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Classical nonlinear random waves can exhibit a process of condensation. Itoriginates in the singularity of the Rayleigh-Jeans equilibrium distributionand it is characterized by the macroscopic population of the fundamental modeof the system. Several recent experiments revealed a phenomenon of spatial beamcleaning of an optical field that propagates through a graded-index multimodeoptical fiber (MMF). Our aim in this article is to provide physical insightinto the mechanism underlying optical beam self-cleaning through the analysisof wave condensation in the presence of structural disorder inherent to MMFs.We consider experiments of beam cleaning where long pulses are injected in theand populate many modes of a 10-20 m MMF, for which the dominant contributionof disorder originates from polarization random fluctuations (weak disorder).On the basis of the wave turbulence theory, we derive nonequilibrium kineticequations describing the random waves in a regime where disorder dominatesnonlinear effects. The theory reveals that the presence of a conservative weakdisorder introduces an effective dissipation in the system, which is shown toinhibit wave condensation in the usual continuous wave turbulence approach. Onthe other hand, the experiments of beam cleaning are described by a discretewave turbulence approach, where the effective dissipation induced by disordermodifies the regularization of wave resonances, which leads to an accelerationof condensation that can explain the effect of beam self-cleaning. Thesimulations are in quantitative agreement with the theory. The analysis alsoreveals that the effect of beam cleaning is characterized by a repolarizationas a natural consequence of the condensation process. In addition, the discretewave turbulence approach explains why optical beam self-cleaning has not beenobserved in step-index multimode fibers.

Wave condensation with weak disorder versus beam self-cleaning in multimode fibers