Spurious-free analysis of two-dimensional low-loss metallic gratings

Transmission line formulation is used to analyze two-dimensional low-loss metallic gratings at optical frequencies when plasmonic waves propagate in the structure. This method, like the Fourier modal method, suffers from numerical instabilities when applied to such structures. A systematic approach to avoid these instabilities is presented. These numerical artifacts are attributed to the violation of Li's inverse rule and the appearance of higher-order spurious modes. In this paper, a new approach is proposed to identify and to greatly reduce the effect of these spurious modes based on the accuracy by which these modes are satisfying the conservation of momentum. Furthermore, the proposed scheme conserves power and improves the convergence, i.e., reduces the required truncation order. (paper)