Li Lifeng
J Opt Soc Am A Opt Image Sci Vis. 2021 Mar 1;38(3):426-436. doi: 10.1364/JOSAA.417769.
A systematic and formal study of the global and elemental properties of the propagating-order scattering matrix of conically mounted and crossed gratings is presented. The most general formulation of the scattering matrix is established. Expressions of the global properties (reciprocity and unitarity) of the scattering matrix ( matrix) in the general form previously not available in the literature are presented in the main text, and their full mathematical derivations are given in two appendices. The distinctive contribution of this work is an exposition of the elemental properties of the matrix. The elemental tensor and the elemental matrix, the latter being the linear-space representation of the former, for a pair of an incident plane wave and a diffracted order are defined and studied. The key results of the exposition are two sum rules of diffraction efficiencies and a dot-product-free, vectorial reciprocity theorem.
本文对锥形安装和交叉光栅的传播级散射矩阵的全局和元素特性进行了系统而正式的研究。建立了散射矩阵最一般的公式。正文中给出了散射矩阵（矩阵）全局特性（互易性和幺正性）的表达式，其形式在文献中前所未见，并在两个附录中给出了完整的数学推导。这项工作的独特贡献在于阐述了矩阵的元素特性。定义并研究了一对入射平面波和衍射级的元素张量和元素矩阵，后者是前者的线性空间表示。阐述的关键结果是两个衍射效率求和规则和一个无点积的矢量互易定理。
