Rigorous Coupled-Wave Analysis Algorithm for Stratified Two-Dimensional Gratings with Unconditionally Stable H-Matrix Methods

Nanostructures with the two-dimensional (2D) periodicity are attracting increasing attention due to their promising applications in planar optical devices and their potential for scalable industrial production. While Rigorous Coupled-Wave Analysis (RCWA) has proven to be an efficient electromagnetic solver for simulating the diffraction of large-scale periodic nanostructures, it has been largely applied in nanostructures with one-dimensional (1D) periodicity and suffers from potentially low computational stability. In this study, we present a step-by-step formulation of the RCWA algorithm for 2D stratified grating structures. Through dimensionality reduction, we show that the boundary conditions in 2D gratings can be transformed into forms analogous to those of 1D gratings. Additionally, we implement a hybrid matrix algorithm to enhance the computational stability of the RCWA. The stability and accuracy of the hybrid matrix-enhanced RCWA algorithm are compared with other recursive methods. An exemplary application in metalens demonstrates the effectiveness of our algorithms.