Zhao Jiexin, Tian Xiaoqing, Wang Jiyong
J Opt Soc Am A Opt Image Sci Vis. 2023 Oct 1;40(10):1940-1946. doi: 10.1364/JOSAA.499890.
Rigorous coupled-wave analysis (RCWA) has become one of the most efficient electromagnetic solvers to cope with the diffractions of large-scale periodic nanostructures. Conventional RCWAs focus on planar diffractions and their iterative stabilities. Conical diffractions, as more general incidence cases, are paid little attention in developing their universal and stable implementations for multilayered gratings. Here, we reformulate RCWA algorithms step by step for conical diffractions in a global Cartesian coordinate system. By applying some mathematics tricks, it is found that boundary conditions in conical diffractions can be reduced to the same forms as that of planar diffractions. Conventional stable algorithms including enhanced transmittance matrices and scattering matrices can be directly implemented to attain robust diffraction efficiencies as well as electromagnetic fields for multilayered gratings. An exemplary application in diffractive-waveguide-based augmented reality verified our algorithms.
严格耦合波分析（RCWA）已成为处理大规模周期性纳米结构衍射问题最有效的电磁求解器之一。传统的RCWA主要关注平面衍射及其迭代稳定性。作为更一般的入射情况，锥形衍射在开发用于多层光栅的通用且稳定的实现方法方面很少受到关注。在此，我们在全局笛卡尔坐标系中逐步重新制定用于锥形衍射的RCWA算法。通过运用一些数学技巧，发现锥形衍射中的边界条件可以简化为与平面衍射相同的形式。包括增强透射矩阵和散射矩阵在内的传统稳定算法可以直接用于实现多层光栅的稳健衍射效率以及电磁场。基于衍射波导的增强现实中的一个示例性应用验证了我们的算法。
