An analytical way of the fundamental cavity mode construction

In this work the analytical way of the fundamental cavity mode construction is proposed. It in not necessary to find eigenvectors of the monodromy matrix. The algorithm can be used both to obtain explicit formulae for Gaussian beam and to perform numerical calculations. The procedure offered consists in sequential simplification of a problem using homothetic transformations to reduce it to one of basic variants being solved explicitly-in some cases as a continuous set of matrices. The correspondence between these variants and spectral characteristics of an initial monodromy matrix is established