High Order Finite Difference Modal Method for Diffraction Gratings

A new high order finite difference modal method (FDMM) is developed for analyzing diffraction gratings in conical and classical mountings. The difference scheme is constructed by enforcing the internal interface conditions in each grating layer to high order derivatives, and it gives a high order of accuracy for computing the eigenmodes of the grating layer. Between different layers, the interface conditions are implemented using a Fourier matching scheme and a point matching scheme. Compared with the standard Fourier modal method, the high order FDMM is more efficient since the matrices in the discretized eigenvalue problems are sparse. Numerical examples are used to illustrated the performance of the method.