Explicit formulae for higher modes of a nonplanar cavity with odd number of mirrors

For optical ring-type cavity with a nonplanar contour and one astigmatic focusing element (a curved mirror or a lens), stability conditions were investigated and explicit formulae for the fundamental mode were obtained in using technique outlined in. Unlike the traditional approach, these formulae do not contain eigenvectors of a cavity´s monodromy matrix (i.e. round-trip ray matrix). In this paper, on the contrary, the solution in question is used to find analytical expressions for eigenvectors mentioned, to construct rising operators and to obtain cavity´s higher modes in the case of odd number of mirrors.