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.
