Abstract
A modal method for designing the one-dimensional (1-D) dielectric multilevel antireflection gratings (ARGs) used for TE polarized waves is proposed based on the effective refractive indices concept of the modal method (MM). In this method, the effective refractive index (ERI) for each level is determined by the effective mode index of the modal method. The refractive indices under and above the grating region are equivalent to their effective refractive indices that is determined by the 0th order propagating wave vector of the Fourier expansion of the electric fields under and above the grating region, which are different from the conventional effective medium theory (EMT), and the relationship between the ERI in MM and that in EMT are also revealed. As an example, we designed and analyzed the fused-silica multilevel ARGs by using the MM and the commonly used second-order effective medium theory (SEMT). The designed results are numerically verified by using the rigorous coupled-wave analysis method (RCWA) and the thin-film theory.
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