Nonlinear Waves and Turbulence in Photonics 2022 - Abstract
Picozzi, Antonio
Different studies on wave turbulence revealed that purely classical waves can exhibit a process of condensation that originates from the thermalization of the waves toward the Rayleigh-Jeans (RJ) equilibrium distribution [1,2]. Although this phenomenon of condensation of classical waves differs from the quantum Bose-Einstein condensation, the underlying mathematical origin is analogous because of the common singular behavior (vanishing denominator) of the equilibrium Bose distribution for quantum particles and the equilibrium Rayleigh-Jeans distribution for classical waves [1]. However, the observation of condensation of optical waves in a conservative (e.g., cavity-less) configuration is hindered by the prohibitive large propagation lengths required to achieve RJ thermalization. The observation of the RJ condensation of light waves has been reported [3,4], in relation with the observation of RJ thermalization [5,6]. Our experiments are based on a phenomenon of spatial beam cleaning recently discovered in multimode optical fibers [7,8] and whose underlying mechanism still remains debated [9-11]. As a matter of fact, light propagation in multimode optical fibers is affected by a structural disorder of the material. We have formulated a wave turbulence kinetic description of the random waves that account for the presence of structural disorder. The theory unveils a dramatic acceleration of the process of thermalization and condensation that is induced by the disorder [3]. This fast process of condensation can explain the effect of spatial beam cleaning as a consequence of the macroscopic population of the fundamental mode of the fiber [3,9]. Our experiments in multimode fibers evidence the transition to light condensation: By decreasing the kinetic energy ('temperature') below the critical value, we observe a transition from the incoherent thermal RJ distribution to wave condensation [4]. The experimental results show that the chemical potential reaches the lowest energy level at the critical value of the energy to condensation, which leads to the macroscopic population of the fundamental mode of the optical fiber. The near-field and far-field measurements of the condensate fraction across the transition to condensation are in quantitative agreement with the RJ theory [12]. We have also characterized the thermodynamics of classical condensation through the analysis of the specific heat: In opposition to quantum Bose-Einstein condensation, the heat capacity takes a constant value in the condensed state and tends to vanish above the transition in the normal state [4]. Finally, we will present recent results about the development of a wave turbulence theory accounting for the impact of strong disorder.
References:
[1] C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, S. Rica, Condensation of classical nonlinear waves, PRL 95, 263901 (2005)
[2] P. Aschieri et al., Condensation and thermalization of classsical optical waves in a waveguide, PRA 83, 033838 (2011)
[3] A. Fusaro et al., Dramatic Acceleration of Wave Condensation Mediated by Disorder in Multimode Fibers, PRL 122, 123902 (2019)
[4] K. Baudin et al., Classical Rayleigh-Jeans condensation of classical light waves: Observation and thermodynamic characterization, PRL 125, 244101 (2020)
[5] F. Mangini et al., Statistical mechanics of beam self-cleaning in GRIN multimode optical fibers, Optics Express 30, 10850 (2022)
[6] H. Pourbeyram et al., Direct measurement of thermalization to Rayleigh-Jeans distribution in optical beam self cleaning, Nature Physics (2022).
[7] K. Krupa et al., Spatial beam self-cleaning in multimode fibers, Nature Photon. 11, 237 (2017)
[8] L.G. Wright et al., Self-organized instability in graded-index multimode fibres, Nature Photon. 10, 771 (2016)
[9] J. Garnier et al., Wave condensation with weak disorder versus beam self-cleaning in multimode fibers, PRA 100, 053835 (2019)
[10] E. Podivilov et al, Hydrodynamic 2D Turbulence and Spatial Beam Condensation in Multimode Optical Fibers, PRL 122, 103902 (2019)
[11] F. O. Wu et al., Thermodynamic theory of highly multimoded nonlinear optical systems, Nature Photon. 13, 776 (2019)
[12] K. Baudin et al., Energy and wave-action flows underlying Rayleigh-Jeans thermalization of optical waves propagating in a multimode fiber, EPL 134, 14001 (2021)