Efficient Analysis of Periodic Structures with Arbitrary Shape Using Volume-surface Integral Equation Method

Abstract

A coupled volume-surface integral equation method is presented for analyzing arbitrarily shaped periodic structure of mixed dielectric and conducting objects. Free space periodic Green’s function is used in the formulation of both integral equations. In the method of moments solution to the integral equations, the target is discretized using triangular patches for conducting surfaces and tetrahedral cells for dielectric volume. Ewald’s method is used to accelerate the convergence of computing each element in the impedance matrix. Numerical results are presented to demonstrate the accuracy and efficiency of the technique. I. Introduction Electromagnetic analysis of periodic structures has a wide range of application. The spectral method of moments is a power tool in analyzing periodic structures [1]. To improve the flexibility in modeling various geometries, the Rao-Wilton-Gillison (RWG) [2] triangular discretization was reported in [3]. In this paper, the coupled volume-surface integral equation method [4] is presented for the electromagnetic wave scattering from arbitrarily shaped periodic structures composed of dielectrics and conducting objects. Free space periodic Green’s function is used in the formulation of both integral equations. The triangular patches and tetrahedral elements are used to mesh the dielectric and conducting objects, respectively. The coupled integral equations are solved by the method of moments (MoM) [5] with surface RWG and volume SWG basis functions [6] discretization. To rapidly generate the impedance elements, Ewald’s method [7] is used to speed the computation of the periodic Green function due to the fact that the periodic Green function, which is a summation of series, converges very slowly. The proposed technique can also be extensively applied to analyze the periodic structure consisted of inhomogeneous dielectric material and conducting body. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed technique for analyzing the scattering problem of arbitrarily shaped periodic structure.