A boundary integral equation approach to three dimensional electromagnetic wave scattering problems

Abstract

<p>Electromagnetic scattering models are finding increasing interest in many applications ranging from nondestructive evaluation (NDE) to design of optical systems. The availability of a computational scattering model characterizing the underlying system serves several purposes. First, it serves as an inexpensive test bed to simulate a variety of test situations. For instance, the forward model can be used to evaluate various polarizations and incidence angles of the incident source fields and the corresponding spatial distribution of the scattered fields which in turn provides information useful for optimizing the measurement of scattered fields. By preserving some of the realism that is usually possible in purely analytical methods, it provides valuable insight into the physics of actual problems. Second, forward scattering models are important in solving the inverse problem where the scattered fields are used for characterizing the size, the shape and the constitution of the scatterer;The development of theoretical models largely relies on the use of numerical techniques such as boundary element method (BEM), finite element method (FEM), or finite difference method (FDM). However, no single numerical method has emerged as the optimal method for solving all electromagnetic scattering problems. One numerical method might be preferred over others, depending on the nature of the problem. For instance, problems which involve homogeneous scatterers and propagation of waves in an infinite medium are typically solved using the BEM whereas problems which involve a naturally truncated region are modeled using FEM and FDM;This dissertation presents a boundary integral equation (BIE) formulation for the problem of electromagnetic scattering due to homogeneous dielectric scatterers. The governing BIEs are then evaluated numerically using the BEM. Several fundamental electromagnetic scattering geometries are considered. The first problem involves solving for the scattered fields in the presence of a single, three dimensional, arbitrarily shaped, dielectric scatterer suspended in an infinite medium. The formulation is then extended to modeling the scattered fields in the presence of multiple dielectric scatterers as well as a dielectric scatterer in the proximity of an infinite perfect conducting plane. Lastly, the problem of a dielectric scatterer situated close to a dielectric half-space is discussed. The geometries are chosen so that the work presented in this dissertation will serve as a basic model and solutions to a large range of problems can be obtained by modifying one or more of the configurations presented.</p>