting Theorem 45
1.10 Specific Absorption Rate 48
1.11 Green's Function Method 49
1.11.1 Green's Identities 50
1.11.2 Inhomogeneous Scalar Helmholtz Equation 51
1.11.3 Green's Function of the First Kind 53
1.11.4 Green's Function of the Second Kind 53
1.11.5 The Free Space Green's Function 54
1.11.6 The Modified Green's Function 58
1.11.7 Eigenfunction Presentation 58
1.12 Inhomogeneous Vector Helmholtz Equation 63
2 Radiation 70
2.1 General Considerations 70
2.2 Elementary Sources 71
2.2.1 The Short Electric Dipole 72
2.2.2 The Small Magnetic Dipole 76
2.3 Wire Antennas 78
2.4 Field Regions 80
2.4.1 Point Sources 80
2.4.2 Extended Sources 81
2.5 Far Field Calculation for General Antennas 82
2.6 Antenna Parameters 85
2.6.1 Antenna Patterns and Radiation Intensity 85
2.6.2 Directive Gain 86
2.6.3 Gain 87
2.6.4 Effective Aperture 88
2.6.5 Antenna Impedance 88
2.6.6 Friis Transmission Formula 91
3 Fundamental Theorems 94
3.1 Uniqueness Theorem 94
3.2 Duality 96
3.3 Image Theory 99
3.4 Reciprocity 101
3.5 Equivalence Principles 105
3.5.1 Equivalent Volumetric Currents 105
3.5.2 Equivalent Surface Currents 107
3.6 Babinet's Principle 115
4 Wave Harmonics and Guided Waves 121
4.1 Plane Waves 121
4.1.1 Planar Harmonics 122
4.1.2 The Sheet Current Source 125
4.1.3 Wave Polarization 127
4.1.4 Lossless Medium 129
4.1.5 Lossy Medium 132
4.1.6 Reflection from Plane Dielectric Interfaces 135
4.1.7 Propagation in Layered Media 143
4.1.8 Reflection from Inhomogeneous Layers 145
4.1.9 Wave Velocities 150
4.2 Planar Waveguides 154
4.2.1 The Parallel Plate Waveguide 155
4.2.2 Grounded Dielectric Slab 158
4.2.3 The Dielectric Slab Waveguide 164
4.3 Hollow Waveguides 168
4.3.1 Waveguide Modes 169
4.3.2 Cutoff Frequency 171
4.3.3 Guide Wavelength 171
4.3.4 Orthogonality of Modes 172
4.3.5 The Rectangular Hollow Waveguide 173
4.3.6 The Corrugated Rectangular Waveguide 177
4.4 Radiation from Sources in a Plane 184
4.5 Cylindrical Waves 187
4.5.1 Line Sources 190
4.5.2 Cylindrical Wave Transformation 193
4.5.3 Addition Theorem 194
4.5.4 The Circular Metallic Waveguide 196
4.5.5 Circular Corrugated Horns 199
4.5.6 The Coaxial Waveguide 203
4.5.7 The Dielectric Rod 208
4.6 Spherical Waves 209
4.6.1 Spherical Wave Transformation 214
4.6.2 Point Sources 214
4.6.3 Addition Theorem 215
Part II Scattering Theory 223
5 Radar 224
5.1 Historical Remarks 224
5.2 Operation 225
5.2.1 Transmitters 226
5.2.2 Radar Antennas 227
5.2.3 Receivers 227
5.2.4 Computer Processing 227
5.2.5 Radar Displays 227
5.3 Secondary-Radar System 228
5.3.1 Transponder 228
5.3.2 Radar Identification (IFF) 228
5.4 Countermeasures 228
5.5 Radar Cross Section 229
5.6 Radar Equation 233
5.7 Doppler Effect 235
5.8 Radar Clutter 236
5.8.1 Clutter Statistics 239
5.9 Non-Meteorological Echoes 240
6 Canonical Scattering Problems 241
6.1 The Circular Cylinder 241
6.1.1 The Conducting Cylinder 241
6.1.2 The Homogeneous Dielectric Cylinder 254
6.2 The Conducting Wedge 257
6.2.1 The Half Plane 260
6.2.2 The Edge Condition 261
6.3 The Sphere 265
6.3.1 Low Frequency Scattering 265
6.3.2 Mie Scattering 270
7 Approximate Methods 278
7.1 Rayleigh-Debye Approximation 278
7.2 Physical Optics Approximation 282
7.2.1 Scattering from a Right Triangular Plate 286
7.2.2 Scattering from a Convex Target 287
8 Integral Equation Method 291
8.1 Types of Integral Equations 291
8.2 Perfectly Conducting Scatterers 292
8.2.1 Electric Field Integral Equation (EFIE) 292
8.2.2 Magnetic Field Integral Equation (MFIE) 293
8.3 Two-Dimensional Problems 295
8.3.1 Scattering from a Resistive Strip 296
8.3.2 Cylindrical Strips 306
8.3.3 Cylindrical Reflector Antennas 307
8.4 The Linear Wire Antenna 308
8.4.1 Source Modeling 311
8.4.2 Input Impedance 313
8.5 Dielectric Scatterers 314
9 Method of Moments 316
9.1 Formulation 316
9.2 Resistive Strips 319
9.2.1 Flat Strips 319
9.2.2 Circular Cylindrical Strips 322
9.3 The Linear Wire Antenna 328
9.4 The Dielectric Cylinder 331
10 Periodic Structures 336
10.1 Floquet's Theorem 336
10.2 Scattering From Strip Gratings 337
11 Inverse Scattering 343
11.1 Dielectric Bodies 343
11.1.1 Born Approximation 343
11.2 Perfectly Conducting Bodies 348
11.2.1 Physical Optics Inverse Scattering 348
Appendix A Vector Analysis 351
Appendix B Vector Calculus 355
Appendix C Bessel Functions 359