Preface to the First Edition ................................... xv
Preface to the Second Edition ................................. xix
Chapter 1. Basic Equations for Electromagnetic Fields .......... 1
1.1 Maxwell's Equations ......................................... 1
1.2 Wave Equations .............................................. 3
1.3 Conservation Laws ........................................... 4
1.4 Scalar Theory of Optical Problems ........................... 6
1.5 Lorentz's Reciprocity Theorem ............................... 7
1.6 Integral Equations for the Electromagnetic Field.
The Extinction Theorem ...................................... 8
1.6.1 The vector form of Green's theorem .................... 9
1.6.2 Integral theorems .................................... 10
1.6.3 Integral theorems for scalar fields .................. 13
1.6.4 Natural modes ........................................ 15
1.6.5 Other extensions and uses of the extinction
theorem .............................................. 15
Problems ....................................................... 16
References ..................................................... 17
Appendix 1.1: A Generalized Extinction Theorem and Its Role
in Scattering Theory ............................. 18
Chapter 2. Angular Spectrum Representation of Wavefields ...... 33
2.1 Introduction .............................................. 33
2.2 Expansion of Scalar Wavefields into Plane Waves in
Source-Free Regions ....................................... 34
2.3 Connection between U(x,y,z) and its Boundary Value at
z = 0 ..................................................... 36
2.4 Wavelength Resolution Limit ............................... 38
2.5 On the Validity of the Angular Spectrum Representation .... 39
2.6 An Alternative Representation in Angular Variables ........ 40
2.7 Source-Free Fields ........................................ 41
2.7.1 Source-free fields satisfying the homogeneous
Helmholtz equation everywhere and having
components propagating in all directions ........... 42
2.7.2 Source-free fields propagating in a half-space ..... 44
2.8 Asymptotic Approximation to Source-Free Fields ............ 45
2.8.1 Fields propagating in a half-space free of
sources ............................................ 45
2.8.2 Fields satisfying the Helmholtz equation
everywhere and with angular components
propagating in all directions ...................... 47
2.9 Angular Spectrum Representation of Electromagnetic
Fields .................................................... 47
2.10 Divergent and Convergent Spherical Waves and their
Angular Spectrum Representation ........................... 48
2.11 Optical Beams: Diffraction-Free Beams ..................... 51
2.12 Asymptotic Approximations to Angular Spectrum
Representations ........................................... 55
2.12.1 Approximations for 0 < θ < π/2, 0 ≤ ф ≤ 2π ......... 56
2.12.2 Approximations for θ = π/2 ......................... 56
2.12.3 Approximations in the axial direction .............. 57
2.13 Contribution of the Evanescent Components in
the Asymptotic Expressions ................................ 58
Problems ....................................................... 65
References ..................................................... 70
Chapter 3. Radiated and Scattered Fields ...................... 73
3.1 Radiated Fields from a Localized Charge-Current
Distribution .............................................. 74
3.2 Angular Spectrum Representation of Radiated Fields ........ 74
3.3 The Field and the Intensity Radiated in the Far Zone ...... 76
3.4 Scalar Theory of Radiated Wavefields ...................... 77
3.5 Examples of Radiation Fields: Charged Particle with
Two-Dimensional Motion .................................... 78
3.5.1 Field due to a charged particle moving in vacuum .... 79
3.5.2 Particle moving uniformly in vacuum ................. 81
3.5.3 Čerenkov radiation .................................. 83
3.6 Integro-Differential Equations for the Scattered
Electromagnetic Field in a Time-Independent Medium.
Angular Spectrum Representation Outside the Strip
0 < z < L ................................................. 86
3.7 Angular Spectrum Representation of the Scattered
Electromagnetic Field Inside the Strip 0 < z < L .......... 88
3.7.1 Scattered field outside the scattering volume ...... 88
3.7.2 Scattered field inside the scattering volume.
The slowly varying amplitude approximation ......... 91
3.8 The First Born Approximation .............................. 94
3.9 Scattering from a Weakly Fluctuating Random Medium ........ 97
3.10 Scalar Approach to Scattered Scalar Wavefields ........... 100
3.10.1 The first Born approximation for scalar
wavefields ........................................ 102
3.10.2 The Rytov approximation ........................... 103
3.10.3 The Eikonal approximation ......................... 105
3.11 Multiple Scattering Theories ............................. 108
Problems ...................................................... 109
References .................................................... 114
Chapter 4. Mathematical Properties of Radiated and
Scattered Fields .................................. 117
4.1 Introduction .............................................. 117
4.2 The Angular Spectrum of Wavefields in Free-Space as
the Boundary Value of an Entire Function .................. 117
4.3 Consequences for Radiated and Scattered Fields ............ 118
4.4 Consequences for Homogeneous and Evanescent Components .... 121
4.5 Consequences for Source-Free Fields ....................... 124
4.6 Conclusions and Extensions ................................ 125
Problems ...................................................... 126
References .................................................... 127
Appendix 4.1: Entire Functions of Exponential Type ............ 128
Appendix 4.2: Dispersion Relations ............................ 133
Appendix 4.3: The Whittaker-Shannon Sampling Theorem .......... 137
Chapter 5. S-Matrix and Reciprocity .......................... 138
5.1 Representation of Fields Outside a Scatterer ............. 139
5.2 Definition of the S-Matrix ............................... 143
5.3 Reciprocity and Unitarity ................................ 143
5.4 The S-Matrix for Scalar Wavefields ....................... 145
5.5 The Partitioned S-Matrix ................................. 146
5.6 Incident Plane Wave ...................................... 149
5.7 Incident Source-Free Field ............................... 150
5.8 The Generalized Transmission and Reflection
Coefficients ............................................. 151
5.9 The Transition Matrix .................................... 153
5.10 The Generalized Transmission and Reflection
Coefficients for an Incident Source-Free Field ........... 154
5.11 The Generalized Stokes Relations ......................... 158
5.12 Example: Stokes Relations for Stratified Media ........... 161
5.13 Reciprocity of the Impulse Response for Scattering from
Inhomogeneous Media ...................................... 164
5.13.1 Definition of the impulse response ................ 164
5.13.2 Reciprocity relations ............................. 167
Problems ...................................................... 168
References .................................................... 170
Chapter 6. Elements of the Theory of Diffraction ............. 171
6.1 The Scalar Theory of Diffraction ......................... 172
6.2 Uniqueness of the Solution. Boundary Conditions .......... 174
6.3 The Kirchhoff Approximation .............................. 175
6.4 The Rayleigh-Sommerfeld Diffraction Integrals ............ 177
6.5 The Rayleigh-Sommerfeld Integrals and the Angular
Spectrum Representation .................................. 180
6.6 Reciprocity, Diffraction for Small Angles ................ 182
6.7 The Fresnel Approximation ................................ 185
6.8 The Fraunhofer Approximation ............................. 188
6.9 Comparison with the Angular Spectrum Representation ...... 189
6.9.1 Fresnel approximation .............................. 189
6.9.2 Fraunhofer approximation ........................... 190
6.10 Example: Scalar Theory of Diffraction by a Circular
Aperture ................................................. 191
6.11 Theory of the Boundary Diffraction Wave .................. 193
6.11.1 The vector potential .............................. 193
6.11.2 A mathematically consistent interpretation of
the Kirchhoff diffraction integral ................ 197
6.12 Comparison with Experiment ............................... 198
6.13 Debye Approximation. Symmetries of Focused Wavefields
and Phase Anomaly Near the Focus ......................... 201
6.14 Vector Theory of Diffraction ............................. 205
6.15 Uniqueness of the Electromagnetic Solution.
Boundary Conditions ...................................... 207
6.16 Three Vector Formulations of Diffraction ................. 208
6.17 The Fraunhofer Approximation for the Vector Solution.
Comparison with the Scalar Result ........................ 209
6.18 Diffraction Problems and the Extinction Theorem .......... 211
Problems ...................................................... 212
References .................................................... 215
Chapter 7. Scattering from Rough Surfaces .................... 217
7.1 Introduction ............................................. 217
7.2 Statistical Characterization of Random Rough Surfaces .... 219
7.3 Boundary Condition for Scattering from Perfectly
Conductive Surfaces ...................................... 219
7.4 Angular Spectrum Representation .......................... 220
7.5 The Kirchhoff Approximation .............................. 222
7.5.1 Example: scattering of a linearly polarized
plane wave ........................................ 225
7.5.2 The mean scattered intensity ...................... 226
7.5.3 On the validity of the Kirchhoff approximation .... 228
7.6 The Method of Small Perturbations ........................ 231
7.6.1 Expansions for the mean scattered intensity ....... 233
7.6.2 On the range of validity of the method of small
perturbations ..................................... 235
7.7 The Rayleigh Method ...................................... 242
7.8 Illustration of the Scattering Equations for
One-Dimensional Surfaces ................................. 244
7.9 Numerical Solution of the Scattering Equations ........... 246
7.9.1 Numerical generation of random surfaces ........... 246
7.9.2 Numerical calculation of the scattering
integrals ......................................... 247
7.10 Scattering from Deeply Rough Surfaces.
Enhanced Backscattering .................................. 249
7.10.1 Comparison of experimental data and numerical
results from one-dimensional surfaces ............. 252
7.11 Scattering from Metal and Dielectric Rough Surfaces ...... 253
7.11.1 Example: one-dimensional surfaces ................. 256
7.12 Diffraction from Periodic Surfaces: Reflection
Gratings ................................................. 261
7.13 Variation of the Diffracted Intensities .................. 265
Problems ...................................................... 268
References .................................................... 271
Chapter 8. Propagation and Scattering of Phase-Conjugate
Wavefields ........................................ 275
8.1 Introduction .............................................. 276
8.2 Phase-Conjugation of Wavefields Propagating in Free
Space ..................................................... 279
8.2.1 Phase-conjugation of fields that propagate into
the same half-space ................................. 279
8.2.2 Phase-conjugation of fields that propagate into
complementary half-spaces ........................... 284
8.3 Scattering and Distortion Correction by
Phase-Conjugation ......................................... 288
8.3.1 Self-consistent formulation ......................... 291
8.3.2 Multiple bounce approach ............................ 293
8.4 Other Studies ............................................. 296
Problems ...................................................... 297
References .................................................... 300
Chapter 9. Inverse Diffraction ............................... 302
9.1 The Inverse Wavefleld Propagator ......................... 303
9.2 Alternative Form of the Inverse Propagator ............... 305
9.3 Inversion Formula for Fields without Evanescent
Components ............................................... 306
9.4 Connection with the Reciprocity Theorem of
Phase-Conjugated Wavefields .............................. 306
9.5 Connection with the Pseudoscopic Image in Holography ..... 307
9.6 System Approach to Inverse Diffraction ................... 310
9.7 Degrees of Freedom ....................................... 312
9.8 Representation by Eigenfunctions ......................... 314
9.9 Ill-Posed Nature of Inverse Diffraction .................. 316
9.10 The Problem of Phase Retrieval ........................... 319
9.11 Conclusions and Other Studies ............................ 321
Problems ...................................................... 322
References .................................................... 323
Chapter 10. Inverse Source and Scattering Problems in
Optics ............................................ 326
10.1 Introduction ............................................. 326
10.2 Formulation of Inverse Source and Scattering Problems .... 328
10.3 Information Content of One Experiment .................... 330
10.4 Integral Equations for Fields over Arbitrary Surfaces .... 334
10.4.1 Vector theory ..................................... 334
10.4.2 Scalar theory ..................................... 336
10.5 Information Contained in the Imaging Equation.
Physical Meaning of the Backpropagation Equation .............. 337
10.6 Ambiguity in Inverse Source and Scattering Problems.
Nonradiating Sources and Nonscattering Scatterers ........ 340
10.6.1 Eigenfunction analysis ............................ 343
10.7 Reconstruction Using Fourier Series ...................... 345
10.8 Diffraction Tomography ................................... 347
10.8.1 The central slice theorem ......................... 347
10.8.2 Principles of computed tomography ................. 349
10.8.3 The basic equation of diffraction tomography ...... 351
10.8.4 The filtered backpropagation equation ............. 352
10.8.5 The geometrical optics limit ...................... 356
10.8.6 An example ........................................ 357
10.9 Other Inverse Scattering Methods Multiple Scattering
Approaches ............................................... 358
Problems ...................................................... 361
References .................................................... 362
Chapter 11. Fundamentals of Near Field Optics (NFO) ........... 366
11.1 Introduction ............................................ 367
11.2 The Optical Signal at the Tip ........................... 369
11.3 Inverse Scattering Problem in Near Field Optics ......... 371
11.4 Inverse Scattering. Coherence. Artifacts ................ 373
11.5 Surface Plasmon Polaritons .............................. 375
11.5.1 An example of existence of surface polariton
excitations ..................................... 379
11.6 Reciprocity and Unitarity of the S-Matrix of Fields
Containing Evanescent Components ........................ 382
11.6.1 Transmission and reflection coefficients
containing evanescent components ........................ 383
11.6.2 Reciprocity relations for transmission and
reflection coefficients with evanescent
components ...................................... 385
11.6.3 Reciprocity relations for the S-matrix .......... 387
11.7 Time-Reversal Symmetry of the S-Matrix of Fields
Containing Evanescent Components ........................ 390
11.7.1 Time-reversal invariance. Consequence for
the S-matrix .................................... 390
11.7.2 Time-reversal invariance and reciprocity ........ 391
11.8 Superresolution by Near Field Propagation in
Left-Handed Material Slabs .............................. 392
11.9 Slab of Ideal Dispersiveless and Absorptionless
Left-Handed Material .................................... 394
11.9.1 Field inside a left-handed medium ............... 394
11.9.2 Field transmitted by a slab of lossless
left-handed material ............................ 396
11.9.3 Singularity of the propagator inside the slab
of left-handed material ......................... 397
11.10 Field Transmitted by an Absorbing Slab.
Image Resolution ........................................ 400
11.10.1 Resolution of the LHM slab lens and
the inverse diffraction propagator .............. 403
Problems ...................................................... 407
Appendix 11.1: Lorentz's Reciprocity Theorem with Sources ..... 407
Appendix 11.2: Generalized Stokes Relations for Fields
Containing Evanescent Components ............... 408
References .................................................... 409
Author Index .................................................. 415
Subject Index ................................................. 423
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