We analyze pattern for mation 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.
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机译：我们分析了在存在竞争性非简并参量下变频的情况下在双共振腔内二次谐波产生中的定量模式。我们表明，对于基频的正腔失谐，参数振荡的阈值低于横向，图案形成不稳定性的阈值。参数振荡极大地改变了先前在简化分析中发现的模式动力学，该简化分析忽略了参数不稳定性[Phys。 E 56、4803（1997）]。在数值上发现存在参数振荡的平稳和动态模式。
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