基于正切函数变换的改进型全域基展开法及其应用

A Modified Global Base Expansion Method Based on the Tangent Function Transformation and Its Application

基于正切函数变换 ,本文提出了改进型全域基展开法 (MGBEM) .该方法将无限xy平面映射成为单位平面 ,使单位平面边界上的电磁场自然为零 ,等效于自然边界条件 ,因而避免了边界截断问题 ,消除了人工反射 ,提高了计算精度 .另外 ,本方法导致的矩阵阶数小 ,有较高的计算效率 .本文选用正弦函数作为展开基 ,并将MGBEM应用于二维光波导标量模分析 。

Based on the tangent function transformation, a modified global base expansion method(MGBEM) is proposed. The infinite x-y plane is mapped into a unit square, so its electric field on the boundary is equal to zero naturally, which equates to the natural boundary conditions. Consequently, the boundary truncation is not necessary. As a result, the artificial reflection is eliminated and the computational accuracy is promoted. In addition, small matrix derived from this method promotes the computational efficiency. Selecting sine function as expanded base, we applied MGBEM to the scalar modal analysis of the two-dimensional optical waveguides. The effective index of the fundamental mode and its electric field distributions for the buried rectangular and rib optical waveguides are obtained respectively.