用黎卡提变换法分析平板波导传播特性

Method of Ricatti Transformation for Analyzing Propagation Characteristics of Planar Waveguides

给出用黎卡提变换对光波导传播特性进行分析的一种适用面广、计算简便且精度较高的数值计算方法 ,可应用于线性及非线性的平板波导及圆光纤 .方法的要点是用黎卡提变换将波动方程由二阶常微分方程转换为一阶常微分方程 ,用四阶龙格库塔方法求解 .以多层、渐变折射率线性平板光波导为例说明本方法的有效性 。

Method of Ricatti Transformation is applied to the analysis of propagation characteristics of slab waveguides. The method is simple, efficient and can be applied to linear and nonlinear planar waveguides and optical fibers with arbitrary refractive index profile and nonlinearity. In this method, second order ordinary differential equation for guided modes is converted into first order ordinary differential equation, which is solved by standard fourth order Runge Kutta method. Multi layer step index and graded index linear slab waveguides are taken as examples to demonstrate the effectiveness of this method. Numerical results for some typical graded index profiles are given which agree well with exact results.