Path integral method in classical electromagnetics

Abstract

Path integral formulations in coordinate space and phase space have been derived and applied to the analysis of the electromagnetic scattering and propagation problems. An analytical solution for the Green's function in multi-dimensional free space and some two-dimensional perfect electric conductor (PEC) boundary value problems which are amenable to classical solutions prove that our formulations are rigorous and exact. Two numerical techniques for the evaluation of the path integrals are developed and their relative merits discussed. One of them, called the stationary phase Monte Carlo (SPMC) method, which is found to be particularly well suited for wave propagation over long distances, is implemented to analyze wave propagation in a system involving arbitrary-shaped, smoothly varying, and transversely inhomogeneous dielectrics. The other technique, called the Fourier transform path integral (FTPI) method, which provides a unified treatment for computing electromagnetic fields in a region that contains intersecting or isolated dielectric bodies that are homogeneous, inhomogeneous or perfect conductors, is implemented to analyze general wave scattering in one- or two-dimensional configurations. The SPMC method is specifically applied to wave propagation in a graded-index waveguide, while the FTPI method is used to solve for the scattered field from a variety of one- and two-dimensional planar structures due to line source excitation. Numerical results sire presented and, wherever possible, compared with analytical solutions and data in the literature.