Wave propagation and scattering in dense random media.

Abstract

This dissertation addresses the important problem of electromagnetic field propagation through and scattering from random media. The mathematical parameter that characterizes the coherent interaction of an electromagnetic field with a random medium is embodied in the fundamental constant of effective permittivity. Effective permittivity relates the small scale interaction of fields in an inhomogeneous medium to the macroscopic behavior of the aggregate. In granular or aerosol media, these inhomogeneities are represented as discontinuities or inclusions, separate from a homogeneous background such as free space. The ability to relate the theoretically understood microscopic behavior of fields in random media to the observed macroscopic behavior is a fundamental problem of applied physics and remote sensing. This dissertation is the culmination of a thorough investigation into this phenomenon and presents a unique, rigorous and consistent method of determining the fundamental parameter of effective permittivity for both two- and three-dimensional random media. In the development of this work, a number of new tools were implemented to model electromagnetic fields in random media. These were (i) a packing algorithm to simulate particle arrangements in gravity-deposited random media such as sand, snow or soils, and (ii) a numerical method for determining effective permittivity independent of particle density, shape, dielectric contrast and arrangement method. The packing algorithm referenced to here, provides essential unknowns such as the correlation function and/or the pair distribution function for use with commonly applied theoretical methods like the Born approximation and the quasi-crystalline approximation. Additionally, the packing algorithm may be used as the first step in the full numerical method for determining effective permittivity. This numerical method surpasses existing theoretical techniques by directly solving the integral form of Maxwell's equations, thereby eliminating approximations employed by theoretical methods to make them tractable. Thus, the numerical method is capable of modeling complex problems often found in nature. As a result, this work represents a solid step forward in our basic understanding of how electromagnetic fields propagate through, and scatter from, random media.