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Thermodynamic theory of highly multimoded nonlinear optical systems

Nature Photonics volume 13, pages 776–782 (2019)Cite this article

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Abstract

Lately, there has been a resurgence of interest in nonlinear multimode optical systems. The sheer complexity emerging from the presence of a multitude of nonlinearly interacting modes has led not only to new opportunities in observing a host of novel optical effects but also to new theoretical challenges in understanding their collective dynamics. Here, we present a consistent thermodynamical framework capable of describing in a universal fashion the exceedingly intricate behaviour of such photonic configurations. In this respect, we derive new equations of state and show that both the ‘internal energy’ and optical power always flow in accord to the second law of thermodynamics. The laws governing isentropic processes are derived and the prospect for realizing Carnot-like cycles is presented. In addition to shedding light on fundamental issues, our work may pave the way towards a new generation of high-power multimode optical structures and could have ramifications in other disciplines, such as Bose–Einstein condensates and optomechanics.

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Fig. 1: Thermalization dynamics in nonlinear multimode waveguides and cavity structures.
Fig. 2: Thermalization in a canonical-like optical multimode nonlinear configuration involving two circular polarizations.
Fig. 3: Thermalization of two different optical waveguide lattices in thermal contact.
Fig. 4: Thermalization in a grand canonical-like configuration involving a Lieb and a rectangular nonlinear optical lattice.
Fig. 5: All-optical refrigeration via Carnot cycles.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank G. Tan and Y. Huang for computing support. We acknowledge financial support by the Office of Naval Research (ONR) (MURI N00014-17-1-2588 and N00014-18-1-2347), the National Science Foundation (NSF) (EECS-1711230) and the Qatar National Research Fund (NPRP9-020-1-006).

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Authors and Affiliations

  1. CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, FL, USA

    Fan O. Wu, Absar U. Hassan & Demetrios N. Christodoulides

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  1. Fan O. Wu
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  2. Absar U. Hassan
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Contributions

All authors contributed extensively to the work presented in this paper. F.O.W., A.U.H. and D.N.C. developed the theoretical formalism. F.O.W. performed the calculation. F.O.W., A.U.H. and D.N.C. wrote the paper. D.N.C. supervised the project.

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Correspondence to Demetrios N. Christodoulides.

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Supplementary Information

Supplementary methods and derivations and Figs. 1–7.

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Wu, F.O., Hassan, A.U. & Christodoulides, D.N. Thermodynamic theory of highly multimoded nonlinear optical systems. Nat. Photonics 13, 776–782 (2019). https://doi.org/10.1038/s41566-019-0501-8

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