Electromagnetic Waves, Second Edition

0......Page 1
Electromagnetic Waves......Page 2
Contents......Page 5
Preface......Page 11
Acknowledgments......Page 13
Preface to the Second Edition......Page 14
1......Page 16
Electromagnetic Waves......Page 17
Contents......Page 20
Preface......Page 26
Acknowledgments......Page 28
Preface to the Second Edition......Page 29
2.1 Introduction......Page 31
2.2 Steinmetz representation of time-harmonic vectors......Page 32
2.3 Parallel and orthogonal complex vectors......Page 33
2.4 Properties of time-harmonic vectors......Page 34
2.5 Properties of the complex vectors......Page 35
2.6 Linear polarization ratio......Page 36
2.7 Circular polarization ratio......Page 37
2.8 Stokes parameters......Page 38
2.9 The Poincaré sphere......Page 41
2.10 Evolution of polarization in a linear medium: Jones matrix......Page 42
Problems......Page 44
References......Page 47
3.2 Poynting’s theorem. Wave impedance......Page 48
CHAPTER 14: An introduction to radiation statistics and to the theory of coherence......Page 0
3.2.1 Time domain......Page 49
3.2.2 Frequency domain......Page 51
3.3.1 Time domain......Page 53
3.3.2 Frequency domain......Page 54
3.4 Reciprocity theorem......Page 56
3.5.1 Preliminaries......Page 58
3.5.2 Theorem......Page 61
3.5.3 Absorbing currents......Page 62
3.6 Induction theorem......Page 64
3.7 Duality theorem......Page 66
3.8 TE-TM field decomposition theorem......Page 67
3.9 Spatial symmetries. Reflection operators......Page 70
3.10 Further applications and suggested reading......Page 74
Problems......Page 76
References......Page 81
4.1 Separability of variables in the homogeneous Helmholtz equation......Page 82
4.2 Solution of the homogeneous Helmholtz equation in Cartesian coordinates......Page 83
4.3 Plane waves: Terminology and classification......Page 86
4.4 Traveling waves. Phase velocity......Page 89
4.5 Standing waves......Page 91
4.6 Poynting vector and wave impedance......Page 94
4.7 Completeness of plane waves......Page 98
4.8 Reflection and refraction of plane waves......Page 101
4.9 Fresnel formulas......Page 106
4.10 Reflection in multilayer structures......Page 108
4.11 Total reflection......Page 111
4.12 Reflection on the surface of a good conductor......Page 115
4.13 Further applications and suggested reading......Page 117
Problems......Page 118
References......Page 123
5.1 Modulated waves. Group velocity......Page 124
5.2 Dispersion......Page 128
5.3 The scalar approximation......Page 131
5.4 The equations of geometrical optics......Page 133
5.5 Geometrical optics: Electromagnetic implications......Page 138
5.6 Examples of ray tracing in radio propagation and in optics......Page 140
5.7 The WKBJ method......Page 143
5.8 Further comments on the WKBJ method......Page 146
5.9 Gaussian beams......Page 148
5.10 Hermite-Gauss and Laguerre-Gauss modes......Page 153
5.11 Reflection and refraction of Gaussian beams......Page 159
5.12 On the completeness of a series......Page 162
5.13 Further comments on rays and beams......Page 164
5.14 Further applications and suggested reading......Page 165
Problems......Page 167
References......Page 173
6.1 General properties of anisotropic media......Page 175
6.2 Wave equations and potentials in anisotropic media......Page 178
6.3 Birefringent media......Page 179
6.4 Fresnel’s equation of wave normals......Page 183
6.5 An application: Phase matching of two waves......Page 187
6.6 Gyrotropic media......Page 191
6.7 The Appleton-Hartree formula......Page 193
6.8 An example of permittivity dyadic......Page 196
6.9 Second example of permeability dyadic......Page 200
6.10 Faraday rotation......Page 201
6.11 Further applications and suggested reading......Page 206
Problems......Page 207
References......Page 211
7.1 Introduction......Page 213
7.2 Homogeneously filled cylindrical structures: Simplified proof of the TE-TM decomposition theorem......Page 214
7.3 Waveguides with ideal conducting walls......Page 218
A2. Critical frequency......Page 219
A5. Phase and group velocities......Page 220
A6. The fundamental mode......Page 222
B2. Poynting vector......Page 223
D2. Existence of the TEM mode......Page 224
7.5 Mode orthogonality......Page 225
7.5.1 Orthogonality between two TE modes or two TM modes......Page 226
7.5.3 Consequences of mode orthogonality......Page 227
7.6 Some remarks on completeness......Page 228
7.7 Rectangular waveguides......Page 229
7.8 Circular waveguides and coaxial cables......Page 234
7.9 Waveguides with nonideal walls......Page 240
7.10 On wall impedances......Page 244
7.11 Hybrid modes......Page 248
7.12 Further applications and suggested reading......Page 250
Problems......Page 252
References......Page 257
8.1 Introduction......Page 258
8.2 Uniform transmission lines......Page 259
8.3 Impedance transformation along a transmission line......Page 261
8.4 Lossless transmission lines......Page 262
8.5 Low-loss transmission lines......Page 264
8.6 Partially standing waves......Page 265
8.7 The Smith chart......Page 267
8.8 Remote measurement of the load impedance......Page 271
8.9 Impedance matching......Page 273
8.9.1 The quarter-wavelength transformer......Page 275
8.9.2 Impedance matching with one or two stubs......Page 277
8.10 Transmission-line equations: An alternative derivation......Page 280
8.11 TEM and quasi-TEM propagation in planar lines......Page 286
8.11.1 First example: the stripline......Page 287
8.11.2 Second example: the microstrip......Page 288
8.12 The coupled-mode equations......Page 290
8.13 Further applications and suggested reading......Page 294
Problems......Page 296
References......Page 300
9.1 Introduction......Page 302
9.2 Separable coordinate systems in three dimensions......Page 303
9.3 Completeness of resonator modes......Page 304
9.4 Mode orthogonality in a perfect resonator......Page 306
9.5 Lossless cylindrical cavities......Page 307
9.6.1 Rectangular resonators......Page 310
9.6.2 Cavities of circular cross-section......Page 312
9.6.3 Spherical cavities......Page 313
9.7 Lossy resonators: Perturbation analysis. Intrinsic Q-factor......Page 314
9.8 Resonators coupled to external loads. Loaded Q-factor......Page 316
9.9 Open resonators......Page 317
9.10 Stability of open resonators......Page 319
9.11 Q-factor of an open resonator......Page 322
9.12 Further applications and suggested reading......Page 324
Problems......Page 326
References......Page 330
10.1 Introduction......Page 331
10.2 Waves guided by a surface of discontinuity. The characteristic equation......Page 332
10.3 Guided modes of a slab waveguide......Page 337
10.4 Radiation modes of a slab waveguide......Page 342
10.5 The cylindrical rod: Exact modes......Page 344
10.6 Modal cut-off in the cylindrical rod......Page 348
10.7 Weakly guiding rods: The LP modes......Page 351
10.8 Dispersion in dielectric waveguides......Page 357
10.9 Graded-index waveguides......Page 363
10.10 The alpha profiles: An important class of multimode graded-index fibers......Page 368
10.11 Attenuation in optical fibers......Page 373
10.12 Further applications and suggested reading......Page 377
Problems......Page 379
References......Page 383
11.1 Introduction......Page 385
11.2 Green’s functions for the scalar Helmholtz equation......Page 386
11.3 Lorentz-gauge vector potentials in a homogeneous medium......Page 389
11.4 Field vectors in terms of dyadic Green’s functions......Page 392
11.5 Inhomogeneous media: Polarization currents......Page 394
11.6 Time-domain interpretation of Green’s functions......Page 395
11.7 Green’s function expansion into orthogonal eigenfunctions......Page 398
11.8 An example: Field in a rectangular box......Page 400
11.9 Spherical harmonics......Page 402
11.10 Multipole expansion......Page 408
11.11 An introduction to cylindrical harmonics......Page 412
11.12 Further applications and suggested reading......Page 414
Problems......Page 415
References......Page 418
12.1 Introduction......Page 419
12.2 Equivalent dipole moment of an extended source......Page 421
12.3 Far-field approximations......Page 423
12.4 First example: Short electric-current element......Page 425
12.5 Characterization of antennas......Page 430
12.6 Behavior of receiving antennas. Reciprocity......Page 434
12.7 Examples......Page 440
12.7.1 Short electric dipole......Page 441
12.7.2 Thin linear antennas......Page 442
12.7.3 Circular loop......Page 445
12.7.5 Huygens source......Page 447
12.8 Antenna arrays......Page 450
12.8.2 Uniform arrays......Page 452
12.9 Broad-side and end-fire arrays......Page 455
12.10 Further applications and suggested reading......Page 457
Problems......Page 459
References......Page 463
13.2 The diffraction integral: The vector formulation......Page 464
13.3 Illumination conditions. Babinet’s principle......Page 469
13.4 The scalar theory of diffraction......Page 473
13.4.1 The Helmholtz-Kirchhoff formulation......Page 474
13.4.2 The Rayleigh-Sommerfeld formulation......Page 476
13.5 Diffraction formulas and Rayleigh-Sommerfeld......Page 478
13.6 The Fresnel diffraction region......Page 480
13.7 The Fraunhofer diffraction region......Page 482
13.8 Examples......Page 485
13.8.1 Rectangular aperture......Page 486
13.8.2 Circular aperture: the scalar approach......Page 487
13.8.3 Circular aperture: the vector approach......Page 489
13.8.5 Sinusoidal gratings......Page 491
13.9 The field near a focus: First example of Fresnel diffraction......Page 493
13.10 Diffraction from a straight edge: Second example of Fresnel diffraction......Page 495
13.11 A short note on the geometrical theory of diffraction......Page 500
13.12 Further applications and suggested reading......Page 501
Problems......Page 502
References......Page 506
14.2 The analytical signal......Page 507
14.3 Complex degree of coherence......Page 510
14.4 Temporal coherence of a source......Page 511
14.5 Spatial coherence of a source......Page 513
14.6 Higher-order coherence: An introduction......Page 515
14.7 An introduction to photocount distributions......Page 519
14.8 Modal noise in optical-fiber transmission systems: A short outline......Page 523
14.9 Further applications and suggested reading......Page 524
Problems......Page 526
References......Page 529
Appendices......Page 530
APPENDIX A: Vector calculus: Definitions and fundamental theorems......Page 531
APPENDIX B: Vector differential operators in frequently used reference systems......Page 534
APPENDIX C: Vector identities......Page 536
D.1 Bessel, Neumann and Hankel functions......Page 537
D.2 Modified Bessel functions......Page 540
Asymptotic forms......Page 541
Recurrence formulas......Page 542
Integrals......Page 543
References......Page 544
Further Suggested Reading......Page 545