椭圆光波导解析解及第一个高阶模的截止频率研究

The Study of Analytical Solution and Cutoff Frequency of First-Higher-Order Mode for Elliptical Optical Waveguide

本文对椭圆光波导进行了严格的求解，得到了模场的精确解析解，导出了模式特征方程，并且证明了圆光波导仅是椭圆光波导的一个特例。文中还对第一个高阶模的特征方程进行数值求解，得出不同椭圆度下的有效折射率与归一化频率的关系曲线及第一个高阶模的归一化截止频率随椭圆比的变化。

The analytical solutions of electromagnetic wave equations for elliptical optical waveguide are studied and the mode field distribution is presented. The mode characteristic equations are derived. Circular waveguide is only a special case of elliptical waveguide. The numerical solution for the characteristic equation of first-higher-order mode is obtained. The variations of the effective refractive index as a function of the normalized frequency for various values of the core aspect ratio are presented. As the core aspect ratio increases,the normalized cutoff frequency of the first-higher-order mode decreases.