Numerical performance of finite-difference modal methods for the electromagnetic analysis of one-dimensional lamellar gratings

Abstract : The numerical performance of a finite-difference modal method for the analysis of one-dimensional lamellar gratings in a classical mounting is studied. The method is simple and relies on first-order finite difference in the grating to solve the Maxwell differential equations. The finite-difference scheme incorporates three features that accelerate the convergence performance of the method: (1) The discrete permittivity is interpolated at the lamellar boundaries, (2) mesh points are located on the permittivity discontinuities, and (3) a nonuniform sampling with increased resolution is performed near the discontinuities. Although the performance achieved with the present method remains inferior to that achieved with up-to-date grating theories such as rigorous coupled-wave analysis with adaptive spatial resolution, it is found that the present method offers rather good performance for metallic gratings operating in the visible and near-infrared regions of the spectrum, especially for TM polarization.