Direct Observation of Thermalization to a Rayleigh-Jeans Distribution in Multimode Optical Fibers

Recent years have witnessed a resurgence of interest in nonlinear multimode optical systems where a host of intriguing effects have been observed that are impossible in single-mode settings. While nonlinearity can provide a rich environment where the chaotic power exchange among thousands of modes can lead to novel behaviors, at the same time, it poses a major challenge in terms of understanding and harnessing these processes to advantage. Over the years, statistical models have been developed to macroscopically describe the response of these complex systems. One of the cornerstones of these theoretical formalisms is the prediction of a photon-photon mediated thermalization process that leads to a Rayleigh-Jeans distribution of mode occupations. Here we report the use of mode-resolved measurement techniques to make the first direct observations of thermalization to a Rayleigh-Jeans power distribution in a multimode optical fiber. We experimentally demonstrate that the underlying system Hamiltonian remains invariant during propagation while power equipartition takes place among degenerate groups of modes - all in full accord with theoretical predictions. Our results may pave the way toward a new generation of high-power optical sources whose brightness and modal content can be controlled using principles from thermodynamics and statistical mechanics.