We present an analytic variational scheme which predicts the modes and losses for empty resonators with large Fresnel number <i>N</i>. The method is most accurate for stable cavities, with decreasing effectiveness as the cavity becomes unstable. We consider mainly the boundary area between the stable and unstable regimes described by neither Gaussian beams nor approximate asymptotic solutions. Numerical results in this region for circular mirrors are presented. The method may be extended to stable cavities.
© 1980 Optical Society of America
J. Nagel and D. Rogovin, "Analytic variational method for determining the modes of marginally stable resonators," J. Opt. Soc. Am. 70, 1525-1538 (1980)