The differential method for arbitrary profiled onedimensional gratings made of anisotropic media is reformulated by taking into account Li's Fourier factorization rules  though the present formulation uses the intuitive Laurent rule only. The study concerns arbitrary profiled gratings with both types of electric and magnetic anisotropy, and includes the case of lossy materials. Diffraction efficiencies computed by the present formulation are compared with previous ones, and numerical results show that convergence of the present formulation is superior to the conventional one and comparable convergence with the previous works based on Li's rules.
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