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We show that the orbital angular momentum (OAM) of a light field can bethermalized in a nonlinear cylindrical multimode optical waveguide. We find,that upon thermal equilibrium, the maximization of the optical entropy leads toa generalized Rayleigh-Jeans distribution that governs the power modaloccupancies with respect to the discrete OAM charge numbers. This distributionis characterized by a temperature that is by nature different from thatassociated with the longitudinal electromagnetic momentum flow of the opticalfield. Counterintuitively and in contrast to previous results, we demonstratethat even under positive temperatures, the ground state of the fiber is notalways the most populated in terms of power. Instead, because of OAM, thethermalization processes may favor higher order modes. A new equation of stateis derived along with an extended Euler equation -- resulting from theextensivity of the entropy itself. By monitoring the nonlinear interactionbetween two multimoded optical wavefronts with opposite spins, we show that theexchange of angular momentum is dictated by the difference in OAM temperatures,in full accord with the second law of thermodynamics. The theoretical analysispresented here is corroborated by numerical simulations that take into accountthe complex nonlinear dynamics of hundreds of modes. Our results may pave theway towards high power optical sources with controllable orbital angularmomenta, and at a more fundamental level, could shed light on the physics ofother complex multimoded nonlinear bosonic systems that display additionalconservation laws.

Thermalization of light's orbital angular momentum in nonlinear multimode waveguide systems