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

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 consider ably simpler procedure for solution of eigenvectors of the matrix eigen-equation replaces the complicated iteration in traditional methods,and there is no depen dence on the initial field distribution,and a number of modes can be derived on ce and the discrimination capability of the resonator can be evaluated easily. T he 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 approx imatie analytical solution,prove that EM is highly effective and reasonable.