Wu Yumao, Lu Ya Yan
Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China.
J Opt Soc Am A Opt Image Sci Vis. 2011 Jun 1;28(6):1191-6. doi: 10.1364/JOSAA.28.001191.
Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Green's function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y. Y. Lu, J. Opt. Soc. Am. A26, 2444 (2009)] is extended to conical diffraction problems. The method uses boundary integral equations to calculate the so-called Neumann-to-Dirichlet maps for homogeneous subdomains of the grating, so that the quasi-periodic Green's functions can be avoided. Since wave field components are coupled on material interfaces with the involvement of tangential derivatives, a least squares polynomial approximation technique is developed to evaluate tangential derivatives along these interfaces for conical diffraction problems. Numerical examples indicate that the method performs equally well for dielectric or metallic gratings.
用于衍射光栅的边界积分方程方法特别适用于具有复杂材料界面的光栅，但由于准周期格林函数和角点处的奇异积分，该方法难以实现。本文将用于光栅面内衍射问题的边界积分方程诺伊曼到狄利克雷映射方法[Y. Wu和Y. Y. Lu，《美国光学学会志》A26，2444(2009)]扩展到锥形衍射问题。该方法使用边界积分方程来计算光栅均匀子域的所谓诺伊曼到狄利克雷映射，从而可以避免准周期格林函数。由于波场分量在材料界面上通过切向导数耦合，因此开发了一种最小二乘多项式逼近技术来评估锥形衍射问题中沿这些界面的切向导数。数值例子表明，该方法对介质光栅或金属光栅的效果同样良好。
