Photonic plasma instabilities and soliton turbulence in spatially incoherent light

We develop a plasma theory of nonlinear statistical optics. In this model, partially spatially incoherent light is treated as an ensemble of speckles which can interact through the nonlinearity. A photonic plasma frequency is defined, as is a photonic Debye length. This approach unifies previous observations using partially coherent light and predicts a new class of optical phenomena. Examples include the two-scale energy transfer common to modulation instability and the continuous excitation of modes from the gradient-driven bump-on-tail instability. The latter example, well-known from plasma physics, represents a new regime for optical experiments. We observe it here by considering the nonlinear coupling of two partially coherent beams in a self-focusing photorefractive crystal. For weak wave coupling, determined by small modal density within a Debye sphere, we observe momentum exchange with no variation in intensity. For strong wave coupling, modulations in intensity appear, as does evidence for wave (Langmuir) collapse at large scales. To achieve a broader range of wave coupling, we consider a double bump-on-tail geometry. This system can be modeled as a pair of coupled single-hump instabilities whose interaction involves general issues of nonlinear competition, synchronization, etc. For the case of strong wave coupling, the multiple humps merge into a single-peaked profile with an algebraic k^-2 inertial range. This self-similar spectrum, representing an ensemble of dynamically-interacting solitons atop a sea of radiation modes, is a definitive observation of soliton (Langmuir) turbulence.