Hexagonal Patches and Modes in Degenerated Nonlinear Cavities : The Role of Aberrations

We consider the transverse nonlinear dynamics of an optical system with spherical aberrations. We assume the simplest possible system which consists in a cavity composed of a nonlinear mirror (a MIXSEL), a lens, and a curved mirror. Close to the self-imaging condition, small defects such as the spherical aberration become relevant and we derive analitically a model for the effective dynamics of the transverse profile, assuming that we have either a temporal localized state or CW emission along the propagation axis. In both cases, we find that the latter is a Rosanov Equation [1] perturbed by a bi-laplacian term.