Propagation of incoherent “white” light and modulation instability in noninstantaneous nonlinear media

We develop a theory describing propagation of spatially and temporally incoherent light in noninstantaneous nonlinear media, and predict the existence of modulation instability of “white” light. We find that the modulation instability of white light is fundamentally a collective effect, where all the temporal frequencies participate in the formation of a pattern, and self-adjust their respective contributions.