APPLICATIONS OF, AND ENHANCEMENTS TO, FINITE-DIFFERENCE-BASED SOLUTIONS TO PROBLEMS IN ELECTROMAGNETICS

Abstract

We describe how the analytic field propagation (AFP) technique can be coupled with a total-field/scattered-field (TFSF) boundary to obtain a novel implementation of a "gen-eralized" total-field/scattered-field (G-TFSF) boundary. Using a G-TFSF boundary,one can directly model "infinite" objects, such as wedges, corners, and edges. Exampleapplications of the AFP-based G-TFSF technique are shown that model not just scatter-ing from wedges, but also scattering from 3D "defects" in wedges or edges. As describedin the thesis, the AFP-based G-TFSF method described in this thesis possesses variousadvantages over the original G-TFSF method presented by Anantha and Taflove [IEEETrans. Antennas and Propagat., 50(10):1337-1349, 2002].We revisit the long-standing debate surrounding whether or not "enhanced totalinternal reflection" (ETIR) is possible. ETIR implies that the magnitude of the reflectioncoefficient is greater than unity and is conjectured to be possible when a field is incidentfrom a lossless material to a gainy material beyond the critical angle. We examine thisproblem using FDTD modeling where the Poynting vector is used to examine the flowof energy. The two-dimensional simulations employ a Gaussian incident beam and makeno a priori assumptions about the reflection coefficient. We consider illumination ofgainy, lossless, and lossy materials. For gainy material, the magnitude of the reflectioncoefficient is found to be greater than unity, but there is a delay between when energyenters the gainy material and when the "excess" energy is reflected from the interface.Corona onset conditions in periodic micro- and nano-materials are analyzed via a dis-cretization of Gauss's Law. A numerical model is developed to examine the mechanismby which nano-materials may provide superior performance relative to micro-materials.Starting from a single-cell layered structure, the electrical field distribution is computedusing the finite difference method (FDM) and a sparse matrix solver. From these results,a general model is inferred by comparing results from the multi-cell layered structures tothe single-cell layered ones. Next, the corona onset condition is calculated for materialwith any particle size. Finally, the relationship between the breakdown voltage and theparticle size is derived based on the numerical findings.