基于复模式匹配的半矢量硅基光波导模式求解方法

[摘要] 提出了一种基于半矢量复模式匹配方法的类矩形波导模式求解方法，利用一维复模式求解和复模式匹配方法，求解包括矩形波导在内的任何类矩形波导的电磁场分布和有效折射率。首先在波导一个维度进行差分离散，得到一维复模式分布，在另一个维度利用波导的边界条件和电磁场在波导内的奇偶分布特性得到解析关系，最后通过求解特征矩阵得到类矩形波导中电磁场的分布。与传统方法相比，利用复模式匹配方法求解类矩形波导中的模场具有计算精度高，适用范围广等优点。

[关键词] 矩形波导；复模式匹配；半矢量

[Abstract] In this paper, a new two dimensional rectangle-like waveguide mode based on semi-vectorial complex mode-matching-method is proposed. Utilizing one-dimensional complex modes and complex mode-matching method, the electromagnetic filed distribution and effective index of waveguide modes can be obtained. The one-dimensional mode distribution can be obtained by using difference discrete in one dimension of the waveguide and the analytic relationship of the other dimension can be solved by using the boundary condition and parity distribution characteristic of the electromagnetic field in the waveguide. The electromagnetic field can be derived by solving the eigenmatrix. Compared with the full vector method, the solution we proposed has the wide application and high accuracy.

[Keywords] wo-dimensional waveguide; complex mode-matching-method; semi-vector