Multiphase patterns in self-phase-locked optical parametric oscillators

Multiphase patterns are found in a mean-field model of a singly-resonant op tical parametric oscillator that converts a pump field at frequency 3 omega into signal and idler fields at frequencies 2 omega and omega. A complex G inzburg-Landau equation without diffusion and with a quadratic phase-sensit ive nonlinear term is derived under single-longitudinal and paraxial propag ation approximations. Owing to the phase-matched multistep parametric proce ss omega + omega = 2 omega, phase locking of the resonated signal field is possible with three distinct phase states. Three-armed rotating spirals. ta rget patterns and light filamentation are found by a numerical analysis of the mean-field equation.