基于积分方程的平面光波导模式场分析方法

Mode Field Analysis Method of the Planar Optical Waveguides Based on an Integral Equation

通过傅里叶变换将波动方程转化为空间频域的积分方程,并采用Nystrm方法将积分方程转化成标准的矩阵特征问题.通过Lapack程序包求解矩阵的特征值和特征向量,同时得到平面介质光波导模式的色散关系和模式场.数值计算结果表明该方法适用于分析任何折射率分布的平面光波导模式场,使用阶数很小的矩阵就可以得到高准确度的结果.

The one dimensional wave equation was transformed into space-frequency domain by Fourier transform,and became an integral equation which could be solved by Nystrm method.A solver of standard matrix eigenvalue problem from the integral equation was given by Lapack packages.The dispersion relation and mode fields of a planar dielectric waveguide could be obtained simultaneously.The numerical results showed that the proposed method was flexible for planar optical waveguides with any refractive index profiles and high accuracy only using a low order matrix.