Polynomial modal method for crossed slanted gratings

Slanted gratings have emerged as a promising area of research due to their distinct properties, such as polarization control, beam steering, and enhanced interactions between light and matter. However, accurately and efficiently modeling these structures, particularly in the case of two-dimensional (2D) slanted gratings, has proven to be challenging. Traditional methods like the Fourier modal method (FMM or RCWA) and finite difference time domain (FDTD) are commonly used but involve approximations of the geometry to accommodate the slant effect. In this study, we address these challenges by employing the polynomial modal method (PMM) for 2D slanted gratings, which, to our knowledge, is a novel approach not previously explored for this type of grating. We introduce a 2D slanted coordinate system to rigorously handle the grating profile. For 2D slanted gratings, the PMM offers several advantages over the FMM, as it overcomes limitations associated with factorization rules and/or staircase approximation of the profile.