An Accurate Integral Equation Formulation to Scattering of Periodic Grating Structures

Abstract

Broadband wave transmission grating structures have potentials in many engineering applications. Theoretical predictions of the transmission spectra and near field characteristics of such structures are crucial for the understanding and design of wave functional gratings. However, accurate theoretical modeling of the wave interactions with such periodic grating structures turns out to be difficult, especially at near grazing incidence angles. In this paper, an efficient and accurate method to solve the scattering of periodic grating structures is proposed based upon integral equation formulations utilizing periodic lattice Green's functions. The method of moments is used to discretize the integral equation with the pulse basis function and the point matching scheme. The imaginary wavenumber extraction technique and the integral transformation approach are combined to efficiently and accurately evaluate the period Green's function. Meanwhile, an over-determined testing scheme on the integral equation is devised to overcome the intrinsic internal resonance of surface integral equations. Such strategy has significantly improved the numerical accuracy of the proposed approach. Calculation results are compared with Comsol simulations for various scenarios, and the proposed approach is found to be predicting physically sound results when Comsol fails at certain frequencies and incident angles. The proposed method is applicable to grating periodic structures of various shapes and it provides a useful reference and tool for researchers and designers.