光腔模式及光束传输的特征向量算法

An Eigenvector Method for the Mode Simulation of Optical Resonators and Beam Propagation

发展了一种新颖的适用于光腔模式及光束传输模拟计算的特征向量法.该方法的核心是基于菲涅耳—基尔霍夫衍射积分理论构造了一种新的光腔传输矩阵,通过求解激光谐振腔的本征积分方程,即可一次求解得到表征腔镜上多个光场模式振幅及相位分布的特征向量组;而谐振腔内或腔外任意地方的光场分布,也可采用该方法进行光束传输模拟而求得.对与该方法有关的单元划分、形函数选取、误差及稳定性分析等问题进行了论述,分析表明:合适的单元划分和形函数选取有利于提高计算速度、精度和稳定性.

A novel Eigenveetor Method（EM）for the calculation of resonator modes and beam propagation is developed. A new transit matrix for the optical resonator is obtained based on the Fresnel-Kirchhoff diffracted integral equation. The eigenvectors of the transit matrix, that represent multi-mode characteristics of the resonator,are calculated with the integral eigen-equation. The field inside or outside the resonator resulting from the eigenvectors can be derived by EM as well. The partition of grids,choice of shape functions,error and convergence analyses are discussed. It shows that a suitable partition of grids and choice of shape functions are of benefit to increase calculation rate, precision and stability.