Modal analysis of unstable resonators

The analysis of the modes of optical resonators is crucial to understanding how actual laser devices operate. A consistent formulation that treats both the empty and loaded resonator modes is presented in this report. The study centers on unstable resonators and, in particular, strip resonators. The analysis of the bare cavity modes uses a matrix expansion technique with the linear prolate functions as a basis set. These functions form an optimal basis set in that they are related to the Schmidt expansion functions for the integral equation that describes the modes of the bare cavity. As a consequence, the matrix eigenvalue problem is solved using the minimum number of basis functions. The analysis is implemented in a numerical model that generates the linear prolate functions using a finite difference algorithm. The model was used to study the validity of the asymptotic approach at low Fresnel numbers. The results show that the first few lower loss modes predicted by the asymptotic approach are accurate but that the higher loss modes are inaccurately represented by that approach. The linear prolate function expansion is also used to numerically demonstrate the orthogonality of the resonator modes.