Preface ...................................................... xiii
Acknowledgments ................................................ xv
Preface to the Second Edition ................................ xvii
1 Basic equations for electromagnetic fields ................... 1
1.1 Introduction: Experimental laws ........................ 1
1.2 Maxwell's equations and the charge continuity
equation ............................................... 4
1.3 Constitutive relations ................................. 5
1.4 Imposed currents ....................................... 9
1.5 Divergence equations .................................. 11
1.6 Continuity conditions ................................. 13
1.7 The wave equation. The Helmholtz equation ............. 15
1.8 Magnetic vector potential ............................. 18
1.9 Fitzgerald electric vector potential .................. 23
1.10 Hertz vector potential ................................ 25
1.11 Further applications and suggested reading ............ 26
References ..................................................... 33
2 Polarization ................................................ 35
2.1 Introduction .......................................... 35
2.2 Steinmetz representation of time-harmonic vectors ..... 36
2.3 Parallel and orthogonal complex vectors ............... 37
2.4 Properties of time-harmonic vectors ................... 38
2.5 Properties of the complex vectors ..................... 39
2.6 Linear polarization ratio ............................. 40
2.7 Circular polarization ratio ........................... 41
2.8 Stokes parameters ..................................... 42
2.9 The Poincare sphere ................................... 45
2.10 Evolution of polarization in a linear medium:
Jones matrix .......................................... 46
2.11 Further applications and suggested reading ............ 48
References ..................................................... 51
3 General theorems ............................................ 53
3.1 Introduction .......................................... 53
3.2 Poynting's theorem. Wave impedance .................... 53
3.3 Uniqueness theorem .................................... 58
3.4 Reciprocity theorem ................................... 61
3.5 Equivalence theorem ................................... 63
3.6 Induction theorem ..................................... 69
3.7 Duality theorem ....................................... 71
3.8 TE-TM field decomposition theorem ..................... 72
3.9 Spatial symmetries. Reflection operators .............. 75
3.10 Further applications and suggested reading ............ 79
References ..................................................... 87
4 Plane waves in isotropic media .............................. 89
4.1 Separability of variables in the homogeneous
Helmholtz equation .................................... 89
4.2 Solution of the homogeneous Helmholtz equation in
Cartesian coordinates ................................. 90
4.3 Plane waves: Terminology and classification ........... 93
4.4 Traveling waves. Phase velocity ....................... 96
4.5 Standing waves ........................................ 98
4.6 Poynting vector and wave impedance ................... 101
4.7 Completeness of plane waves .......................... 105
4.8 Reflection and refraction of plane waves ............. 108
4.9 Fresnel formulas ..................................... 113
4.10 Reflection in multilayer structures .................. 115
4.11 Total reflection ..................................... 118
4.12 Reflection on the surface of a good conductor ........ 122
4.13 Further applications and suggested reading ........... 124
References .................................................... 131
5 Plane wave packets and beams ............................... 133
5.1 Modulated waves. Group velocity ...................... 133
5.2 Dispersion ........................................... 137
5.3 The scalar approximation ............................. 140
5.4 The equations of geometrical optics .................. 142
5.5 Geometrical optics: Electromagnetic implications ..... 147
5.6 Examples of ray tracing in radio propagation and in
optics ............................................... 149
5.7 The WKBJ method ...................................... 152
5.8 Further comments on the WKBJ method .................. 155
5.9 Gaussian beams ....................................... 157
5.10 Hermite-Gauss and Laguerre-Gauss modes ............... 162
5.11 Reflection and refraction of Gaussian beams .......... 168
5.12 On the completeness of a series ...................... 171
5.13 Further comments on rays and beams ................... 173
5.14 Further applications and suggested reading ........... 174
References .................................................... 183
6 Plane waves in anisotropic media ........................... 185
6.1 General properties of anisotropic media .............. 185
6.2 Wave equations and potentials in anisotropic media ... 188
6.3 Birefringent media ................................... 189
6.4 Fresnel's equation of wave normals ................... 193
6.5 An application: Phase matching of two waves .......... 197
6.6 Gyrotropic media ..................................... 201
6.7 The Appleton-Hartree formula ......................... 203
6.8 An example of permittivity dyadic .................... 206
6.9 Second example of permeability dyadic ................ 210
6.10 Faraday rotation ..................................... 211
6.11 Further applications and suggested reading ........... 216
References .................................................... 221
7 Waveguides with conducting walls ........................... 223
7.1 Introduction ......................................... 223
7.2 Homogeneously filled cylindrical structures:
Simplified proof of the TE-TM decomposition
theorem .............................................. 224
7.3 Waveguides with ideal conducting walls ............... 228
7.4 Transmission modes of lossless cylindrical
structures ........................................... 229
7.5 Mode orthogonality ................................... 235
7.6 Some remarks on completeness ......................... 238
7.7 Rectangular waveguides ............................... 239
7.8 Circular waveguides and coaxial cables ............... 244
7.9 Waveguides with nonideal walls ....................... 250
7.10 On wall impedances ................................... 254
7.11 Hybrid modes ......................................... 258
7.12 Further applications and suggested reading ........... 260
References .................................................... 267
8 Waves on transmission lines ................................ 269
8.1 Introduction ......................................... 269
8.2 Uniform transmission lines ........................... 270
8.3 Impedance transformation along a transmission line ... 272
8.4 Lossless transmission lines .......................... 273
8.5 Low-loss transmission lines .......................... 275
8.6 Partially standing waves ............................. 276
8.7 The Smith chart ...................................... 278
8.8 Remote measurement of the load impedance ............. 282
8.9 Impedance matching ................................... 284
8.10 Transmission-line equations:
An alternative derivation ............................ 291
8.11 ТЕМ and quasi-TEM propagation in planar lines ........ 297
8.12 The coupled-mode equations ........................... 301
8.13 Further applications and suggested reading ........... 305
References .................................................... 311
9 Resonant cavities .......................................... 313
9.1 Introduction ......................................... 313
9.2 Separable coordinate systems in three dimensions ..... 314
9.3 Completeness of resonator modes ...................... 315
9.4 Mode orthogonality in a perfect resonator ............ 317
9.5 Lossless cylindrical cavities ........................ 318
9.6 Simple examples ...................................... 321
9.7 Lossy resonators: Perturbation analysis.
Intrinsic Q-factor ................................... 325
9.8 Resonators coupled to external loads.
Loaded Q-factor ...................................... 327
9.9 Open resonators ...................................... 328
9.10 Stability of open resonators ......................... 330
9.11 Q-factor of an open resonator ........................ 333
9.12 Further applications and suggested reading ........... 335
References .................................................... 341
10 Dielectric waveguides ...................................... 343
10.1 Introduction ......................................... 343
10.2 Waves guided by a surface of discontinuity.
The characteristic equation .......................... 344
10.3 Guided modes of a slab waveguide ..................... 349
10.4 Radiation modes of a slab waveguide .................. 354
10.5 The cylindrical rod: Exact modes ..................... 356
10.6 Modal cut-off in the cylindrical rod ................. 360
10.7 Weakly guiding rods: The LP modes .................... 363
10.8 Dispersion in dielectric waveguides .................. 369
10.9 Graded-index waveguides .............................. 375
10.10 The alpha profiles: An important class of multimode
graded-index fibers .................................. 380
10.11 Attenuation in optical fibers ........................ 385
10.12 Further applications and suggested reading ........... 389
References .................................................... 395
11 Retarded potentials ........................................ 397
11.1 Introduction ......................................... 397
11.2 Green's functions for the scalar Helmholtz
equation ............................................. 398
11.3 Lorentz-gauge vector potentials in a homogeneous
medium ............................................... 401
11.4 Field vectors in terms of dyadic Green's functions ... 404
11.5 Inhomogeneous media: Polarization currents ........... 406
11.6 Time-domain interpretation of Green's functions ...... 407
11.7 Green's function expansion into orthogonal
eigenfunctions ....................................... 410
11.8 An example: Field in a rectangular box ............... 412
11.9 Spherical harmonics .................................. 414
11.10 Multipole expansion .................................. 420
11.11 An introduction to cylindrical harmonics ............. 424
11.12 Further applications and suggested reading ........... 426
References .................................................... 431
12 Fundamentals of antenna theory ............................. 433
12.1 Introduction ......................................... 433
12.2 Equivalent dipole moment of an extended source ....... 435
12.3 Far-field approximations ............................. 437
12.4 First example: Short electric-current element ........ 439
12.5 Characterization of antennas ......................... 444
12.6 Behavior of receiving antennas. Reciprocity .......... 448
12.7 Examples ............................................. 454
12.8 Antenna arrays ....................................... 464
12.9 Broad-side and end-fire arrays ....................... 469
12.10 Further applications and suggested reading ........... 471
References .................................................... 477
13 Diffraction ................................................ 479
13.1 Introduction ......................................... 479
13.2 The diffraction integral: The vector formulation ..... 479
13.3 Illumination conditions. Babinet's principle ......... 484
13.4 The scalar theory of diffraction ..................... 488
13.5 Diffraction formulas and Rayleigh-Sommerfeld ......... 493
13.6 The Fresnel diffraction region ....................... 495
13.7 The Fraunhofer diffraction region .................... 497
13.8 Examples ............................................. 500
13.9 The field near a focus: First example of Fresnel
diffraction .......................................... 508
13.10 Diffraction from a straight edge: Second example of
Fresnel diffraction .................................. 510
13.11 A short note on the geometrical theory of
diffraction .......................................... 515
13.12 Further applications and suggested reading ........... 516
References .................................................... 521
14 An introduction to the theory of coherence ................. 523
14.1 Background and purpose of the chapter ................ 523
14.2 The analytical signal ................................ 523
14.3 Complex degree of coherence .......................... 526
14.4 Temporal coherence of a source ....................... 527
14.5 Spatial coherence of a source ........................ 529
14.6 Higher-order coherence: An introduction .............. 531
14.7 An introduction to photocount distributions .......... 535
14.8 Modal noise in optical-fiber transmission systems:
A short outline ...................................... 539
14.9 Further applications and suggested reading ........... 540
References .................................................... 545
Appendices .................................................... 547
A Vector calculus: Definitions and fundamental theorems ...... 549
В Vector differential operators in frequently used
reference systems .......................................... 553
С Vector identities .......................................... 555
D Fundamentals on Bessel functions ........................... 557
D.1 Bessel, Neumann and Hankel functions ................. 557
D.2 Modified Bessel functions ............................ 560
D.3 Bessel function formulas ............................. 561
References .................................................... 565
Further Suggested Reading ..................................... 567
Index ......................................................... 568
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