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arXiv:1908.01708 · Optics Letters

Thermodynamic conditions governing the optical temperature and chemical potential in nonlinear highly multimoded photonic systems

Midya Parto, Fan O. Wu, Pawel S. Jung, Konstantinos G. Makris, Demetrios N. Christodoulides

Published Aug 4, 2019• 61 citations
arXivHTMLPDF

Abstract

We show that, in general, any complex weakly nonlinear highly multimode system can reach thermodynamic equilibrium, characterized by a unique temperature and chemical potential. The conditions leading to either positive or negative temperatures are explicitly obtained in terms of the linear spectrum of the system, the input power, and the corresponding Hamiltonian invariant. Pertinent examples illustrating these results are provided in various scenarios.

DOI
10.1364/ol.44.003936

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We show that, in general, any complex weakly nonlinear highly multimode system can reach thermodynamic equilibrium, characterized by a unique temperature and chemical potential. The conditions leading to either positive or negative temperatures are explicitly obtained in terms of the linear spectrum of the system, the input power, and the corresponding Hamiltonian invariant. Pertinent examples illustrating these results are provided in various scenarios.
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By utilizing notions from statistical mechanics, we develop a general and self-consistent theoretical framework capable of describing any weakly nonlinear optical multimode system involving conserved quantities. We derive the fundamental relations that govern the grand canonical ensemble through maximization of the Gibbs entropy at equilibrium. In this classical picture of statistical photo-mechanics, we obtain analytical expressions for the probability distribution, the grand partition function, and the relevant thermodynamic potentials. Our results universally apply to any other weakly nonlinear multimode bosonic system.
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The past few years have witnessed a resurgence of interest in multimode structures, predominantly driven by the ever-increasing demand for higher information capacities. This renaissance, in turn, incited a flurry of activities in the general area of nonlinear multimode optics. The sheer complexity associated with the presence of hundreds or thousands of nonlinearly interacting modes that collectively act as a many-body system, has led to new opportunities in observing a multitude of novel optical effects that would have been otherwise impossible in single mode settings. In this talk, a thermodynamic theory capable of describing complex, highly multimoded, nonlinear optical systems is presented. It is shown that the mode occupancies in such nonlinear multimode arrangements follow a universal behavior that always tends to maximize the system’s entropy at steady-state. This thermodynamic response takes place irrespective of the type of nonlinearity involved and can be utilized to either heat or cool an optical multimode system. Aspects associated with adiabatic compressions and expansions will be discussed along with the possibility for all-optical Carnot cycles.
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