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

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