  Classical nonlinear random waves can exhibit a process of condensation. It
originates in the singularity of the Rayleigh-Jeans equilibrium distribution
and it is characterized by the macroscopic population of the fundamental mode
of the system. Several recent experiments revealed a phenomenon of spatial beam
cleaning of an optical field that propagates through a graded-index multimode
optical fiber (MMF). Our aim in this article is to provide physical insight
into the mechanism underlying optical beam self-cleaning through the analysis
of wave condensation in the presence of structural disorder inherent to MMFs.
We consider experiments of beam cleaning where long pulses are injected in the
and populate many modes of a 10-20 m MMF, for which the dominant contribution
of disorder originates from polarization random fluctuations (weak disorder).
On the basis of the wave turbulence theory, we derive nonequilibrium kinetic
equations describing the random waves in a regime where disorder dominates
nonlinear effects. The theory reveals that the presence of a conservative weak
disorder introduces an effective dissipation in the system, which is shown to
inhibit wave condensation in the usual continuous wave turbulence approach. On
the other hand, the experiments of beam cleaning are described by a discrete
wave turbulence approach, where the effective dissipation induced by disorder
modifies the regularization of wave resonances, which leads to an acceleration
of condensation that can explain the effect of beam self-cleaning. The
simulations are in quantitative agreement with the theory. The analysis also
reveals that the effect of beam cleaning is characterized by a repolarization
as a natural consequence of the condensation process. In addition, the discrete
wave turbulence approach explains why optical beam self-cleaning has not been
observed in step-index multimode fibers.
