Spirals and vortex lattices in quasi-self-imaging divide-by-three optical parametric oscillators

M. Le Berre, E. Ressayre, and A. Tallet

Phys. Rev. E 73, 036220 – Published 29 March 2006

Abstract

A linear stability analysis is derived in self-imaging cavities for which the conditions for large Fresnel number are stated. In cases of both Fabry-Pérot and ring cavities a Hopf bifurcation is predicted at finite transverse wave number. The self-imaging Fabry-Pérot resonator operates as a longitudinal multimode cavity that invalidates the mean-field model. Above the bifurcation threshold, either vortex lattices, spirals, or targets occur, depending on the Fresnel number, the input intensity, and the mistunings. The time and spatial characteristics have different scales in the case of a self-imaging ring cavity, but the same sort of patterns are reported.