Nonlinear Waves and Turbulence in Photonics 2022 - Abstract
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 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. The latter is a Rosanov Equation perturbed by a bilaplacian term. When the product of the phase front curvature and of the residual diffraction is negative, which corresponds to a stable cavity, we recover nonlinear Hermite-Gauss like modes. Interestingly, in the opposed situation that corresponds to an unstable cavity, we disclose another family of stable modes that are supported by the aberrations. They correspond to off-axis emission and an enlightening analogy with a quantum particle in a double potential can be observed in the Fourier domain. These eigenmodes can be analytically calculated and corresponds to spatially modulated Hermite-Gauss modes. We relate the value of the tilt to the cavity parameters. Beyond this regime, a short wavelength Turing instability is observed in the stable cavity configuration for some specific parameter set.