非齐次波导方程基于状态转移算子和DtN映射的算法

针对存在内光源的导波方程,即非齐次Helmholtz方程,将波导方程的边值问题转化为可用步进算法的类“初值”处置问题,然后给出了一种基于Dirichlet to Neumann (DtN)映射和状态转移算子的算法。并给出了两个算例,算例表明此算法是非齐次周期波导问题的一种高效的计算方法。

An algorithm of the transfer operator P for a non-homogeneous waveguide equation based on Dirichlet-to-Neumann maps

An algorithm for the equation of a guided wave with an internal light source, i. e. a non-homogeneous Helmholtz waveguide equation, based on Dirichlet to Neumann(DtN) maps, where the boundary value problem of the waveguide equation is changed to an initial value like problem (IVP) which can be computed in a segmented manner by marching along the propagation direction is described, and the state transfer operators have been constructed. Two numerical examples are given which demonstrate that the algorithm is an efficient algorithm for periodic waveguide problems.