In this talk, the operator marching method for the scattering problems of nano-periodic structures is introduced. The scattered fields are fast calculated with high accuracy. Then, the surface integral equation method for analyzing the scattered electromagnetic fields on diffraction grating structures will be presented. Next, we propose the numerical steepest descent path method for solving the high frequency scattered fields. Numerical results on the engineering scatterer models illustrate that the proposed method is frequency independent in computational cost and error controllable in accuracy.

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