Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods.

Integral Equation Methods for Electromagnetic and Elastic Waves

Printed dipole antennas find increasing use in microwave as well as far infrared frequencies. The current distribution, input impedance, and radiation pattern are computed for wire antennas printed on a dielectric substrate. The current distribution is obtained by solving Pocklington's equation by moment methods. The Green's function pertinent to the problem involves improper Sommerfeld-type integrals. These integrals are computed by a real-axis integration technique which involves analytical and numerical steps. The effect of surface modes is carefully taken into account.

Current distribution and input impedance of printed dipoles

In this paper we provide a general formulation for the electromagnetic wave interaction with stratified media and then specialize to slabs of negative isotropic media. The field solutions are obtained in all regions of the stratified medium. The characteristic waves in negative isotropic media are backward waves. We derive the field solutions and show that a Gaussian beam is laterally shifted by a negative isotropic slab. The amount of beam center shift is calculated for both cases of transmission and reflection. Guided waves in stratified media are studied. Placing a linear antenna and all types of Hertzian dipole antennas in a stratified medium, we obtained solutions in all regions. We demonstrate and locate the positions of the perfect images of the antenna sources in the presence of negative isotropic slabs.

/pdf/electromagnetic-wave-interaction-with-stratified-negative-53vc2atw65.pdf

Electromagnetic wave interaction with stratified negative isotropic media

Numerical studies of the radiation patterns of resistively loaded dipoles

Integro-differential equations are obtained for the electric and magnetic fields inside a linear, lossy, and anisotropic scatterer, in the frequency domain. The material of the scatterer is characterized by arbitrary values of the elements of the relative permittivity tensor \bar{\epsilon} , the relative permeability tensor \bar{\mu} , and the conductivity tensor \bar{\sigma} . The results are specialized to the case of oblique scattering in two dimensions, for which a numerically efficient computer code has been developed and tested, as described in a companion paper (Part II). The method developed herein is based on a comparison between macroscopic and microscopic descriptions of electromagnetic fields in material media, and is of general applicability.

Electromagnetic scattering from anisotropic materials, part I: General theory

Solutions to the problem of radiation of dipole antennas in the presence of a stratified anisotropic media are facilitated by decomposing a general wave field into transverse magnetic (TM) and transverse electric (TE) modes. Employing the propagation matrices, wave amplitudes in any region are related to those in any other regions. The reflection coefficients, which embed all the information about the geometrical configuration and the physical constituents of the medium, are obtained in closed form. In view of the general formulation, various special cases are discussed.

Electromagnetic fields due to dipole antennas over stratified anisotropic media.

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Electromagnetic fields due to dipole antennas over stratified anisotropic media.