Direct Measurement of Thermalization to Rayleigh-Jeans Distribution in Optical Beam Self-Cleaning.

An equilibrium thermodynamic framework that describes highly-multimode optical processes was introduced recently. This theory predicts the outcomes of complex linear and nonlinear multimode interactions based on thermodynamic principles and provides analytic results for the distributions of mode occupancies in optical systems. Here, we present direct experimental measurements of irreversible thermalization of initial distributions of mode occupancies to the predicted equilibrium Rayleigh-Jeans distribution in nonlinear wave propagation in multimode optical fiber. Kerr self-cleaning of femtosecond light pulses is shown to yield the Rayleigh-Jeans distribution, which confirms that the process maximizes entropy. Analytic theory, numerical simulations, and experimental results agree.