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The input power-induced transformation of the transverse intensity profile at the output of graded-index multimode optical fibers from speckles into a bell-shaped beam sitting on a low intensity background is known as spatial beam self-cleaning. Its remarkable properties are the output beam brightness improvement and robustness to fiber bending and squeezing. These properties permit to overcome the limitations of multimode fibers in terms of low output beam quality, which is very promising for a host of technological applications. In this review, we outline recent progress in the understanding of spatial beam self-cleaning, which can be seen as a state of thermal equilibrium in the complex process of modal four-wave mixing. In other words, the associated nonlinear redistribution of the mode powers which ultimately favors the fundamental mode of the fiber can be described in the framework of statistical mechanics applied to the gas of photons populating the fiber modes. This description has been corroborated by a series of experiments by different groups. However, some open issues still remain, and we offer a perspective for future studies in this emerging and controversial field of research.

On spatial beam self-cleaning from the perspective of optical wave thermalization in multimode graded-index fibers