Theory of Incoherent Self-Focusing in Biased Photorefractive Media

A theory describing propagation and self-focusing of partially spatially incoherent light beams in nonlinear media is developed. It is shown that this process is effectively governed by an infinite set of coupled nonlinear Schr\"odinger-like equations, provided they are initially appropriately weighted with respect to the incoherent angular power spectrum of the source. The particular case of spatially incoherent beam propagation in biased photorefractive media is considered in detail. Numerical simulations indicate that spatial compression as well as self-trapped states are possible under appropriate conditions. Our results are in good agreement with recent experimental observations.