基于DtN映射和三次样条逼近的二维分段均匀波导的算法

基于DtN映射的双向传播算法是计算具有二维分段均匀结构波导的最有效的算法之一。本文发展了一种新的计算DtN映射的算法，该算法主要利用三次样条函数逼近来计算每一均匀段上的DtN映射。此方法可以直接解析地表出需计算的特征值与特征向量，直接给出一阶导数的计算公式，减少了近似计算过程，从而减少计算误差。另外，它对解的光滑性要求较低，因此具有更好的适用性。本文给出的Cost 268 modeling task算例表明，这种基于DtN映射的三次样条函数逼近算法是一种高效的算法。

An algorithm for 2-D piecewise uniform waveguides based on Dirichlet-to-Neumann (DtN) maps and the spline approximation

The bidirectional propagation method based on Dirichlet-to-Neumann (DtN) maps is one of the most effective numerical methods for 2-D piecewise uniform waveguides developed to date. In this paper, a new method is developed to calculate the DtN map of each uniform segment using the spline approximation. In the method, the eigenvalues and eigenvectors—which need to be calculated for simplification—can be given analytically and a formula to calculate the first derivatives can be derived directly. Thus, the computational error is reduced. Furthermore, less smoothness of the solution is required so that the method has better applicability. A numerical example is given and the result shows that the method is efficient.