Abstract
Recent studies have shown that light propagating in a nonlinear, highly multimode system can thermalize in a manner totally analogous to that encountered in traditional statistical mechanics. At thermal equilibrium, the system’s entropy is at a maximum, in full accord with the second law of thermodynamics. In such arrangements, the entropy is extremized once the statistical power allocation among modes associated with this photon gas attains a Rayleigh-Jeans distribution that is fully characterized by an optical temperature and a chemical potential . However, it has been theoretically argued that the variables and represent actual thermodynamic forces that control the exchange of the respective conjugate quantities between two subsystems. In this work, we report, for the first time, optical calorimetric measurements in nonlinear multimode fibers, which unambiguously demonstrate that both the temperature and the chemical potential dictate the flow of their associated extensive quantities, i.e., the energy and the optical power. Specifically, we study the process of light thermalization associated with two orthogonally polarized laser beams. Our observations are enabled by recently developed techniques that allow one to judiciously multiplex/demultiplex the optical power within various mode groups. Our results indicate that because of photon-photon collisions, “heat” only flows from a hot to a cold photon gas subsystem—thus providing an unequivocal demonstration of the second law in such all-optical thermodynamic arrangements. In addition to being fundamental, our findings provide a new approach to manipulate laser beams using thermodynamic principles.
- Received 27 November 2022
- Accepted 11 December 2023
DOI:https://doi.org/10.1103/PhysRevX.14.021020
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
In a multimode optical system, light can behave like a gas of photons. As such, it can have thermodynamiclike parameters. These parameters must not be confused with actual physical parameters: The photon temperature cannot be measured with a thermometer. In fact, the physical meaning of these parameters is debated. Specifically, the definition of photon entropy can be questioned since no studies have yet reported on “heat” exchanges between photon gases in multimode systems. In this study, we carry out calorimetry experiments with optical beams in multimode fibers. We find that the heat flows only from a hotter to a colder photon gas, thus demonstrating that nonlinear beam propagation respects the second law of thermodynamics.
In complete analogy with the thermodynamics of classical gases, the heat of a photon gas represents the exchange of energy between two optical beams, whereas the temperature is a parameter that accounts for the modal content of the beam (the lower the temperature, the higher the fraction of power in the fundamental mode). Using a state-of-the-art holographic mode decomposition tool, we measure the modal content of optical beams, thus calculating their associated thermodynamic parameters. In our experiments, we inject two orthogonally polarized laser beams at different temperatures and chemical potentials into an optical fiber. We then measure the mode power distribution at the fiber output and find out how the temperature of each beam is modified after their nonlinear interaction in the fiber.
The finding paves the way for the development of all-optical devices for the control of laser beam spatial quality: By exchanging heat with a colder photon gas, an initially hot beam cools down, significantly increasing its fundamental mode content. As a result, the output beam transforms from a speckled, low-quality beam into a clean bell-shaped beam with much higher quality.
