Propagation of partially incoherent light in nonlinear media via the Wigner transform method

The propagation of partially incoherent light in nonlinear media is analyzed using the Wigner transform method. The power and versatility of this approach is illustrated by several examples which clearly demonstrate how partial incoherence tends to suppress coherent instabilities by weakening the nonlinearity. In particular, it is found that the effect of partial incoherence on modulational instabilities can be described in terms of a Landau-like damping effect, which counteracts the coherent growth rate of the instability. Similarly, in the case of the self-focusing collapse instability, the nonlinear focusing effect becomes successively smaller as the coherence length of the light decreases and eventually no collapse phenomenon occurs