Analysis of diffraction gratings by using an edge element method

Abstract

Typically the grating problem is formulated for the TE and TM polarizations, respectively, by using the electric and magnetic fields aligned with the grating wall and perpendicular to the plane of incidence and this leads to a one field component problem. For some grating profiles such as metallic gratings with a triangular profile, the prediction of TM polarization using standard finite element method experiences a slower convergence rate and this reduces the accuracy of the computed results and also introduces a numerical polarization effect. This discrepancy cannot be seen as a simple numerical issue since it has been observed for different types of numerical methods based on the classical formulation. Hence this paper proposes an alternative formulation where the grating problem is modeled by taking the electric field as unknown for TM polarization. The application of this idea to both TE and TM polarizations leads to a two component field problem. The purpose of the present paper is to propose an edge finite element method to solve this wave problem. The comparison between the results of the proposed formulation and the classical formulation shows improvement and robustness by the new approach.