The eigenvalues for all the significant low-order resonant modes of an unstable optical resonator with circular mirrors are computed using an eigenvalue method called the Prony method. A general equivalence relation is also given, by means of which one can obtain the design parameters for a single-ended unstable resonator of the type usually employed in practical lasers, from the calculated or tabulated values for an equivalent symmetric or double-ended unstable resonator.
A. E. Siegman and H. Y. Miller, "Unstable Optical Resonator Loss Calculations Using the Prony Method," Appl. Opt. 9, 2729-2736 (1970)