Bischoff Joerg
OSIRES Optical Engineering, Schillerstr. 19, D-98693 Ilmenau, Germany.
J Opt Soc Am A Opt Image Sci Vis. 2010 May 1;27(5):1024-31. doi: 10.1364/JOSAA.27.001024.
The utilization of symmetries in rigorous coupled wave analysis in order to reduce the matrix sizes and thus the computation time is an appropriate measure for an effective numerical implementation with no loss of accuracy. Another method to improve the convergence is the so-called normal vector method. This method is based on the transformation of the components of the electromagnetic fields in a lateral plane (or slice) from global coordinates into local normal and tangential coordinates relative to the boundaries between two different materials. In this way, the lateral boundary conditions of the electromagnetic field can be imposed more correctly as opposed to the traditional approximation introduced by Li, resulting in a better convergence in many cases. This paper shows how both methods can be combined to attain an optimum solution.
在严格耦合波分析中利用对称性以减小矩阵规模从而缩短计算时间，是一种在不损失精度的情况下进行有效数值实现的恰当措施。另一种提高收敛性的方法是所谓的法向量法。该方法基于将横向平面（或切片）中电磁场分量从全局坐标转换为相对于两种不同材料之间边界的局部法向和切向坐标。这样，与Li引入的传统近似方法相比，电磁场的横向边界条件能够更准确地施加，在许多情况下会带来更好的收敛性。本文展示了如何将这两种方法结合起来以获得最优解。
