Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Unified framework of optical thermodynamics and optical pressure

Nikolaos K. Efremidis*

Huizhong Ren and Demetrios N. Christodoulides

  • *Contact author: nefrem@uoc.gr

Phys. Rev. Research 8, 033188 – Published 17 August, 2026

DOI: https://doi.org/10.1103/kf4x-yq24

Abstract

Optical thermodynamics is a recently developed framework that applies principles from statistical mechanics to describe the intricate behavior of weakly nonlinear, multimode photonic systems. Utilizing this theory, the collective dynamics of complex optical arrangements can be systematically uncovered and understood. The purpose of this work is to examine fundamental aspects of optical thermodynamics, including optical pressure, and provide a unified framework that can be applied effectively to any optical setting within the domain of validity of optical thermodynamics. We find that in addition to the conservation laws, the remaining extensive and intensive parameters of the system are naturally provided by the parameters of the propagation constants. At this point, several thermodynamic approaches exist for analyzing optical forces in multimode settings. Here, we develop a theoretical methodology that unifies these perspectives in a variety of different configurations, irrespective of whether they are discrete or continuous. We apply our theory in four different settings. By studying Su-Schrieffer-Heeger lattices, we elucidate the thermodynamics of polyatomic chains and show that intercell and intracell bonds can display different optical forces. In addition, we provide a thermodynamic formalism to predict and understand the optical pressure at equilibrium arising in arrangements characterized by a continuous index variation and apply our results to graded-index fibers.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (44)

  1. F. O. Wu, A. U. Hassan, and D. N. Christodoulides, Thermodynamic theory of highly multimoded nonlinear optical systems, Nat. Photonics 13, 776 (2019).
  2. Systems without such conservation laws require a different description, e.g., open-system or nonequilibrium thermodynamics, and fall outside the scope of the present theory. In addition, the thermodynamics of a photon gas in equilibrium with matter is a different physical problem: photons can be absorbed and emitted by the material reservoir, the photon number N is not conserved, and therefore its thermodynamic conjugate variable (the photon chemical potential) vanishes. In this case, the probability is described by a canonical ensemble ρ∼exp(−βU).
  3. M. Parto, F. O. Wu, P. S. Jung, K. Makris, and D. N. Christodoulides, Thermodynamic conditions governing the optical temperature and chemical potential in nonlinear highly multimoded photonic systems, Opt. Lett. 44, 3936 (2019).
  4. G. Lopez-Galmiche, Z. S. Eznaveh, M. A. Eftekhar, J. A. Lopez, L. G. Wright, F. Wise, D. Christodoulides, and R. A. Correa, Visible supercontinuum generation in a graded index multimode fiber pumped at 1064 nm, Opt. Lett. 41, 2553 (2016).
  5. Z. Liu, L. G. Wright, D. N. Christodoulides, and F. W. Wise, Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber, Opt. Lett. 41, 3675 (2016).
  6. K. Krupa, A. Tonello, B. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, Spatial beam self-cleaning in multimode fibres, Nat. Photonics 11, 237 (2017).
  7. H. Pourbeyram, P. Sidorenko, F. O. Wu, N. Bender, L. Wright, D. N. Christodoulides, and F. Wise, Direct observations of thermalization to a Rayleigh–Jeans distribution in multimode optical fibres, Nat. Phys. 18, 685 (2022).
  8. F. Mangini, M. Gervaziev, M. Ferraro, D. S. Kharenko, M. Zitelli, Y. Sun, V. Couderc, E. V. Podivilov, S. A. Babin, and S. Wabnitz, Statistical mechanics of beam self-cleaning in GRIN multimode optical fibers, Opt. Express 30, 10850 (2022).
  9. A. L. Marques Muniz, F. O. Wu, P. S. Jung, M. Khajavikhan, D. N. Christodoulides, and U. Peschel, Observation of photon-photon thermodynamic processes under negative optical temperature conditions, Science 379, 1019 (2023).
  10. K. Baudin, J. Garnier, A. Fusaro, N. Berti, C. Michel, K. Krupa, G. Millot, and A. Picozzi, Observation of light thermalization to negative-temperature Rayleigh-Jeans equilibrium states in multimode optical fibers, Phys. Rev. Lett. 130, 063801 (2023).
  11. F. O. Wu, Q. Zhong, H. Ren, P. S. Jung, K. G. Makris, and D. N. Christodoulides, Thermalization of light's orbital angular momentum in nonlinear multimode waveguide systems, Phys. Rev. Lett. 128, 123901 (2022).
  12. E. V. Podivilov, F. Mangini, O. S. Sidelnikov, M. Ferraro, M. Gervaziev, D. S. Kharenko, M. Zitelli, M. P. Fedoruk, S. A. Babin, and S. Wabnitz, Thermalization of orbital angular momentum beams in multimode optical fibers, Phys. Rev. Lett. 128, 243901 (2022).
  13. M. S. Kirsch, G. G. Pyrialakos, R. Altenkirch, M. A. Selim, J. Beck, T. A. Wolterink, H. Ren, P. S. Jung, M. Khajavikhan, A. Szameit, et al., Observation of Joule–Thomson photon-gas expansion, Nat. Phys. 21, 214 (2025).
  14. K. G. Makris, F. O. Wu, P. S. Jung, and D. N. Christodoulides, Statistical mechanics of weakly nonlinear optical multimode gases, Opt. Lett. 45, 1651 (2020).
  15. N. K. Efremidis and D. N. Christodoulides, Fundamental entropic processes in the theory of optical thermodynamics, Phys. Rev. A 103, 043517 (2021).
  16. P. S. Jung, G. G. Pyrialakos, F. O. Wu, M. Parto, M. Khajavikhan, W. Krolikowski, and D. N. Christodoulides, Thermal control of the topological edge flow in nonlinear photonic lattices, Nat. Commun. 13, 4393 (2022).
  17. N. Berti, K. Baudin, A. Fusaro, G. Millot, A. Picozzi, and J. Garnier, Interplay of thermalization and strong disorder: Wave turbulence theory, numerical simulations, and experiments in multimode optical fibers, Phys. Rev. Lett. 129, 063901 (2022).
  18. A. Y. Ramos, C. Shi, L. J. Fernández-Alcázar, D. N. Christodoulides, and T. Kottos, Theory of localization-hindered thermalization in nonlinear multimode photonics, Commun. Phys. 6, 189 (2023).
  19. G. Yang, D. Bongiovanni, D. Song, R. Morandotti, Z. Chen, and N. K. Efremidis, Thermalization dynamics in photonic lattices of different geometries, APL Photonics 9, 066115 (2024).
  20. G. Yang, J. Wang, Y. Chen, L. Song, S. Xia, D. Song, Z. Chen, and N. K. Efremidis, Unveiling prethermalization and thermal processes through the simplest one-dimensional topological model, APL Photonics 10, 076114 (2025).
  21. M. Ferraro, K. Baudin, M. Gervaziev, A. Fusaro, A. Picozzi, J. Garnier, G. Millot, D. Kharenko, E. Podivilov, S. Babin, F. Mangini, and S. Wabnitz, Wave turbulence, thermalization and multimode locking in optical fibers, Physica D 481, 134758 (2025).
  22. M. L. Povinelli, M. Lončar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, Evanescent-wave bonding between optical waveguides, Opt. Lett. 30, 3042 (2005).
  23. M. L. Povinelli, S. G. Johnson, M. Lončar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators, Opt. Express 13, 8286 (2005).
  24. P. T. Rakich, M. A. Popović, and Z. Wang, General treatment of optical forces and potentials in mechanically variable photonic systems, Opt. Express 17, 18116 (2009).
  25. P. T. Rakich, Z. Wang, and P. Davids, Scaling of optical forces in dielectric waveguides: Rigorous connection between radiation pressure and dispersion, Opt. Lett. 36, 217 (2011).
  26. H. Ren, H. Luo, M. A. Selim, G. G. Pyrialakos, F. O. Wu, M. Khajavikhan, and D. Christodoulides, Rigorous analysis of optical forces in dielectric structures based on the Minkowski-Helmholtz formula, Phys. Rev. A 106, 033517 (2022).
  27. M. Li, W. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. Tang, Harnessing optical forces in integrated photonic circuits, Nature (London) 456, 480 (2008).
  28. M. Li, W. H. P. Pernice, and H. X. Tang, Tunable bipolar optical interactions between guided lightwaves, Nat. Photonics 3, 464 (2009).
  29. J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, Tunable optical forces between nanophotonic waveguides, Nat. Nanotechnol. 4, 510 (2009).
  30. D. Van Thourhout and J. Roels, Optomechanical device actuation through the optical gradient force, Nat. Photonics 4, 211 (2010).
  31. M. Metcalfe, Applications of cavity optomechanics, Appl. Phys. Rev. 1, 031105 (2014).
  32. J. Rosenberg, Q. Lin, and O. Painter, Static and dynamic wavelength routing via the gradient optical force, Nat. Photonics 3, 478 (2009).
  33. J. Huang, L. K. Chin, H. Cai, H. Li, J. H. Wu, T. Chen, M. Li, and A.-Q. Liu, Dynamic phonon manipulation by optomechanically induced strong coupling between two distinct mechanical resonators, ACS Photonics 6, 1855 (2019).
  34. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, Near-field cavity optomechanics with nanomechanical oscillators, Nat. Phys. 5, 909 (2009).
  35. M. W. Pruessner, D. Park, T. H. Stievater, D. A. Kozak, and W. S. Rabinovich, Optomechanical cavities for all-optical photothermal sensing, ACS Photonics 5, 3214 (2018).
  36. M. Ren, J. Huang, H. Cai, J. M. Tsai, J. Zhou, Z. Liu, Z. Suo, and A.-Q. Liu, Nano-optomechanical actuator and pull-back instability, ACS Nano 7, 1676 (2013).
  37. N. K. Efremidis and D. N. Christodoulides, Thermodynamic optical pressures in tight-binding nonlinear multimode photonic systems, Commun. Phys. 5, 286 (2022).
  38. H. Ren, G. G. Pyrialakos, F. O. Wu, P. S. Jung, N. K. Efremidis, M. Khajavikhan, and D. N. Christodoulides, Nature of optical thermodynamic pressure exerted in highly multimoded nonlinear systems, Phys. Rev. Lett. 131, 193802 (2023).
  39. H. Ren, G. G. Pyrialakos, F. O. Wu, N. K. Efremidis, M. Khajavikhan, and D. N. Christodoulides, Dalton's law of partial optical thermodynamic pressures in highly multimoded nonlinear photonic systems, Opt. Lett. 49, 1802 (2024).
  40. N. K. Efremidis and D. N. Christodoulides, Statistical mechanics and pressure of composite multimoded weakly nonlinear optical systems, Opt. Lett. 49, 2777 (2024).
  41. H. A. Haus and H. Kogelnik, Electromagnetic momentum and momentum flow in dielectric waveguides, J. Opt. Soc. Am. 66, 320 (1976).
  42. R. Pathria and P. D. Beale, Statistical Mechanics, 3rd ed. (Butterworth-Heinemann, Oxford, 2011).
  43. N. K. Efremidis, Topological photonic Su-Schrieffer-Heeger-type coupler, Phys. Rev. A 104, 053531 (2021).
  44. K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, Burlington, MA, 2006).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation