An eigenvector method for optical field simulation

In this paper, an eigenvector method (EM) is developed to calculate the optical field in resonators. A new transit matrix of an optical resonator is obtained based on the Fresnel-Kirchhoff diffraction integral equation by dividing the mirrors into finite elements. The hundreds of times of iteration in the traditional methods are transferred into the solution of eigenvalues of the transit matrix. Each eigenvalue can easily deduced one eigenvector matrix, which just describes the characteristics of one mode in the resonator. The beam propagation can be simulated with EM as well. The main advantages of EM are that a series of multi-modes can be obtained at one time and there is no dependence on the initial field distribution. As an example, the field distribution of an unstable resonator is illustrated, which is consistent well with the experimental result. (C) 2004 Elsevier B.V. All rights reserved.