Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials

By the use of the correct Fourier factorization rules presented in an earlier paper by Li the Fourier modal method (FMM) for anisotropic surface-relief gratings is reformulated. The newly formulated FMM converges much faster than the old formulation when the permittivity contrast in the grating groove region is large. Highly conducting lamellar gratings coated with anisotropic materials can now be analysed easily. In addition, a simple set of criteria are given for determining the energy propagation directions of the plane waves associated with the real solutions of the Booker quartic.