Formation and interaction of spatially incoherent solitons in a slow nonlinear medium

Spatial soliton represents an optical beam propagating in nonlinear medium without changing its shape. The process of diffraction is exactly counter-balanced by nonlinear refractive index change so the beam is self-trapped and propagates effectively as a mode (or modes) of the self-induced waveguide. So far the term spatial soliton has been associated with coherent optical beam. An interesting situation may arise if the light beam is derived from the incoherent light source. The light emitted from different points of such source is completely uncorrelated. In effect, the phase across the beam exhibits randomness. This so-called partially coherent beam is fully described by the mutual coherence function. Partially coherent beam diverges stronger than corresponding coherent beam of the same transversal extent. Recent work has shown that partially coherent beam can propagate as a spatial soliton. However, the necessary condition for soliton formation is that the nonlinearity has to be inertial. More precisely, the medium has to respond in a time scale, which is slower than that of the fast variation of beam´s phase. Under such circumstances the medium will “see” a time averaged light intensity which is a smooth function of spatial coordinates. Then, the beam will be trapped and propagate in a form of a superposition of many mutually incoherent components. We studied experimentally the interaction of the multicomponent incoherent solitons in a photorefractive crystal. We found that indeed these solitons change their profile in collision. However, since the photorefractive nonlinearity is of saturable character the soliton collisions are inelastic. Consequently, the solitons have oscillatory dynamics after the collision