Spatial beam self-cleaning: from non-equilibrium to thermalization of nonlinear multimode fiber modes

We present a direct experimental demonstration that spatial beam self-cleaning in nonlinear multimode gradedindex optical fibers arises from the nonequilibrium evolution of the mode population toward a state of thermal equilibrium. This process is shown to be a result of the maximization of the optical entropy of the modal distribution. Entropy maximization is observed both when the input beam power is increased with a fixed length of fiber, and when the fiber length grows larger while keeping the input beam power constant.