Spatiotemporal structures in the internally pumped optical parametric oscillator

We analyze pattern formation in doubly resonant second-harmonic generation in the presence of a competing parametric process, also named the internally pumped optical parametric oscillator. Different scenarios are established where either the up- or down-conversion processes dominate the spatiotemporal behavior. The possibility of obtaining exact solutions above threshold for the parametric oscillation process allows detailed analytical investigations of the parametric instability, that are supplemented by numerical analysis. We identify secondary instabilities that lead to formation of negative patterns and gray solitons. Estimates of the thresholds for pattern formation under experimentally relevant conditions are given.