TM Electromagnetic Scattering from Multilayered Dielectric Bodies – Numerical Solution

An integral equation approach is derived for an electromagnetic scattering from an M multilayered dielectric domain. The integral equation is valid for 2D and 3D Helmholtz equation. Here we show the numerical solution for the 2D case by using the Nyström method. For validating the method we develop a mode matching method for the case when the domains are multilayered circular cylinders and give numerical results for illustrating the algorithm. Introduction Problems in layered media are of significant importance in many areas of technology (cf. [1] and the references therein). In this paper we discuss some analytical and computational results for the problem of approximating the scattered electromagnetic field from M layered two-dimensional scatterer. The scatterer is a nested body consisting of a finite number of homogeneous layers (annular regions) with boundary conditions on the interfaces. The straightforward way for solving this type of problems via boundary element methods is by using Green’s theorem in each domain [1]. Another alternative is to consider the use of single and/or double layer potentials [2]. In the case of one interface, both methods yield a single integral equation for a single unknown if the interface is impenetrable (e.g. impedance core). However, when the body is penetrable with one interface (e.g. dielectric core), they lead to a pair of integral equations for a pair of unknowns [2]. We deduce that, by using these approaches in the multilayered dielectric domain, for N interfaces we have 2N unknown functions to determine. From a computational point of view, it is highly desirable to obtain less equations and less unknowns. In the case of one interface, the so called transmission problem, one integral equation involving one unknown was obtained by a few authors (see [5] and the references therein). The purpose of this paper is to obtain a single integral equation on each interface for the multilayered domain case. In [5] the transmission problem was studied and a single integral equation for one unknown was obtained by using a hybrid of Green’s theorem and layer potentials. Here we alternate the layer potentials and Green’s theorems in the multilayered domain. We implement numerical computations using the Nyström method. Our results are validated by developing a mode matching approach for the case of a multilayered circular cylinder and compare the two algorithms.