Limitation of using absorbing boundary condition to solve the problem of scattering from a cavity in metallic screens

Abstract

Interest in accurate modeling of electromagnetic wave scattering from grating surfaces has been renewed due to the emergence of novel application of plasmonic resonance such as near-field microscopy, sub-wavelength lithography, surface defect detection, and developing tunable optical filters. Several methods were reported in the literature to solve the problem of scattering from cavities engraved in a metallic screen [1–4]. Although these methods are powerful they are not general enough to address cavities with general shapes or inhomogeneous and anisotropic fillings. In contrast, the methods based on finite mathematics such as finite element method (FEM) are highly suited when the gratings have arbitrary shapes and fillings [5–7]. This work briefly reviews the methods used to truncate the solution region of infinite structures while using FEM and highlights the inherent limitation in truncation the infinite structure using local boundary operators such as absorbing boundary condition (ABC) or perfectly matched layer (PML) in the context of the problem of scattering from infinite gratings. In fact we show that significant errors can be generated in the solution when using ABC or PML for grazing incidence even if the truncation boundary is receded appreciably. The error in field computation due to mesh truncation using ABC or PML in problem of scattering from a single cavity engraved in an infinite metallic screen is calculated by an accurate recently published finite-element based method and the mode matching technique.