Extended asymptotic theory of unstable resonator modes.
The modes in an unstable resonator can be computed within the limit of a large Fresnel number using the asymptotic expansion of the diffraction integral, as shown by Horwitz, Butts, and Avizonis. The expansion is not valid for the points of interest around or beyond the shadow boundary of the output light. We use a better numerical representation, which extends the regions of use. The comparison of several cases with earlier work shows that the asymptotic theory can be successfully applied for all parameters without restrictions.