New formulation of the Fourier modal method for crossed surface-relief gratings

A new formulation of the Fourier modal method (FMM) that applies the correct rules of Fourier factorization for crossed surface-relief gratings is presented. The new formulation adopts a general nonrectangular Cartesian coordinate system, which gives the FMM greater generality and in some cases the ability to save computer memory and computation time. By numerical examples, the new FMM is shown to converge much faster than the old FMM. In particular, the FMM is used to produce well-converged numerical results for metallic crossed gratings. In addition, two matrix truncation schemes, the parallelogramic truncation and a new circular truncation, are considered. Numerical experiments show that the former is superior.