VarRCWA: An Adaptive High-Order Rigorous Coupled Wave Analysis Method

Semianalytical methods, such as rigorous coupled wave analysis, have been pivotal in the numerical analysis of photonic structures. In comparison to other numerical methods, they have a much lower computational cost, especially for structures with constant cross-sectional shapes (such as metasurface units). However, when the cross-sectional shape varies even mildly (such as a taper), existing semianalytical methods suffer from high computational costs. We show that the existing methods can be viewed as a zeroth-order approximation with respect to the structure's cross-sectional variation. We derive a high-order perturbative expansion with respect to the cross-sectional variation. Based on this expansion, we propose a new semianalytical method that is fast to compute even in the presence of large cross-sectional shape variation. Furthermore, we design an algorithm that automatically discretizes the structure in a way that achieves a user-specified accuracy level while at the same time reducing the computational cost.