Entropic thermodynamics of nonlinear photonic chain networks

Fan O Wu,Pawel S Jung,Midya Parto,Mercedeh Khajavikhan,Demetrios N Christodoulides

doi:10.1038/s42005-020-00484-1

Fan O Wu, Pawel S Jung + Show 3 more

Open Access

https://doi.org/10.1038/s42005-020-00484-1

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Abstract

The convoluted nonlinear behaviors of heavily multimode photonic structures have been recently the focus of considerable attention. The sheer complexity associated with such multimode systems, allows them to display a host of phenomena that are otherwise impossible in few-mode settings. At the same time, however, it introduces a set of fundamental challenges in terms of comprehending and harnessing their response. Here, we develop an optical thermodynamic approach capable of describing the thermalization dynamics in large scale nonlinear photonic tight-binding networks. For this specific system, an optical Sackur-Tetrode equation is obtained that explicitly provides the optical temperature and chemical potential of the photon gas. Processes like isentropic expansion/compression, Joule expansion, as well as aspects associated with beam cleaning/cooling and thermal conduction effects in such chain networks are discussed. Our results can be used to describe in an effortless manner the exceedingly complex dynamics of highly multimoded nonlinear bosonic systems.

Highlights

The convoluted nonlinear behaviors of heavily multimode photonic structures have been recently the focus of considerable attention
To correctly account for all the nonlinear processes unfolding in this structure, one has to first estimate at least a trillion or so four-wave mixing coefficients, before even attempting to numerically solve the evolution problem—a formidable task which is by itself computationally intensive. To overcome these hurdles, a statistical approach has to be deployed that can effectively deal with many-body configurations. This calls for the development of a theoretical framework, akin to that of statistical mechanics, that has so far allowed us to understand the macroscopic properties of matter, in spite of the fact that on most occasions one has to deal with a great multitude of atoms or molecules—most often exceeding Avogadro’s number[17]
An optical thermodynamic theory was put forward, that can self-consistently describe by means of statistical mechanics the utterly complex processes of energy exchange in nonlinear multimode systems at thermal equilibrium[18]

Summary

Results and discussion

In heavily multimode arrangements, the thermodynamically extensive variables ðU; M; PÞ are related to each other through the optical temperature T ( called temperature) and chemical potential μ associated with the system This relation is given through a global equation of state, given by U À μP 1⁄4 MT that explicitly involves the total number of modes M The above results can be used to predict the outcome of more complex processes like, for example, that associated with Joule expansion of the photon gas in such nonlinear heavily multimoded environments This prospect is shown schematically, where as an example, χ(3) nonlinear array supporting M modes suddenly expands to four times its size (M → 4M), while all the lattice parameters are kept the same. Since M and P are invariant, an isentropic transition can only occur provided that

Conclusion

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