分析介质光波导传播特性的Cole-Hopf变换法

Method of Cole-Hopf Transformation for Analyzing Propagation Characteristics of Planar Optical Waveguides

采用 Cole- Hopf变换法 ,将平板光波导导模所满足的二阶常微分方程 (Helmholtz方程 )变换成一阶常微分方程 (Riccati方程 ) ,用较简单且有效的方法分析导模的特性。给出了多层阶跃型及渐变型平板波导导模的精确解析解和数值解法及实例 ;给出了非线性平板波导传播特性的数值计算法及实例。

Using method of Cole Hopf transformation,Helmholtz equation was transformed to Riccati equation,and propagation characteristics of guided modes in planar optical waveguides was analyzed in a simple and direct way.Exact analytic solutions for guided modes in multilayer step index guides and graded index guides were given and illustrated by examples.Numerical melhod for analyzing propagation characteristics of nonlinear planar waveguides was also given and illustrated by example.