Wakabayashi Hideaki, Asai Masamitsu, Yamakita Jiro
J Opt Soc Am A Opt Image Sci Vis. 2018 Nov 1;35(11):1861-1870. doi: 10.1364/JOSAA.35.001861.
In the theory of gratings, a diffraction solution must satisfy the energy balance and the reciprocity. This paper examines the diffraction by multilayered dielectric gratings, including lossy layers of which the solutions do not satisfy the energy balance. Applying the shadow theory to the matrix eigenvalues method, the symmetry of scattering factors in the theory and that of diffraction efficiencies are shown in some formulae and then are validated numerically. In addition, the reciprocity errors for diffraction efficiencies and scattering factors are newly considered as an accuracy criterion. It is shown that, on numerical calculations, the reciprocity errors for diffraction efficiencies have only to be checked.
在光栅理论中，衍射解必须满足能量平衡和互易性。本文研究多层介质光栅的衍射问题，其中包括解不满足能量平衡的有损层。将阴影理论应用于矩阵特征值方法，在一些公式中展示了理论中散射因子的对称性和衍射效率的对称性，然后进行了数值验证。此外，新考虑了衍射效率和散射因子的互易误差作为精度标准。结果表明，在数值计算中，只需检查衍射效率的互易误差。
