Discrete complex image method for periodic Green’s function

Abstract

Abstract The electromagnetic scattering of periodic structure may be expressed by integral equation with periodic Green function as the core. The periodic Green’s function can be expressed as infinite sum in spectral domain. In order to avoid the numerical calculation of infinite sum, the discrete complex image method is proposed. By using the Generalized pencil-of-function method, the closed form can be obtained without any numerical integration. It can be expressed as one group of real sources and two groups of complex sources with complex amplitude and complex position. The accuracy of the method is demonstrated through numerical examples.