  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.
