We present a finite-difference modal method (FDMM) combined with higher-order interface conditions to analyze the diffraction of grating structures. The generalized Douglas (GD) scheme is also adopted to further enhance the convergence. Numerical results show the FDMM generally results in faster convergence than the commonly used coupled-wave analysis (RCWA) as higher-order formulation, such as the GD with five points, is adopted in both TE and TM polarizations. The FDMM is also relatively stable in a highly conductive lossless rectangular grating, while the RCWA suffers instabilities in such a frequently studied structure.
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