Accuracy analysis of simplified and rigorous numerical methods applied to binary nanopatterning gratings in non-paraxial domain

A set of simplified and rigorous electromagnetic vector theories is used for analyzing the transmittance characteristics of diffraction phase gratings. The scalar diffraction theory and the effective medium theory are validated with the exact results obtained via the rigorous coupled-wave theory and the finite-difference time-domain method. The effects of surface profile parameters and also the angle of incidence is demonstrated to be a limiting factor in the accuracy of these theories. Therefore, the error of both simplified theories is also analyzed in non-paraxial domain with the intention of establishing a specific range of validity for both simplified theories.