Fast converging formulation of differential theory for nonsmooth gratings made of anisotropic materials

Li's Fourier factorization rules have contributed greatly to the differential theory that is one of the most commonly used approaches in the analysis of diffraction gratings. This paper gives a differential formulation for nonsmooth profiled anisotropic gratings by taking into account Li's remark, but a coupled first-order differential-equation set is derived using only the Laurent rule. The present formulation is applied to sinusoidal and echelette gratings, and numerical results show that the present formulation provides significant improvement of convergence.