一种新颖的用于光腔模式及光束传输模拟的特征向量法

A novel eigenvector method for calculation of optical resonator modes and beam propagation

根据有限元法单元划分的思想 ,提出了一种新颖的模拟光腔模式及光束传输的特征向量法 .该方法的关键之处在于基于衍射积分理论构造了一种新的光束传输矩阵 ,通过求解特征矩阵方程可一次性得到谐振腔的一系列特征向量 ,每一列特征向量即代表了腔镜上光场的一个确定模式的振幅及相位分布 .并可采用该方法模拟光场传输到腔内或腔外任意地方的场分布 .该方法将传统方法中大量的迭代过程转化成为本征积分方程特征向量的求解过程 ,并与初值取值无关 ,且可一次性求得多个模式分布 ,从而可方便地分析谐振腔的模式鉴别能力 .特征向量法对圆形镜共焦腔的计算结果与Fox_Li法迭代结果和拉盖尔_高斯近似法所得到的解析结果完全相符 。

In this paper,a novel eigenvector method (EM) for calculation of optical resonator modes and beam propagation is introduced,in which the new transit matrix of an optical resonator is obtained by dividing the mirror into finite grids based on Fresnel_Kirchhoff diffracted integral equation. Then,the eigenvectors of the transit matrix,representing the multi_mode characteristics of the resonator,can be calculated by solving the matrix eigen_equation. The field distributions inside or outside the resonator,resulting from the known eigenvectors on the resonator mirror,can be derived by EM. The merits of EM include that the considerably simpler procedure for solution of eigenvectors of the matrix eigen_equation replaces the complicated iteration in traditional methods,and there is no dependence on the initial field distribution,and a number of modes can be derived once and the discrimination capability of the resonator can be evaluated easily. The example of using EM to simulate the confocal resonator is given,and the calculated results,well matched with the Fox_Li method and Laguerre_Gaussian approximatie analytical solution,prove that EM is highly effective and reasonable.