Modification of pattern formation in doubly resonant second-harmonic generation by competing parametric oscillation

We analyze pattern formation in doubly resonant intracavity second-harmonic generation in the presence of competing nondegenerate parametric downconversion. We show that for positive cavity detuning of the fundamental frequency the threshold for parametric oscillation is lower than that of transverse, pattern forming instabilities. The parametric oscillation strongly modifies the pattern dynamics found previously in a simplified analysis that neglects parametric instability [Phys. Rev. E 56, 4803 (1997)]. Stationary and dynamic patterns in the presence of parametric oscillation are found numerically.