Spiral waves supported by competing quadratic and cubic nonlinearities

Summary form only given. In this work we predict the existence of a novel class of optical spiral waves supported by the competition of quadratic and cubic nonlinearities in an optical cavity that differ from optical vortices and spiral structures previously found in nonlinear optics. These new structures are found in a mean-field model of a type-II frequency-degenerate optical parametric oscillator with an intracavity isotropic cubic medium, and bear a close connection to phase-locked spiral waves recently observed in a parametrically-forced chemical system.