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Turbulence in the quantum (superfluid) regime, similarly to its classicalcounterpart, continues to attract a great deal of scientific inquiry, due tothe yet high number of unresolved problems. While turbulent states can beroutinely created in degenerate atomic gases, there is no generic scheme toproduce turbulence in fluids of light. Under paraxial propagation, light inbulk nonlinear media behaves as a two-dimensional superfluid, described by anonlinear Schr\"{o}dinger equation formally equivalent to the Gross-Pitaevskiimodel of a weakly interacting Bose gas, where photon-photon interactions aremediated by a third order (Kerr) nonlinearity. Here, we develop the theorydescribing the onset of a kinetic instability when two paraxial optical fluidswith different streaming velocities interact via the optical nonlinearity. Fromnumerical simulations of the nonlinear Schr\"{o}dinger equation, we furthercharacterize the onset of the instability and describe its saturation in theform of vortex nucleation and excitation of turbulence. The experimentalobservation of such effects is also discussed. The class of instabilitiesdescribed here thus provide a natural route towards the investigation ofquantum (superfluid) turbulence, structure formation and out-of-equilibriumdynamics in superfluids of light.

Turbulence Excitation in Counter-Streaming Paraxial Superfluids of Light