Waves and Fields in Inhomogenous Media

by Chew, Weng Cho

• ISBN13: 9780780347496
• ISBN10: 0780347498
• Edition: 1st
• Format: Paperback
• Copyright: 1999-02-02
• Publisher: Wiley-IEEE Press

Summary

Electrical Engineering/Electromagnetics Waves and Fields in Inhomogeneous Media A Volume in the IEEE Press Series on Electromagnetic Waves Donald G. Dudley, Series Editor "...it is one of the best wave propagation treatments to appear in many years." Gerardo G. Tango, CPG, Consulting Seismologist-Acoustician, Covington, LA This comprehensive text thoroughly covers fundamental wave propagation behaviors and computational techniques for waves in inhomogeneous media. The author describes powerful and sophisticated analytic and numerical methods to solve electromagnetic problems for complex media and geometry as well. Problems are presented as realistic models of actual situations which arise in the areas of optics, radio wave propagation, geophysical prospecting, nondestructive testing, biological sensing, and remote sensing. Key topics covered include: Analytical methods for planarly, cylindrically and spherically layered media Transient waves, including the Cagniard-de Hoop method Variational methods for the scalar wave equation and the electromagnetic wave equation Mode-matching techniques for inhomogeneous media The Dyadic Green's function and its role in simplifying problem-solving in inhomogeneous media Integral equation formulations and inverse problems Time domain techniques for inhomogeneous media This book will be of interest to electromagnetics and remote sensing engineers, physicists, scientists, and geophysicists. This IEEE Press reprinting of the 1990 version published by Van Nostrand Reinhold incorporates corrections and minor updating. Also in the series... Mathematical Foundations for Electromagnetic Theory by Donald G. Dudley, University of Arizona at Tucson This volume in the series lays the mathematical foundations for the study of advanced topics in electromagnetic theory. Important subjects covered include linear spaces, Green's functions, spectral expansions, electromagnetic source representations, and electromagnetic boundary value problems. 1994 Hardcover 264 pp ISBN 0-7803-1022-5 IEEE Order No. PC3715 About the Series The IEEE Press Series on Electromagnetic Waves consists of new titles as well as reprints and revisions of recognized classics that maintain long-term archival significance in electromagnetic waves and applications. Designed specifically for graduate students, practicing engineers, and researchers, this series provides affordable volumes that explore electromagnetic waves and applications beyond the undergraduate level.

Author Biography

Weng Cho Chew is the author of Waves and Fields in Inhomogenous Media, published by Wiley.

Table of Contents

Preface	xvii
Acknowledgments	xxi
Preliminary Background	1	(44)
Maxwell's Equations	1	(8)
Differential Representations	1	(2)
Integral Representations	3	(1)
Time Harmonic Forms	4	(1)
Constitutive Relations	5	(1)
Poynting Theorem and Lossless Conditions	6	(3)
Duality Principle	9	(1)
Scalar Wave Equations	9	(8)
Acoustic Wave Equation	10	(2)
Scalar Wave Equation from Electromagnetics	12	(1)
Cartesian Coordinates	12	(2)
Cylindrical Coordinates	14	(2)
Spherical Coordinates	16	(1)
Vector Wave Equations	17	(12)
Boundary Conditions	18	(2)
Reciprocity Theorem	20	(2)
Plane Wave in Homogeneous, Anisotropic Media	22	(2)
Green's Function	24	(5)
Huygens' Principle	29	(3)
Scalar Waves	29	(2)
Electromagnetic Waves	31	(1)
Uniqueness Theorem	32	(13)
Scalar Wave Equation	33	(2)
Vector Wave Equation	35	(2)
Exercises for Chapter 1	37	(4)
References for Chapter 1	41	(1)
Further Reading for Chapter 1	42	(3)
Planarly Layered Media	45	(116)
One-Dimensional Planar Inhomogeneity	45	(12)
Derivation of the Scalar Wave Equations	45	(3)
Reflection from a Half-Space	48	(1)
Reflection and Transmission in a Multilayered Medium	49	(4)
Ricatti Equation for Reflection Coefficients	53	(3)
Specific Inhomogeneous Profiles	56	(1)
Spectral Representations of Sources	57	(13)
A Line Source	58	(5)
A Point Source	63	(3)
Riemann Sheets and Branch Cuts	66	(4)
A Source on Top of a Layered Medium	70	(6)
Electric Dipole Fields	71	(3)
Magnetic Dipole Fields	74	(1)
The Transverse Field Components	75	(1)
A Source Embedded in a Layered Medium	76	(3)
Asymptotic Expansions of Integrals	79	(14)
Method of Stationary Phase	79	(3)
Method of Steepest Descent	82	(5)
Uniform Asymptotic Expansions	87	(6)
Dipole Over Layered Media---Asymptotic Expansions	93	(18)
Dipole Over Half-Space (VMD)	93	(5)
Dipole Over Half-Space (VED)	98	(3)
Dipole Over a Slab	101	(5)
Example of Uniform Asymptotic Expansion---Transmitted Wave in a Half-Space	106	(4)
Angular Spectrum Representation	110	(1)
Singularities of the Sommerfeld Integrals	111	(10)
Absence of Branch Points	112	(2)
Bounds on the Locations of Singularities	114	(4)
Numerical Integration of Sommerfeld Integrals	118	(3)
WKB Method	121	(7)
Derivation of the WKB Solution	121	(3)
Asymptotic Matching	124	(4)
Propagator Matrix	128	(5)
Derivation of the State Equation	129	(1)
Solution of the State Equation	129	(1)
Reflection from a Three-Layer Medium	130	(1)
Reflection from an Inhomogeneous Slab	131	(2)
Waves in Anisotropic, Layered Media	133	(28)
Derivation of the State Equation	133	(2)
Solution of the State Equation	135	(1)
Reflection from an Interface of Anisotropic Half Spaces	136	(1)
Reflection from a Slab	137	(1)
Geometrical Optics Series	138	(2)
Exercises for Chapter 2	140	(11)
References for Chapter 2	151	(4)
Further Readings for Chapter 2	155	(6)
Cylindrically and Spherically Layered Media	161	(50)
Cylindrically Layered Media---Single Interface Case	161	(6)
Vector Wave Equation in Cylindrical Coordinates	162	(1)
Reflection and Transmission of an Outgoing Wave	163	(2)
Reflection and Transmission of a Standing Wave	165	(2)
Cylindrically Layered Media---Multi-Interface Case	167	(5)
The Outgoing-Wave Case	167	(3)
The Standing-Wave Case	170	(2)
Source in a Cylindrically Layered Medium	172	(7)
Discrete, Angular-Wave-Number Representation	173	(4)
Continuum, Angular-Wave-Number Representation	177	(2)
Propagator Matrix---Cylindrical Layers	179	(5)
Isotropic, Layered Media	179	(3)
Anisotropic, Layered Media	182	(2)
Spherically Layered Media---Single Interface Case	184	(7)
Vector Wave Equation in Spherical Coordinates	185	(2)
Reflection and Transmission of an Outgoing Wave	187	(2)
Reflection and Transmission of a Standing Wave	189	(2)
Spherically Layered Media---Multi-Interface Case	191	(2)
The Outgoing-Wave Case	191	(1)
The Standing-Wave Case	192	(1)
Source in a Spherically Layered Medium	193	(4)
Propagator Matrix---Spherical Layers	197	(14)
Exercises for Chapter 3	199	(5)
References for Chapter 3	204	(2)
Further Readings for Chapter 3	206	(5)
Transients	211	(60)
Causality of Transient Response	211	(4)
The Kramers-Kronig Relation	212	(2)
Causality and Contour of Integration	214	(1)
The Cagniard-de Hoop Method	215	(12)
Line Source in Free-Space---Two-Dimensional Green's Function	216	(3)
Point Source in Free-Space---Three-Dimensional Green's Function	219	(2)
Line Source Over Half-Space---Transient Response	221	(3)
Dipole Over Half Space---Transient Response	224	(3)
Multi-interface Problems	227	(1)
Direct Inversion	228	(3)
Numerical Integration of Fourier Integrals	231	(4)
Direct Field in a Lossay Medium---Two-Diemnsional Case	232	(1)
Direct Field in a Lossy Medium---Three-Dimensional Case	233	(2)
Finite-Difference Method	235	(11)
The Finite-Difference Approximation	236	(3)
Stability Analysis	239	(3)
Grid-Dispersion Error	242	(2)
The Yee Algorithm	244	(2)
Absorbing Boundary Conditions	246	(25)
Engquist-Majda Absorbing Boundary Condition	246	(3)
Lindman Absorbing Boundary Condition	249	(1)
Bayliss-Turkel Absorbing Boundary Condition	250	(1)
Liao's Absorbing Boundary Condition	251	(5)
Exercises for Chapter 4	256	(6)
References for Chapter 4	262	(3)
Further Readings for Chapter 4	265	(6)
Variational Methods	271	(56)
Review of Linear Vector Space	271	(14)
Inner Product Spaces	271	(3)
Linear Operators	274	(1)
Basis Functions	275	(3)
Parseval's Theorem	278	(1)
Parseval's Theorem for Complex Vectors	279	(1)
Solutions to Operator Equations---A Preview	280	(4)
The Eigenvalue Problem	284	(1)
Variational Expressions for Self-Adjoint Problems	285	(10)
General Concepts	285	(3)
Rayleigh-Ritz Procedure---Self-Adjoint Problems	288	(3)
Applications to Scalar Wave Equations	291	(2)
Applications to Vector Wave Equations	293	(2)
Variational Expressions for Non-Self-Adjoint Problems	295	(6)
General Concepts	295	(2)
Rayleigh-Ritz Procedure---Non-Self-Adjoint Problems	297	(1)
Applications to Scalar Wave Equations	298	(1)
Applications to Vector Wave Equations	299	(2)
Variational Expressions for Eigenvalue Problems	301	(7)
General Concepts	301	(2)
Applications to Scalar Wave Equations	303	(1)
Applications to Electromagnetic Problems	304	(4)
Essential and Natural Boundary Conditions	308	(19)
The Scalar Wave Equation Case	308	(4)
The Electromagnetic Case	312	(3)
Exercises for Chapter 5	315	(6)
References for Chapter 5	321	(2)
Further Readings for Chapter 5	323	(4)
Mode Matching Method	327	(48)
Eigenmodes of a Planarly Layered Medium	327	(8)
Orthogonality of Eigenmodes in a Layered Medium	328	(2)
Guided Modes and Radiation Modes of a Layered Medium	330	(5)
Eigenfunction Expansion of a Field	335	(5)
Excitation of Modes due to a Line Source	335	(2)
The Use of Vector Notation	337	(3)
Reflection and Transmission at a Junction Discontinuity	340	(6)
Derivation of Reflection and Transmission Operators	341	(2)
The Continuum Limit Case	343	(3)
A Numerical Method to Find the Eigenmodes	346	(5)
The Cylindrically Layered Medium Case	351	(9)
Eigenmodes of a Cylindrically Layered Medium	351	(2)
Differential Equations of a Cylindrical Structure	353	(1)
Numerical Solution of the Eigenmodes	354	(2)
Eigenfunction Expansion of a Field	356	(2)
Reflection from a Junction Discontinuity	358	(2)
The Multiregion Problem	360	(15)
The Three-Region Problem	360	(2)
The N-Region Problem	362	(3)
Exercises for Chapter 6	365	(5)
References for Chapter 6	370	(2)
Further Readings for Chapter 6	372	(3)
Dyadic Green's Functions	375	(54)
Dyadic Green's Function in a Homogeneous Medium	375	(12)
The Spatial Representation	376	(2)
The Singularity of the Dyadic Green's Function	378	(3)
The Spectral Representation	381	(3)
Equivalence of Spectral and Spatial Representations	384	(3)
Vector Wave Functions	387	(10)
Derivation of Vector Wave Functions	387	(1)
Orthogonality Relationships of Vector Wave Functions	388	(5)
Vector Wave Functions for Unbounded Media	393	(4)
Dyadic Green's Function Using Vector Wave Functions	397	(13)
The Integral Representations	397	(2)
Singularity Extraction	399	(11)
Dyadic Green's Functions for Layered Media	410	(19)
A General, Isotropic, Inhomogeneous Medium	410	(1)
Planarly Layered Media	411	(3)
Cylindrically Layered Media	414	(2)
Spherically Layered Media	416	(2)
Reciprocity Considerations	418	(3)
Exercises for Chapter 7	421	(3)
References for Chapter 7	424	(2)
Further Readings for Chapter 7	426	(3)
Integral Equations	429	(82)
Surface Integral Equations	430	(13)
Scalar Wave Equation	430	(3)
Vector Wave Equation	433	(4)
The Anisotropic, Inhomogeneous Medium Case	437	(2)
Two-Dimensional Electromagnetic Case	439	(4)
Solutions by the Method of Moments	443	(10)
Scalar Wave Case	443	(3)
The Electromagnetic Case	446	(5)
Problem with Internal Resonances	451	(2)
Extended-Boundary-Condition Method	453	(6)
The Scalar Wave Case	453	(4)
The Electromagnetic Wave Case	457	(2)
The Transition and Scattering Matrices	459	(1)
The Method of Rayleigh's Hypothesis	460	(3)
Scattering by Many Scatterers	463	(6)
Two-Scatterer Solution	463	(2)
N-Scatterer Solution---A Recursive Algorithm	465	(4)
Scattering by Multilayered Scatterers	469	(6)
One-Interface Problem	469	(2)
Many-Interface Problems	471	(4)
Surface Integral Equation with Finite-Element Method	475	(4)
Volume Integral Equations	479	(5)
Scalar Wave Case	480	(1)
The Electromagnetic Wave Case	481	(2)
Matrix Representation of the Integral Equation	483	(1)
Approximate Solutions of the Scattering Problem	484	(27)
Born Approximation	485	(2)
Rytov Approximation	487	(3)
Exercises for Chapter 8	490	(11)
References for Chapter 8	501	(4)
Further Readings for Chapter 8	505	(6)
Inverse Scattering Problems	511	(60)
Linear Inverse Problems	511	(15)
Back-Projection Tomography	514	(2)
Radon Transforms	516	(3)
Diffraction Tomography	519	(3)
Finite-Source Effect	522	(2)
Nonuniqueness of the Solution	524	(2)
One-Dimensional Inverse Problems	526	(21)
The Method of Characteristics	526	(6)
Transformation to a Schrodinger-like Equation	532	(2)
The Gel'fand-Levitan Integral Equation	534	(7)
The Marchenko Integral Equation	541	(2)
The Gel'fand-Levitan-Marchenko Integral Equation	543	(4)
Higher-Dimensional Inverse Problems	547	(24)
Distorted Born Iterative Method	548	(5)
Born Iterative Method	553	(1)
Operator Forms of the Scattering Equtions	554	(3)
Exercises for Chapter 9	557	(6)
References for Chapter 9	563	(3)
Further Readings for Chapter 9	566	(5)
APPENDIX A Some Useful Mathematical Formulas	571	(6)
A.1 Useful Vector Identities	571	(1)
A.2 Gradient, Divergence, Curl, and Laplacian in Rectangular, Cylindrical, Spherical, and General Orthogonal Curvilinear Coordinate Systems	571	(2)
A.3 Useful Integral Identities	573	(1)
A.4 Integral Transforms	574	(3)
APPENDIX B Review of Tensors	577	(6)
APPENDIX C Generalized Functions	583	(8)
APPENDIX D Addition Theorems	591	(8)
References for Appendices	597	(1)
Further Readings for Appendices	598	(1)
Index	599