We show that Kerr beam self-cleaning results from parametric mode mixing instabilities that generate a number of nonlinearly interacting modes with randomized phases - optical wave turbulence, followed by a direct and inverse cascade towards high mode numbers and condensation into the fundamental mode, respectively. This optical self-organization effect is an analogue to wave condensation that is well known in hydrodynamic 2D turbulence.
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Funding: This work was supported by the Russian Ministry of
Science and Education (Grant No. 14.Y26.31.0017),
and the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation
programme (Grant No. 740355). The work of S. K. T. was
supported by the Russian Science Foundation (Grant