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Nonlinear highly multimode photonic systems are ubiquitous in optics. Yet,the sheer complexity arising from the action of nonlinearity in multimodeenvironments has posed theoretical challenges in describing these systems. Inthis work, we deploy concepts from optical thermodynamics to investigate thenear- and far-field emission intensity patterns emerging from nonlinearwaveguide arrays. An exact equation dictating the response of a nonlinear arrayis derived in terms of the systems invariants that act as extensivethermodynamic variables. In this respect, the near- and far-fieldcharacteristics emerging from a weakly nonlinear waveguide lattice areanalytically addressed. We show that statistically, these patterns and theresulting far-field brightness are governed by the optical temperature and itscorresponding chemical potential. The extensivity associated with the entropyof such configurations is discussed. The thermodynamic results presented herewere found to be in good agreement with numerical simulations obtained fromnonlinear coupled-mode theory.

A thermodynamic description of the near- and far-field intensity patterns emerging from multimode nonlinear waveguide arrays