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by Boris Z. Katsenelenbaum
Contents
Preface XI
1 The Maxwell Equations 1
1.1 Complex amplitudes 1
1.1.1 Harmonic (monochromatic) oscillations 1
1.1.2 Complex amplitudes 2
1.1.3 The period-average product of two harmonic functions 3
1.2 The Maxwell equations 4
1.2.1 The conduction current and the extrinsic current 4
1.2.2 The Maxwell equations 5
1.2.3 Dielectric permittivity and magnetic permeability of a medium 6
1.2.4 The polarization current 7
1.2.5 The frequency dispersion and the spatial dispersion (chirality) 10
1.2.6 Complex permittivity 11
1.2.7 The radiation condition 12
1.2.8 The wave equations 14
1.2.9 The reciprocity conditions 16
1.2.10 Average energy losses 18
1.2.11 The dispersion relations 19
1.3 Idealized objects 22
1.3.1 Interface of two media 22
1.3.2 The impedance (one-side) boundary conditions 24
1.3.3 Skin layer 24
1.3.4 Ideal conductor 27
1.3.5 Singularities of fields near the edge or vertex 28
1.3.6 The line current and the point current 32
1.4 Uniqueness and existence of solution 35
1.4.1 Uniqueness of solution 35
1.4.2 Violation of the uniqueness theorem: eigenoscillations 38
2 Plane Waves 41
2.1 Plane waves in an infinite homogeneous medium 41
2.1.1 The phase velocity 41
2.1.2 The elliptic polarization 43
2.1.3 Eigenwaves in chiral media 45
2.1.4 Turning of the polarization plane in the chiral media 47
2.1.5 The group velocity 48
2.1.6 The relativity restrictions on the propagation factor 50
2.2 Plane waves in a plano-layered medium 52
2.2.1 Medium with constant wave resistance 52
2.2.2 The slowly varying wave resistance 55
2.2.3 The periodical layer 57
2.2.4 Nonreflecting coating 59
2.2.5 The oblique incidence 61
2.2.6 Plano-parallel chiral medium 64
2.2.7 Media with ε < 0, μ < 0 66
3 Closed Waveguides 71
3.1 Eigenmodes in nonfilled waveguides 71
3.1.1 Eigenmodes 71
3.1.2 The TM-, TE-, and TEM-modes 74
3.1.3 The functional orthogonality of the fields of eigenmodes 75
3.1.4 The electric and magnetic Hertz vectors 77
3.1.5 Rectangular waveguides 78
3.1.6 Circular waveguides 81
3.1.7 Multiple-connected cross-sections 83
3.2 Waves in waveguides with nonhomogeneous cross-section
filling 86
3.2.1 Nonhomogeneous filling and impedance walls 86
3.2.2 Wave number in impedance waveguide 87
3.2.3 Losses in impedance waveguide 91
3.2.4 Orthogonality condition 93
3.2.5 Complex and associated modes 95
3.3 Excitation of closed waveguides 97
3.3.1 Excitation by extrinsic current 97
3.3.2 The slot excitation and end-plane excitation 100
3.3.3 Integration in the plane of a complex variable 102
3.4 Nonregular closed waveguides 108
3.4.1 The cross-section method 108
3.4.2 Slowly varying parameters 113
3.4.3 The diaphragm: equation for field in the slot 116
3.4.4 The diaphragm: equation for current on strips 119
3.4.5 Diffraction on the screen with a hole 120
3.4.6 Open end of waveguide 125
4 Closed Resonators 129
4.1 Resonators with ideal-conducting walls 129
4.1.1 Waveguide resonators without filling 129
4.1.2 Resonators of arbitrary shape 132
4.1.3 Calculation of eigenfrequencies 134
4.1.4 Variational technique 136
4.1.5 Excitation of resonators 139
4.2 Resonators with impedance walls 143
4.2.1 Complex eigenfrequencies 143
4.2.2 Displacement of eigenfrequencies 146
4.2.3 Impedance as a spectral parameter 147
5 Open Lines 151
5.1 Dielectric waveguides 151
5.1.1 Circular dielectric waveguides 151
5.1.2 Eigenmodes of dielectric waveguides with arbitrary
cross-section 154
5.1.3 Excitation of dielectric waveguides 157
5.1.4 Nonregular dielectric waveguides 163
5.1.5 The optical fiber 166
5.2 The lines with surface wave 170
5.2.1 Nonideal metallic cylinder 170
5.2.2 The ideal metallic cylinder covered by a thin dielectric layer 173
5.2.3 The short-periodical surface 175
5.2.4 The corrugated surface 178
5.2.5 Slow waves in closed waveguides 181
5.2.6 The helix line; the array 184
5.2.7 The microstrip line 187
5.3 The wave beam 189
5.3.1 The wave beam 189
5.3.2 Parabolic equation 193
5.3.3 The energy transmission coefficient 195
5.3.4 Optimal antenna and rectenna shapes 198
5.3.5 Fields in the rectenna plane 201
5.3.6 Free phase of desired field on rectenna 203
5.3.7 The lens line 206
6 Backgrounds of Antenna Theory 211
6.1 Radiation of current set 211
6.1.1 The elementary electric dipole and multipole 211
6.1.2 Field of arbitrary currents 215
6.1.3 The elementary magnetic dipole and multipole 218
6.1.4 The half-wave vibrator 219
6.1.5 The multivibrator antenna 224
6.2 Aperture antennas 225
6.2.1 Radiation from aperture 225
6.2.2 The Green function method 228
6.2.3 The radiation pattern 230
6.2.4 Inverse problem 232
6.2.5 The near field zone, Fresnel zone, and far field zone 234
6.2.6 Geometric optics 236
6.3 Volume antennas 239
6.3.1 Radiation from holes 239
6.3.2 Field in narrow long slot 243
6.3.3 Resonant antennas 245
6.3.4 Transparency of short-periodical array 247
6.3.5 Dielectric antennas 249
6.3.6 The inverse problem for volume antennas 253
6.3.7 Analytical continuation of the field 257
7 Diffraction on Metallic and Dielectric Objects 261
7.1 Diffraction of the plane wave on circular waveguide 261
7.1.1 Scalar potentials 261
7.1.2 The variable separation method: the Rayleigh series 262
7.1.3 The Watson series 264
7.1.4 Dielectric cylinder 269
7.2 Diffraction on metallic half-plane 271
7.2.1 Usage of the variable separation method 271
7.2.2 Currents on metallic surface 273
7.2.3 The far field 274
7.3 The Debye potentials: diffraction on a metallic sphere 277
7.3.1 The Debye potentials 277
7.3.2 The Debye potentials for fields of elementary sources 278
7.3.3 Fields of elementary sources located at point with complex
coordinates 279
7.3.4 Diffraction of the plane wave on metallic sphere: the Rayleigh
series 281
7.3.5 Small sphere: dipole momenta 284
7.3.6 Large sphere: the Watson series 285
7.4 Small bodies; large bodies 288
7.4.1 Diffraction on the body with noncoordinate surface 288
7.4.2 Small metallic bodies 291
7.4.3 The duality principle for the hole in plain screen 294
7.4.4 Thin metallic cylinder of arbitrary cross-section: the
H-polarization 298
7.4.5 Thin metallic cylinder of arbitrary cross-section: the
E-polarization 300
7.4.6 The current on a metallic surface of small curvature 304
7.4.7 Ray structure of the field in shadow: geometro-optical theory of
diffraction 306
7.4.8 The method of auxiliary sources 308
7.4.9 The optical theorem 312
7.4.10 Spectral method for the diffraction problems 316
General References 321
Complementary References 322
Index 325 |
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