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We revisit the mechanisms underlying the process of spectral broadening ofincoherent optical waves propagating in nonlinear media on the basis ofnonequilibrium thermodynamic considerations. A simple analysis reveals that aprerequisite for the existence of a significant spectral broadening of thewaves is that the linear part of the energy (Hamiltonian) has differentcontributions of opposite signs. It turns out that, at variance with theexpected soliton turbulence scenario, an increase of the amount of disorder(incoherence) in the system does not require the generation of a coherentsoliton structure. We illustrate the idea by considering the propagation of twowave components in an optical fiber with opposite dispersion coefficients. Awave turbulence approach of the problem reveals that the increase of kineticenergy in one component is offset by the negative reduction in the othercomponent, so that the waves exhibit, as a general rule, a virtually unlimitedspectral broadening. More precisely, a self-similar solution of the kineticequations reveals that the spectra of the incoherent waves tend to relax towarda homogeneous distribution in the wake of a front that propagates in frequencyspace with a decelerating velocity. We discuss this catastrophic process ofspectral broadening in the light of different important phenomena, inparticular supercontinuum generation, soliton turbulence, wave condensation,and the runaway motion of mechanical systems composed of positive and negativemasses.

On the origins of spectral broadening of incoherent waves:Catastrophic process of coherence degradation