Efficient grating simulation for general incident beam

Abstract

Fourier modal method (FMM) is known as a powerful tool in simulations of periodic micro-structures, e.g., gratings. For an arbitrary plane wave incidence, the Rayleigh coefficients for both reflected and transmitted field can be calculated with the FMM efficiently. When dealing with a general beam incidence, FMM together with plane wave decomposition can still provide solutions. However the needed computational resources increase with the number of plane wave components in the angular spectrum domain. To solve this problem, we put forward an efficient approach which integrates interpolation technique into the method above. For most diffractive thin elements, the complex Rayleigh coefficients distribution is smooth. In this case several well-selected plane wave components are enough to characterize the diffraction property. In our method, only these selected plane wave components are analyzed with FMM while the results of other components are obtained by interpolation technique. Besides that, an efficient approach for especially divergent incident beam is also presented in this article. It enable a parallel FMM analysis which calculates a set of plane wave components in one computational loop.