Optical spiral waves supported by competing nonlinearities

Four-phase spiral waves are predicted to exist in a nonlinear optical cavity with competing quadratic (i.e., χ⁽²⁾) and cubic (i.e., χ⁽³⁾) nonlinearities. These spatial structures are found in the mean-field model of a doubly resonant type-II frequency-degenerate optical parametric oscillator with an intracavity χ⁽³⁾ isotropic medium. Degenerate four-wave mixing of signal and idler fields induced by the χ⁽³⁾ medium breaks the phase invariance of the down-conversion process, producing nonlinear phase locking with four possible phase states. A parametrically forced Ginzburg-Landau equation is derived to explain the existence of multiphase spiral waves.