Analysis of Faceted Gratings Using C-Method and Polynomial Expansion

The coordinate-transformation-based differential method developed by Chandezon et al. is recognized as one of the simplest and most versatile approaches for modeling surface-relief gratings. In this study, we present a novel numerical solution using Legendre polynomial expansion, enabling us to deal efficiently with faceted gratings. Additionally, we introduce an oblique coordinate transformation to analyze overhanging faceted gratings. Notably, the C-method with polynomial expansion (CPE) demonstrates a dramatic improvement in convergence speed compared to the Fourier Modal Method (FMM).