Electromagnetic Wave Theory (eBook)

Front Cover 1
Electromagnetic Wave Theory, Part 2 4
Copyright Page 5
Table of Contents 6
SECTION D: PROPAGATION IN NON-LINEAR MEDIA 10
CHAPTER 1. THE PARAMETRIC COUPLING OF MODES OF PROPAGATION IN NONLINEAR MEDIA 10
I. INTRODUCTION 10
II. ANALYSIS 13
III. PREDICTIONS OF PARAMETRIC INTERACTIONS 17
IV. RESULTS OF COMPUTATIONS 25
V. CONCLUSION 33
REFERENCES 34
CHAPTER 2. SYMMETRY RESTRICTIONS IN NON-LINEAR, NON-ABSORBING, NON-DISPERSIVE MEDIA 36
1. INTRODUCTION 36
2. NON-DISPERSIVE, NON-ABSORBING MEDIA 37
APPENDIX 39
REFERENCES 40
CHAPTER 3. ON ELECTROMAGNETIC WAVE PROPAGATION AND AMPLIFICATION IN SOLID-STATE PLASMAS 42
1. WAVE PROPAGATION IN BISMUTH 42
2. DISPERSION LAW 43
3. THE AMPLIFICATION OF OSCILLATIONS 45
REFERENCES 47
CHAPTER 4. PROPAGATION OF MODULATED WAVES IN NONLINEAR DISPERSIVE MEDIA 48
REFERENCES 52
CHAPTER 5. ELECTROMAGNETIC WAVES IN NONLINEAR TRANSMISSION LINES WITH ACTIVE PARAMETERS 54
A. STATIONARY WAVES IN AN INFINITE LINE 54
B. AUTO-OSCILLATIONS IN ACTIVE LINES OF FINITE LENGTH 60
REFERENCES 62
CHAPTER 6. NONLINEAR INTERACTION BETWEEN TWO BEAMS OF PLANE ELECTROMAGNETIC WAVES IN AN ANISOTROPIC MEDIUM 64
INTRODUCTION 64
THE LINEAR WAVE EQUATION 65
GROUP VELOCITY AND ENERGY TRANSPORT 67
INTERACTION BETWEEN TWO BEAMS OF INTENSE LIGHT IN A UNIAXIAL CRYSTAL 69
THE GREEN'S DYADIC 70
THE ASYMPTOTIC GREEN'S DYADIC 71
RESONANCE CONDITIONS 73
DISCUSSION OF THE RESONANCE CONDITIONS 74
BEAM WIDTH OF SCATTERED WAVE 77
NUMERICAL EXAMPLE 77
CONCLUSIONS 78
REFERENCES 78
CHAPTER 7. THE PHASE DEPENDENCE OF MASER ACTIVE MATERIAL Q-FACTOR UPON THE PUMP INTENSITY AND FREQUENCY 80
SUMMARY 80
CHAPTER 8. RADIATION IN PERIODICALLY-NONSTATIONARY MEDIA 82
SUMMARY 82
CHAPTER 9. ELECTROMAGNETIC WAVE PROPAGATION IN TIME-VARYING MEDIA 86
SUMMARY 86
REFERENCES 88
CHAPTER 10. THE STRUCTURE OF A SHOCK ELECTROMAGNETIC WAVE FRONT IN TRANSMISSION LINES WITH NONLINEAR PARAMETERS 90
SUMMARY 90
CHAPTER 11. NON-LINEAR DIFFRACTION NEAR THE FOCUS OF A CONVERGING WAVE 92
INTRODUCTION 92
ASSUMPTIONS 92
SOLUTION OF THE NON-LINEAR PROBLEM IN THE FOCAL PLANE AND ALONG THE AXIS 93
CONCLUDING REMARKS 95
REFERENCES 96
CHAPTER 12. NONLINEAR SCATTERING BY A PLASMA CYLINDER 98
SUMMARY 98
REFERENCES 99
SECTION E: ANTENNAS 100
CHAPTER 1. EXPERIMENTAL THEORETICAL EVALUATION OF A PASSIVE COMMUNICATIONS SATELLITE (ECHO II) 100
1. INTRODUCTION 100
2. SMALL SEGMENT MEASUREMENTS 101
3. MATHEMATICAL MODEL OF THE BALLOON 105
4. FULL-SCALE BALLOON MEASUREMENT, PRIOR TO FLIGHT 105
5. PRELUDE TO THE ORBITAL BALLOON 109
6. ECHO II ORBITAL FLIGHT RADAR DATA AND ANALYSIS 112
7. EFEFCTIVENESS AS A COMMUNICATION SATELLITE 116
8. COMMUNICATIONS EXPERIMENT 120
APPENDIX A 121
APPENDIX B 123
CHAPTER 2. MINIMUM SPOT SIZE OF FOCUSED APERTURES 128
I. INTRODUCTION 128
II. EDGE RAY THEORY 128
III. ARRAY CALCULATIONS 129
IV. AN HEURISTIC UNCERTAINTY ARGUMENT 132
REFERENCES 134
CHAPTER 3. RADIATION FROM THE PARABOLOID OF REVOLUTION 136
INTRODUCTION 136
I. SCATTERED RADIATION FROM THE MIRROR 137
IIa. THE RADIATED FIELD 144
IIb. RADIATION FROM A REFLECTOR WITH A DIPOLE FEED 145
IIc. THE EFFECT OF HIGHER ORDER TERMS OF THE EXPANSION 149
III. EXPERIMENTAL EQUIPMENT 150
REFERENCES 151
CHAPTER 4. LENTILLES ET REFLECTEURS BIDIMENSIONNELS A GRAND CHAMP ANGULAIRE 152
INTRODUCTION 152
1. ETUDE THEORIQUE DE SYSTEMES CENTRES A QUATRE FOYERS PARFAITS. 153
2. ETUDE EXPERIMENTALE D'UN REFLECTEUR A GRAND CHAMP ANGULAIRE 160
3. CONCLUSION 161
BIBLIOGRAPHIE 161
CHAPTER 5. SPHERICAL OMNIDIRECTIONAL ANTENNA 162
ACKNOWLEDGMENTS 167
REFERENCES 167
CHAPTER 6. DIFFRACTION REFLECTOR ANTENNAS 168
SUMMARY 168
REFERENCES 169
CHAPTER 7. THEORETICAL INVESTIGATION OF VAN ATTA REFLECTORS 170
SUMMARY 170
REFERENCES 172
CHAPTER 8. EXPERIMENTAL INVESTIGATION OF A LINEAR VAN ATTA REFLECTOR 174
SUMMARY 174
REFERENCES 177
CHAPTER 9. BEAM SCANNING BY A DUAL-MODE HORN ANTENNA 178
INTRODUCTION 178
1. RADIATION PATTERN 178
2. WAVEGUIDE APPARATUS FOR DUAL-MODE EXCITATION WITH CONSTANT . AND VARIABLE k 181
3. EXPERIMENTAL RESULTS 183
LITERATURE 184
CHAPTER 10. THE OPTIMIZATION OF THE RADIATION CHARACTERISTICS OF AN OPEN-ENDED WAVEGUIDE 186
REFERENCES 190
CHAPTER 11. ON THE SYNTHESIS PROBLEM FOR AN INFINITE CYLINDER WITH AN AXIAL SLOT 192
INTRODUCTION 192
FORMULATION OF THE PROBLEM 192
QUANTITATIVE RESULTS 194
REFERENCES 195
CHAPTER 12. AN ANALYSIS OF SURFACE WAVE ANTENNAS 196
1. INTRODUCTION 196
2. DERIVATION OF THE RADIATION PATTERN 197
3. LAUNCHING EFFIENCY 202
REFERENCES 205
CHAPTER 13. THE "BACKFIRE" -A HIGH-GAIN CAVITY ANTENNA 206
INTRODUCTION 206
STRUCTURE OF BACKFIRE ANTENNA 206
CAVITY CHARACTERISTICS OF BACKFIRE ANTENNA 208
GAIN OF BACKFIRE ANTENNA 209
PATTERNS OF BACK FIRE ANTENNA 213
DESIGN METHOD FOR BACKFIRE ANTENNAS 214
DISCUSSION OF RESULTS 215
REFERENCES 215
CHAPTER 14. A THEORETICAL STUDY OF THE CONICAL SPIRAL ANTENNA 218
INTRODUCTION 218
THE BACKFIRE BIFILAR HELICAL STRUCTURE 219
APPLICATION OF THE k-ß DIAGRAM TO THE TAPERED STRUCTURE 222
NUMERICAL CALCULATIONS 225
COMPARISON WITH EXPERIMENTAL AND OTHER RESULTS 227
CONCLUSIONS 231
ACKNOWLEDGEMENT 231
REFERENCES 231
CHAPTER 15. ANALYSIS AND SYNTHESIS OF APERTURE FIELDS OF LOG-PERIODIC ANTENNAS 234
1.0 INTRODUCTION 234
1.1 APERTURE FIELD ANALYSIS BY MEANS OF DISPERSION CURVES 235
2.0 MODE COUPLING ON AN L.P. STRUCTURE 237
2.1 COUPLED MODE THEORY FOR APERIODIC STRUCTURES 239
2.2 COUPLED MODES ON THE L.P. DIPOLE ANTENNA 241
3.0 APERTURE FIELD SYNTHESIS 246
3.1 EFFECT OF ELEMENT-TO-TRANSMISSION LINE IMPEDANCE RATIO 247
3.2 ELEMENT COUPLING NETWORKS 247
4.0 CONCLUSIONS 250
REFERENCES 251
CHAPTER 16. THE EQUIANGULAR SPIRAL PLANE EXCITED BY A VERTICAL DIPOLE 252
SUMMARY 252
REFERENCES 254
CHAPTER 17. LINEAR ARRAYS WITH UNEQUALLY-SPACED RADIATORS 256
INTRODUCTION 256
THE UNIFORMLY ILLUMINATED ARRAY 257
THE cos p/2x ILLUMINATED ARRAY 263
REFERENCES 264
CHAPTER 18. ANALYSIS AND SYNTHESIS OF THE RADIATING NEAR-FIELD OF ARRAY AND LINE SOURCE ANTENNAE 266
INTRODUCTION 266
1. BASIC OPERATIONS OF THE ANALOGUE COMPUTER 266
2. RADIATING NEAR-FIELD OF AN ARRAY ANTENNA 267
3. EXAMPLES OF COMPUTED RESULTS 269
4. RADIATING NEAR-FIELD OF A FOCUSED ARRAY ANTENNA 271
5. COMPARISON OF METHOD OF SECTION 4 WITH EXPERIMENTAL RESULTS 273
6. SYNTHESIS OF A DESIRED RADIATING NEAR-FIELD 275
7. CONCLUSION 278
REFERENCES 280
CHAPTER 19. A METHOD FOR SYNTHESIZING A COSECANT RADIATION PATTERN BY PHASE VARIATION OF A CONSTANT AMPLITUDE EQUISPACED LINEAR ARRAY 282
ACKNOWLEDGEMENT 287
REFERENCES 287
CHAPTER 20. OPTIMUM NONUNIFORMLY SPACED ANTENNA ARRAYS 288
SUMMARY 288
REFERENCES 290
CHAPTER 21. MOMENT GENERATED NONUNIFORM ARRAYS 292
SUMMARY 292
CHAPTER 22. IMPEDANCE OF LINEAR ANTENNA IN THE PRESENCE OF A STRATIFIED DIELECTRIC 294
SUMMARY 294
REFERENCES 298
CHAPTER 23. PREPARATION OF CONTINUOUSLY STRATIFIED MEDIUM FOR EXPERIMENTAL STUDIES ON RADIATION AND CIRCUIT PROPERTIES OF ANTENNAS IN DIFFERENT ENVIRONMENTS 300
SUMMARY 300
SECTION F: SCATTERING AND DIFFRACTION 302
CHAPTER 1. RECENT HIGHLIGHTS IN DIFFRACTION THEORY 302
REFERENCES 311
CHAPTER 2. ASYMPTOTIC THEORY OF TRANSIENTS 312
1. INTRODUCTION 312
2. ASYMPTOTIC EXPANSION OF THE SOLUTION OF THE PROBLEM WITH CONSTANT COEFFICIENTS 314
3. RAY METHODS 322
4. ASYMPTOTIC SOLUTION OF THE PROBLEM WITH NON-CONSTANT b(x) 327
APPENDIX: UNIFORM ASYMPTOTIC EXPANSION OF AN INTEGRAL WITH A STATIONARY POINT NEAR AN END POINT 331
REFERENCES 336
CHAPTER 3. ASYMPTOTIC EXPANSIONS OF SOLUTIONS OF INITIAL-BOUNDARY VALUE PROBLEMS FOR A DISPERSIVE HYPERBOLIC EQUATION 338
1. INTRODUCTION 338
2. SOLUTION BY THE RAY METHOD 340
3. ASYMPTOTIC EXPANSION OF THE EXACT SOLUTION 348
4. NUMERICAL COMPARISON OF THE EXACT AND ASYMPTOTIC SOLUTIONS 352
APPENDIX 355
REFERENCES 356
CHAPTER 4. LOW FREQUENCY SOLUTION OF ELECTROMAGNETIC SCATTERING PROBLEMS 358
1. INTRODUCTION 358
2. STATEMENT OF THE PROBLEM 359
3. STEVENSON'S METHOD 360
4. AN ALTERNATE APPROACH 364
5. SUMMARY OF RESULTS 367
APPENDIX 369
REFERENCES 372
CHAPTER 5. APPLICATION OF CONFORMAL MAPPING TO SCATTERING AND DIFFRACTION PROBLEMS 374
1. INTRODUCTION 374
2. INTEGRAL EQUATION 374
3. SCATTERING BY AN ALMOST CIRCULAR CYLINDER WITH SMOOTH SURFACE 375
4. EDGE DIFFRACTION 376
REFERENCES 381
CHAPTER 6. WAVE PROPAGATION NEAR A SMOOTHCAUSTIC 382
ADDED IN PROOF 384
CHAPTER 7. DIFFRACTION BY A TRANSPARENT ELLIPTICAL CYLINDER 386
INTRODUCTION 386
THE SCALAR PRODUCT OF THE ANGULAR FUNCTIONS 392
REFERENCES 395
CHAPTER 8. THE DIFFRACTION OF WAVES BY A PENETRABLE HALF-PLANE 398
REFERENCES 401
CHAPTER 9. CROSS-POLARIZED ELECTROMAGNETIC FIELDS DIFFRACTED BY KNIFE-EDGE OBSTACLES 402
1. INTRODUCTION 402
2. THEORY 402
3. EXPERIMENTAL ARRANGEMENT 408
4. COMPARISON OF EXPERIMENT AND THEORY 409
5. SUMMARY 411
REFERENCES 413
CHAPTER 10. THE SCATTERING OF A PLANE ELECTRO-MAGNETIC WAVE BY A PERFECTLY CONDUCTING SPHERICAL SHELL WITH A CONICAL HOLE 414
INTRODUCTION 414
1. SPACE DIVISION AND FIELD EXPANSION 414
2. BOUNDARY CONDITIONS 416
3. FORMAL SOLUTION 417
4. SCATTERED FIELD BY A FINITE CONE 420
REFERENCES 421
CHAPTER 11. SCATTERING OF MICROWAVES BY DIELECTRIC SLABS AND HOLLOW DIELECTRIC WEDGES 422
REFERENCES 423
CHAPTER 12. HIGH-FREQUENCY SCATTERING BY AN IMPENETRABLE SPHERE 424
SUMMARY 424
CHAPTER 13. ON TRANSITION FUNCTIONS OCCURRING IN THE THEORY OF DIFFRACTION IN INHOMOGENEOUS MEDIA 428
SUMMARY 428
CORRELATED SIGNALS FROM UNCORRELATED DISTRIBUTIONS OF SCATTERERS 430
1. INTRODUCTION 430
2. SCATTERING THEORY 431
3. RELATION TO SIGNAL STATISTICS 442
REFERENCES 444
CHAPTER 14. PROPAGATION IN RANDOM AND PERIODIC MEDIA 446
I. INTRODUCTION 446
II. FORMAL SOLUTION 447
CHAPTER 15. HIGH FREQUENCY WAVE PROPAGATION THROUGH DIELECTRIC IRREGULARITIES 456
1. INTRODUCTION 456
2. COMPARISON OF PRINCIPAL APPROXIMATIONS 456
3. THE CORRELATION FUNCTIONS OF B(r) 459
4. HIGHER ORDER CONTRIBUTIONS 460
5. COMMENT ON SIGNAL DISTRIBUTION 461
6. DISTORTION AND TIME DELAY OF FINITE PULSES 462
REFERENCES 463
CHAPTER 16. SCATTERING AND TRANSMISSION OF ELECTROMAGNETIC WAVES AT A STATISTICALLY ROUGH BOUNDARY BETWEEN TWO DIELECTRIC MEDIA 464
1. INTRODUCTION 464
2. SURFACE DESCRIPTION 465
3. BOUNDARY CONDITIONS 467
4. THE SCATTERED FIELDS 472
5. THE EMITTED FIELDS 476
6. SUMMARY 479
REFERENCES 479
CHAPTER 17. DIFFRACTION BY A HALF-PLANE IN THE TRANSVERSE PLANE OF A UNIAXIALLY ANISOTROPIC MEDIUM 480
SUMMARY 480
REFERENCES 481
CHAPTER 18. DIFFRACTION BY A WIDE APERTURE IN A MAGNETOIONIC MEDIUM 482
1. INTRODUCTION 482
2. DIFFRACTION BY A HALF-PLANE 482
3. DIFFRACTION BY AN APERTURE 484
4. NUMERICAL RESULTS 485
REFERENCES 486
CHAPTER 19. RESONANT ELECTROMAGNETIC SCATTERING FROM GYROTROPIC PLASMAS 488
SUMMARY 488
REFERENCES 490
CHAPTER 20. DIFFRACTION OF ELECTROMAGNETIC WAVES BY PLASMA STRUCTURES 492
RESONANCE PROPERTIES OF HOMOGENEOUS STRUCTURES WITH SHARP BOUNDARIES 492
BOUNDARY-DIFFUSENESS EFFECT 493
NOTE ON TONKS-DATTNER RESONANCES 493
CONCLUDING REMARKS 495
REFERENCES 495
CHAPTER 21. DIFFRACTION BY A SLIT OF INTERMEDIATE WIDTH IN AN ANISOTROPIC PLASMA 496
SUMMARY 496
REFERENCES 499
CHAPTER 22. SCATTERING FROM INHOMOGENEOUS, ANISOTROPIC PLASMA COLUMNS 500
REFERENCES 506
CHAPTER 23. SCATTERING OF SHORT ELECTROMAGNETIC WAVES BY A CIRCULAR CYLINDER OF WARM ENCLOSED PLASMA 508
SUMMARY 508
REFERENCES 511
SECTION G: STATISTICAL OPTICS AND COHERENCE 512
CHAPTER 1. LA FORMATION ET LE FILTRAGE DESIMAGES OPTIQUES 512
I. LA FORMATION DES IMAGES OPTIQUES ET LA TRANSFORMATION DE FOURIER 513
II. LE FILTRAGE OPTIQUE DES IMAGES 516
III. LES DÉVELOPPEMENTS RÉCENTS ET L'UTILISATION DES TECHNIQUES DE MODULATION OPTIQUE 519
BIBLIOGRAPHIE 519
CHAPTER 2. ÉTUDE DE CERTAINS PROBLÉMES D'OPTIQUE STATISTIQUE 522
ABSTRACT 522
I. INTRODUCTION 522
II. LE MODÉLE GAUSSIEN. PROPRIÉTÉS ET LIMITES 523
III. ÉTUDE D ' U N MODÉLE A INTENSITÉ CONSTANTE ET CALCUL DES MOMENTS D'ORDRE SUPERIEUR 524
IV. ÉXPÉRIENCES D'INTERFÉRENCES ET DE CORRÉLATION D'INTENSITÉ 526
V.ÉXPÉRIENCES DE BATTEMENTS OPTIQUES 526
VI. EXPÉRIENCES D'INTERFÉRENCES INSTANTANÉES 527
VII. CONCLUSION 529
RÉFÉRENCES 529
CHAPTER 3. COHERENT TRANSFER CHARACTERISTICS OF AN OPTICAL SYSTEM 530
REFERENCES 532
CHAPTER 4. SOME NEW THEOREMS ON COHERENCE FUNCTIONS AND ON CROSS-SPECTRAL DENSTITIES OF WAVEFIELDS 534
SUMMARY 534
REFERENCES 534
CHAPTER 5. SOME PROPERTIES OF HIGHER ORDER COHERENCE FUNCTIONS 536
INTRODUCTION 536
(M + N)TH ORDER CORRELATIONS 536
QUASI-MONOCHROMATIC FIELDS 539
REDUCED SPECTRAL DENSITY 539
ACKNOWLEDGMENT 542
REFERENCES 542
CHAPTER 6. A " T HERMOSTATIC" CALCULUS FOR SPACE- COHERENT ELECTROMAGNETIC RADIATION, AND ITS APPLICATION TO THE THEORY OF PARTIAL COHERENCE 544
MOTIVATION 544
A THERMOSTATIC CALCULUS FOR SPACE-COHERENT RADIATION 545
NONSTATISTICAL DERIVATION OF THE PARTIAL COHERENCE EQUATION 547
THE QUANTUM STATISTICAL BACKGROUND 548
REFERENCES 549
CHAPTER 7. RIGOROUS DIFFRACTION THEORY WITH PARTIALLY COHERENT ILLUMINATION 550
1. INTRODUCTION 550
2. EIGENFUNCTION EXPANSION METHOD FOR SOLUTION OF PARTIALLY COHERENT DIFFRACTION PROBLEMS 551
REFERENCES 554
CHAPTER 8. COHERENCE MEASUREMENT IN RADIO PROPAGATION 556
1. INTRODUCTION 556
2. THE PROBLEM OF MEASURING THE DEGREE OF COHERENCE 557
3. DESCRIPTION OF THE METHOD OF MEASUREMENT 558
4. SOME MEASURED RESULTS 561
5. CONCLUSIONS 562
APPENDIX 563
REFERENCES 565
CHAPTER 9. RECENT DEVELOPMENTS IN WAVEFRONT RECONSTRUCTION 566
SUMMARY 566