扩展RCWA能力：先进的S矩阵算法
Expanding RCWA capabilities with advanced S-matrix algorithms
- Laboratoire Photonique Numérique et Nanosciences (LP2N), Université de Bordeaux, Institut d’Optique Graduate School, CNRS（光子学与纳米科学实验室，波尔多大学，高等光学学院，法国国家科学研究中心）
- Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry（巴黎萨克雷大学，高等光学学院，法国国家科学研究中心，夏尔·法布里实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种S矩阵重构方法，将S矩阵定义为单层固有属性，分离层传播与界面耦合，保持数值稳定性，支持布洛赫模式散射系数计算及多参数同时评估，并在RETICOLO软件中实现，用于分层光子结构分析。
AI中文摘要：
模态方法特别适用于分层光子结构，因为电磁波在每层内的传播可以用解析方法描述。在此，我们引入了一种散射矩阵（S矩阵）方法的简单重构，其中S矩阵被定义为单个层的固有属性，独立于其相邻界面。这种层传播与界面耦合的分离保持了传统S矩阵形式体系的数值稳定性，同时为多层结构提供了更模块化的描述。它还使得外部平面波与布洛赫模式之间以及布洛赫模式之间的散射系数能够直接计算，为周期性界面提供了广义菲涅耳系数。此外，该重构允许同时评估多个层厚度或入射波矢的光学响应，与单次计算相比仅需适度的计算开销。在RETICOLO免费软件中实现后，这些能力为模态分析、参数扫描和分层光子结构的设计提供了实用框架。
英文摘要：
Modal methods are particularly well suited to layered photonic structures because electromagnetic propagation within each layer is described analytically. Here, we introduce a simple reformulation of the scattering-matrix (S-matrix) approach in which the S-matrix is defined as an intrinsic property of an individual layer, independently of its neighboring interfaces. This separation between layer propagation and interface coupling preserves the numerical stability of the conventional S-matrix formalism while providing a more modular description of multilayer structures. It also enables direct computation of the scattering coefficients between external plane waves and Bloch modes, as well as between Bloch modes themselves, providing generalized Fresnel coefficients for periodic interfaces. In addition, the reformulation allows the optical response to be evaluated simultaneously for many layer thicknesses or incident wavevectors, with only a modest computational overhead compared with a single calculation. Implemented in the RETICOLO freeware, these capabilities provide a practical framework for modal analysis, parameter sweeps, and the design of layered photonic structures.
