Electromagnetic Waves in Stratified Media (eBook)

Front Cover 1
Electromagnetic Waves in Stratified Media 4
Copyright Page 5
Table of Contents 8
PREFACE TO SECOND EDITION 13
PREFACE TO FIRST EDITION 13
Chapter I. GENERAL INTRODUCTION 14
1. SCOPE OF THE SUBJECT 14
2. NOTATION AND SOME BASIC IDEAS 15
3. SUMMARY OF SUBJECT MATTER IN FOLLOWING CHAPTERS 17
GENERAL REFERENCES 19
Chapter II. REFLECTION OF ELECTROMAGNETIC WAVES FROM HORIZONTALLY STRATIFIED MEDIA 21
1. INTRODUCTION 21
2. PLANE WAVE INCIDENCE 23
3. EXTENSION TO PERPENDICULAR INCIDENCE 28
4. IMPEDANCE MATCHING AND NATURAL OSCILLATIONS IN STRATIFIED MEDIA 30
5. LINE SOURCE EXCITATION 34
6. LINE SOURCE ON A HOMOGENEOUS MEDIUM 38
7. LINE SOURCE OVER A THIN LAYER 40
8. THE RADIATION FIELD OF THE LINE SOURCE FOR ANY NUMBER OF LAYERS 44
9. MAGNETIC LINE SOURCE OVER A STRATIFIED MEDIUM 45
10. MAGNETIC LINE SOURCE OVER A DIELECTRIC COATED CONDUCTOR 46
11. THE FIELDS OF A VERTICAL ELECTRIC DIPOLE OVER A STRATIFIED HALF-SPACE 48
12. SOME EXPERIMENTAL MEASUREMENTS 58
Appendix A: EVALUATION OF THE INTEGRAL P 61
Appendix B: NUMERICAL RESULTS FOR SURFACE IMPEDANCE OF A STRATIFIED CONDUCTOR 66
REFERENCES 75
Chapter III. REFLECTION OF ELECTROMAGNETIC WAVES FROM INHOMOGENEOUS MEDIA WITH SPECIAL PROFILES 77
1. INTRODUCTION 77
2. GENERAL CONSIDERATIONS 77
3. INVERSE SQUARE PROFILE 78
4. PROFILE WITH AN EXPONENTIAL TRANSITION 81
5. OTHER EXPONENTIAL PROFILES 83
6. LINEAR PROFILE 88
7. EXTENSION TO VERTICAL POLARIZATION 91
8. EXPONENTIAL PROFILE WITH VERTICAL POLARIZATION 92
9. POWER LAW PROFILE FOR NORMAL INCIDENCE 94
REFERENCES 97
Chapter IV. APPROXIMATE METHODS FOR TREATING REFLECTIONS FROM INHOMOGENEOUS MEDIA 99
1. INTRODUCTION AND THE CONVENTIONAL WKB METHOD 99
2. WKB METHOD FOR OBLIQUE INCIDENCE 100
3. GENERALIZATION OF WKB METHOD 101
4. GENERALIZED WKB METHOD FOR VERTICAL POLARIZATION 103
5. RELATION TO GEOMETRICAL OPTICS 104
6. APPLICATION TO TROPOSPHERIC PROPAGATION 106
7. THE PHASE INTEGRAL APPROACH 108
8. A GENERALIZATION OF THE PHASE INTEGRAL METHOD 111
9. PHASE INTEGRAL FOR VERTICAL POLARIZATION 112
10. RAPIDLY VARYING TRANSITION REGION 113
REFERENCES 118
Chapter V. PROPAGATION ALONG A SPHERICAL SURFACE 120
1. BASIC FORMULATION 120
2. THE WATSON TRANSFORMATION 123
3. FORMULA FOR SMALL CURVATURE 126
4. INFLUENCE OF AN INHOMOGENEOUS ATMOSPHERE 128
5. EQUIVALENT EARTH RADIUS CONCEPT 130
6. EXTENSION TO NON-LINEAR ATMOSPHERE 131
7. ASYMPTOTIC FORM OF THE SOLUTION 135
8. DISTANCE TO THE HORIZON 137
9. CONCLUDING REMARKS 141
REFERENCES 143
Chapter VI. FUNDAMENTALS OF MODE THEORY OF WAVE PROPAGATION 145
1. INTRODUCTION 145
2. BASIC CONCEPTS 147
3. FORMULATION FOR FLAT EARTH 150
4. PROPERTIES OF THE MODES FOR FLAT EARTH CASE 160
5. INFLUENCE OF EARTH CURVATURE 166
6. MODE SERIES FOR A CURVED EARTH 170
7. ANTI-PODAL EFFECTS 175
8. RESONATOR-TYPE OSCILLATIONS BETWEEN EARTH AND THE IONOSPHERE 176
9. EXCITATION BY HORIZONTAL DIPOLES FOR THE CURVED EARTH 181
10. HIGHER APPROXIMATIONS TO THE CURVED EARTH THEORY 187
11. INFLUENCE OF STRATIFICATION AT THE LOWER EDGE OF THE IONOSPHERE 195
12. AVERAGE DECAY LAWS 200
13. APPENDIX 206
REFERENCES 206
Chapter VII. CHARACTERISTICS OF THE MODES FOR V.L.F. PROPAGATION 209
1. INTRODUCTION 209
2. THE GROUND WAVE 209
3. THE SKY WAVES 210
4. THE ROOTS OF THE MODAL EQUATION! 214
5. COMMENTS ON A MORE ACCURATE FORM OF THE MODE EQUATION 226
6. THE HEIGHT-GAIN FUNCTIONS 231
7. THE EXCITATION OF V.L.F. MODES 234
8. DISCUSSION OF THE EARTH DETACHED MODE 237
REFERENCES 238
Chapter VIII. PROPAGATION IN STRATIFIED MAGNETO-PLASMA MEDIA 239
1. INTRODUCTION 239
2. THE DIELECTRIC PROPERTIES OF A PLASMA 240
3. THE FIELD EQUATIONS 243
4. REFLECTION COEFFICIENT FOR A PLANE BOUNDARY BETWEEN FREE SPACE AND PLASMA 244
5. REFLECTION FROM A STRATIFIED PLASMA 246
6. ARBITRARY INCLINATION OF MAGNETIC FIELD 249
7. REFLECTION FROM A HOMOGENEOUS PLASMA WITH ARBITRARY MAGNETIC FIELD 252
8. DERIVATION OF APPROXIMATE REFLECTION COEFFICIENTS 256
9. THE MODE SERIES FOR AN ANISOTROPIC IONOSPHERE 259
10. EFFECT OF EARTH CURVATURE 264
Appendix A 267
Appendix B 269
Appendix C 273
REFERENCES 275
Chapter IX. V.L.F. PROPAGATION—THEORY AND EXPERIMENT 277
1. INTRODUCTION 277
2. APPROXIMATE SOLUTIONS OF THE MODE EQUATION 277
3. MEASURED FIELD STRENGTH VS. DISTANCE DATA AT V.L.F. 290
4. MEASURED PHASE CHARACTERISTICS OF V.L.F. CARRIERS 294
5. MEASUREMENTS OF DIURNAL PHASE SHIFTS AT V.L.F. 297
6. SFERICS AND MODE THEORY 298
REFERENCES 300
Chapter X. E.L.F. (EXTREMELY LOW FREQUENCY) PROPAGATION—THEORY AND EXPERIMENT 302
1. INTRODUCTION 302
2. BASIC THEORETICAL MODEL 302
3. ANTIPODAL EFFECTS 304
4. EARTH-FLATTENING APPROXIMATION 304
5. DISTANCE AND FREQUENCY DEPENDENCE 308
6. NEAR FIELD BEHAVIOR 311
7. EFFECT OF THE EARTH'S MAGNETIC FIELD 313
8. EFFECT OF AN INHOMOGENEOUS ATMOSPHERE 319
9. PROPAGATION OF E.L.F. PULSES 322
10. INTERPRETATION OF HEPBURN'S EXPERIMENTAL DATA 326
11. INFLUENCE OF HORIZONTAL CURRENTS 328
Appendix: SURFACE IMPEDANCE OF A SPHERICALLY STRATIFIED CONDUCTOR 331
REFERENCES 334
Chapter XI. ASYMPTOTIC DEVELOPMENT FOR GUIDED WAVE PROPAGATION 337
1. INTRODUCTION 337
2. FORMULATION OF PROBLEM 337
3. THE COMPLEX INTEGRAL REPRESENTATION 338
4. THE MODE REPRESENTATION 341
5. RAY THEORY AND SADDLE POINT APPROXIMATIONS 342
6. RELATION TO GEOMETRICAL OPTICS 345
7. TREATMENT AT THE CAUSTIC 349
8. APPLICATIONS TO TROPOSPHERIC PROPAGATION 351
9. CONCLUDING REMARKS 352
REFERENCES 353
Chapter XII. SUPERREFRACTION AND THE THEORY OF TROPOSPHERIC DUCTING 354
1. INTRODUCTION 354
2. FORMULATION 354
3. THE ASYMPTOTIC SOLUTION 356
4. THE SPECIAL CASE OF A NORMAL ATMOSPHERE 357
5. REDUCTION TO RAY THEORY FOR "NORMAL" ATMOSPHERE 359
6. EXTENSION OF THEORY TO INCLUDE SUPERREFRACTION 361
7. REFINEMENTS TO THE ASYMPTOTIC APPROXIMATIONS 364
8. A FEW QUANTITATIVE RESULTS FOR TROPOSPHERIC DUCTING 367
9. REDUCTION TO THE PHASE INTEGRAL FORM 369
10. THE MODIFIED INDEX OF REFRACTION METHOD 371
REFERENCES 376
Chapter XIII. APPENDIX—SUPPLEMENTARY MATERIAL 378
1. Influence of the Lower Ionosphere on Propagation of VLF Waves to Great Distances] 380
2. VLF Mode Problem for an Anisotropie Curved Ionosphere 404
3. Reflection of VLF Radio Waves from an Inhomogeneous Ionosphere. Part I Exponentially Varying Isotropìe Model 416
4. Reflection of VLF Radio Waves from an Inhomogeneous Ionosphere. Part II. Perturbed Exponential Model 430
5. Reflection of VLF Radio Waves from an Inhomogeneous Ionosphere. Part III. Exponential Model with Hyperbolic Transition 442
6. Some Remarks on Mode and Ray Theories of VLF Radio Propagation 454
7. Two-Dimensional Treatment of Mode Theory of the Propagation of VLF Radio Waves 458
8. Reflection of Electromagnetic Waves from a Lossy Magnetoplasma 476
9. A Note on VHF Reflection from a Tropospheric Layer 490
10. Concerning the Mechanism of Reflection of Electromagnetic Waves from an Inhomogeneous Lossy Plasma 494
11. Influence of an Inhomogeneous Ground on the Propagation of VLF Radio Waves in the Earth-ionosphere Waveguide 504
12. Propagation in a Model Terrestrial Waveguide of Nonuniform Height: Theory and Experiment 518
13. Transverse Propagation of Waveguide Modes in a Cylindrically Stratified Magnetoplasma 542
14. Cavity Resonator Modes in a Cylindrically Stratified Magnetoplasma 558
15. Electromagnetic Propagation in an Idealized Earth Crust Waveguide 564
16. Illumination of an Inhomogeneous Spherical Earth by an LF Plane Electromagnetic Wave 578
17. Radiation from Dipoles in an Idealized Jungle Environment 588
18. Comments on a Paper "A Numerical Investigation of Classical Approximations Used in VLF Propagation" by R. A. Papperty E. E. Gossard, and I. J. Rothmuller 594
19. On the Calculation of Mode Conversion at a Graded Height Change in the Earth-ionosphere Waveguide at VLF 596
Errata and Addenda 606
AUTHOR INDEX 612
SUBJECT INDEX 616