Abstract
Four-phase spiral waves are predicted to exist in a nonlinear optical cavity with competing quadratic (i.e., ${\ensuremath{\chi}}^{(2)})$ and cubic (i.e., ${\ensuremath{\chi}}^{(3)})$ 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 ${\ensuremath{\chi}}^{(3)}$ isotropic medium. Degenerate four-wave mixing of signal and idler fields induced by the ${\ensuremath{\chi}}^{(3)}$ 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.
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