Preface 1. Introduction 2. The elastodynamics and its simple solutions 3. Seismic rays and travel times 4. Dynamic ray tracing. Paraxial ray methods 5. Ray amplitudes 6. Ray synthetic seismograms Appendix. Fourier transform, Hilbert transform and analytical signals References Index.

Seismic Ray Theory

Wave propagation in a double negative (DNG) medium, i.e., a medium having negative permittivity and negative permeability, is studied both analytically and numerically. The choices of the square root that leads to the index of refraction and the wave impedance in a DNG medium are determined by imposing analyticity in the complex frequency domain, and the corresponding wave properties associated with each choice are presented. These monochromatic concepts are then tested critically via a one-dimensional finite difference time domain (FDTD) simulation of the propagation of a causal, pulsed plane wave in a matched, lossy Drude model DNG medium. The causal responses of different spectral regimes of the medium with positive or negative refractive indices are studied by varying the carrier frequency of narrowband pulse excitations. The smooth transition of the phenomena associated with a DNG medium from its early-time nondispersive behavior to its late-time monochromatic response is explored with wideband pulse excitations. These FDTD results show conclusively that the square root choice leading to a negative index of refraction and positive wave impedance is the correct one, and that this choice is consistent with the overall causality of the response. An analytical, exact frequency domain solution to the scattering of a wave from a DNG slab is also given and is used to characterize several physical effects. This solution is independent of the choice of the square roots for the index of refraction and the wave impedance, and thus avoids any controversy that may arise in connection with the signs of these constituents. The DNG slab solution is used to critically examine the perfect lens concept suggested recently by Pendry. It is shown that the perfect lens effect exists only under the special case of a DNG medium with $\ensuremath{\epsilon}(\ensuremath{\omega})=\ensuremath{\mu}(\ensuremath{\omega})=\ensuremath{-}1$ that is both lossless and nondispersive. Otherwise, the closed form solutions for the field structure reveal that the DNG slab converts an incident spherical wave into a localized beam field whose parameters depend on the values of $\ensuremath{\epsilon}$ and $\ensuremath{\mu}.$ This beam field is characterized with a paraxial approximation of the exact DNG slab solution. These monochromatic concepts are again explored numerically via a causal two-dimensional FDTD simulation of the scattering of a pulsed cylindrical wave by a matched, lossy Drude model DNG slab. These FDTD results demonstrate conclusively that the monochromatic electromagnetic power flow through the DNG slab is channeled into beams rather then being focused and, hence, the Pendry perfect lens effect is not realizable with any realistic metamaterial.

http://esperia.iesl.forth.gr/~ppm/DALHM/bibliography/LHMpdfs/ziolkowski_PRE64_56625_01.pdf

Wave propagation in media having negative permittivity and permeability

To address the need for fundamental universally valid definitions of exact bandwidth and quality factor (Q) of tuned antennas, as well as the need for efficient accurate approximate formulas for computing this bandwidth and Q, exact and approximate expressions are found for the bandwidth and Q of a general single-feed (one-port) lossy or lossless linear antenna tuned to resonance or antiresonance. The approximate expression derived for the exact bandwidth of a tuned antenna differs from previous approximate expressions in that it is inversely proportional to the magnitude |Z'/sub 0/(/spl omega//sub 0/)| of the frequency derivative of the input impedance and, for not too large a bandwidth, it is nearly equal to the exact bandwidth of the tuned antenna at every frequency /spl omega//sub 0/, that is, throughout antiresonant as well as resonant frequency bands. It is also shown that an appropriately defined exact Q of a tuned lossy or lossless antenna is approximately proportional to |Z'/sub 0/(/spl omega//sub 0/)| and thus this Q is approximately inversely proportional to the bandwidth (for not too large a bandwidth) of a simply tuned antenna at all frequencies. The exact Q of a tuned antenna is defined in terms of average internal energies that emerge naturally from Maxwell's equations applied to the tuned antenna. These internal energies, which are similar but not identical to previously defined quality-factor energies, and the associated Q are proven to increase without bound as the size of an antenna is decreased. Numerical solutions to thin straight-wire and wire-loop lossy and lossless antennas, as well as to a Yagi antenna and a straight-wire antenna embedded in a lossy dispersive dielectric, confirm the accuracy of the approximate expressions and the inverse relationship between the defined bandwidth and the defined Q over frequency ranges that cover several resonant and antiresonant frequency bands.

Impedance, bandwidth, and Q of antennas

A compact representation is given of the electric- and magnetic-type dyadic Green's functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the aids normal to the stratification. Furthermore, mixed-potential integral equations are derived within the framework of this transmission-line formalism for arbitrarily shaped, conducting or penetrable objects embedded in the multilayered medium. The development emphasizes laterally unbounded environments, but an extension to the case of a medium enclosed by a rectangular shield is also included.

/pdf/multilayered-media-green-s-functions-in-integral-equation-icv3t901yt.pdf

Multilayered media Green's functions in integral equation formulations

An accurate and general procedure for the analysis of electromagnetic radiation and scattering by perfectly conducting objects of arbitrary shape embedded in a medium consisting of an arbitrary number of planar dielectric layers is developed. The key step in this procedure is a formulation of the so-called mixed-potential electric field integral equation (MPIE) that is amenable to an existing advanced solution technique developed for objects in free space and that employs the method of moments in conjunction with a triangular-patch model of the arbitrary surface. Hence, the goal is to immediately increase analysis capabilities in electromagnetics, yet remain compatible with the large existing base of knowledge concerning the solution of surface integral equations. Three alternative forms of the MPIE in plane-stratified media are developed, and their properties are discussed. One of the developed MPIEs is used to analyze scatterers and antennas of arbitrary shape that penetrate the interface between contiguous dielectric half-spaces. >

Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. I. Theory

As relevant today as it was when it was first published 20 years ago, this book is a classic in the field. Nowhere else can you find more complete coverage of radiation and scattering of waves. The chapter: Asympotic Evaluation of Integrals is considered the definitive source for asympotic techniques. This book is essential reading for engineers, physicists and others involved in the fields of electromagnetics and acoustics. It is also an indispensable reference for advanced engineering courses.

Radiation and scattering of waves

: After a general discussion of non-harmonic electromagnetic processes from the viewpoint of temporal Fourier (or Laplace) analysis and synthesis, a class of problems is considered for which the transient solution may be recovered in simple form. Included in this category are pulsed point, line and plane wave sources in free space, and in the presence of (a) a dielectric half-space, (b) a perfectly absorbing or perfectly conducting wedge or half plane, and (c) a unidirectionally conducting infinite and semi-infinite screen. Explicit expressions for the transient response, found by a systematic application of the modal procedures discussed in earlier chapters in this sequence, are interpreted in physical terms. Attention is then given to a second class of problems wherein an electric charge moves uniformly along a straight trajectory in various environments. The associated radiation is now of the Cerenkov type, and formulas for the fields as well as the radiated power are given. (Author)

Modal analysis and synthesis of electromagnetic fields.

Radiation from electromagnetic sources in layered regions is reviewed and illustrated for the case of planar stratification. Mter a reduction of the vector field problem to equivalent scalar Green's function problems, the latter are expressed in alternative forms by the systematic application of one-dimensional characteristic Green's function techniques. Solutions are derived in this manner without the intervention of the classical Watson procedure and are interpretable as guided-wave representations along various coordinate directions. Considerations pertaining to scalar Green's functions apply directly, upon suitable reinterpretation of the electromagnetic parameters, to other fields such as the acoustic which are derivable from scalar potentials.

Alternative Representations of Source-Excited Vector and Scalar Fields†

This chapter contains sections titled: General Considerations Isolated First-Order Saddle Points Isolated Saddle Points of Higher Order First-Order Saddle Point and Nearby Singularities Nearby First-Order Saddle Points Saddle Points Near an Endpoint Multiple Integrals Integration Around a Branch Point Appendix 4A. Higher-Order Derivatives of G ( s ) = f ( z ) dz/ds Appendix 4B. Properties of the Airy Functions References

Asymptotic Evaluation of Integrals

This chapter contains sections titled: Distinctive Field Characteristics Green's Function Representations in Cylindrical Regions Wedge-Type Problems??-??Integration Techniques Perfectly Absorbing Wedge Perfectly Conducting Wedge and Half Plane Wedge with Variable Impedance Walls Diffraction by a Circular Cylinder Fields in Spherical Regions Appendix 6A. Asymptotic Formulas for H (1) v (z) and H (2) v (z) Appendix 6B. Miscellaneous Formulas Involving Cylinder Functions References

Nathan Marcuvitz

Papers

Radiation and scattering of waves

Modal analysis and synthesis of electromagnetic fields.

Alternative Representations of Source-Excited Vector and Scalar Fields†

Asymptotic Evaluation of Integrals

Fields in Cylindrical and Spherical Regions