Self-organization, Pattern Formation, Cavity Solitons and Rogue Waves in Singly Resonant Optical Parametric Oscillators

Spatio-temporal dynamics of singly resonant optical parametric oscillators with external seeding displays hexagonal, roll and honeycomb patterns, optical turbulence, rogue waves and cavity solitons. We derive appropriate mean-field equations with a sinc$^2$ nonlinearity and demonstrate that off-resonance seeding is necessary and responsible for the formation of complex spatial structures via self-organization. We compare this model with those derived close to the threshold of signal generation and find that back-conversion of signal and idler photons is responsible for multiple regions of spatio-temporal self-organization when increasing the power of the pump field.