Anomalous thermalization of nonlinear wave systems

We report theoretically and experimentally in an optical system a process of anomalous thermalization of one-dimensional nonlinear Hamiltonian waves. It is characterized by an irreversible evolution of the waves towards a specific equilibrium state of a fundamental different nature than the expected thermodynamic equilibrium state. A kinetic approach of the problem reveals that this phenomenon is due to the existence of a local invariant in frequency space. A novel family of equilibrium distributions is discovered, which is found in quantitative agreement with the numerical simulations.

Anomalous thermalization of nonlinear opticalwave systems

In complete analogy with a system of classical particules colliding inside a gas medium, an incoherent optical field can evolve, owing to nonlinearity, towards a thermodynamic equilibrium state [1]. In this respect, the spatiotemporal dynamics of the light field is governed by the nonlinear Schrodinger equation and its equilibrium spectrum has been determined in the framework of the weak turbulence theory [1,2]. It is expected that experiments made in the field of nonlinear optics can possibly lead to the observation of turbulence or thermalization of nonlinear waves [1,2]. Here we present experimental, theoretical and numerical studies of different optical systems presenting an unusual the…

Wave turbulence in integrable systems: nonlinear propagation of incoherent optical waves in single-mode fibers.

International audience; We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a statistically stationary state. The evolution of the power spectrum of the field is characterized by the rapid growth of spectral tails that exhibit damped oscillations, until the whole spectrum ultima…

Thermalisation anormale d'ondes non linéaires

Wave turbulence and thermalization of random nonlinear waves

International audience

Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics

International audience; The nonlinear propagation of coherent optical fields has been extensively explored in the framework of nonlinear optics, while the linear propagation of incoherent fields has been widely studied in the framework of statistical optics. However, these two fundamental fields of optics have been mostly developed independently of each other, so that a satisfactory understanding of statistical nonlinear optics is still lacking. This article is aimed at reviewing a unified theoretical formulation of statistical nonlinear optics on the basis of the wave turbulence theory, which provides a nonequilibrium thermodynamic description of the system of incoherent nonlinear waves. W…

Anomalous thermalization of nonlinear optical waves

We report theoretically and experimentally an anomalous thermalization process characterized by an irreversible evolution of the waves towards a novel family of equilibrium states of a fundamental different nature than the standard thermodynamic equilibrium state.

Catastrophic process of coherence degradation

We predict a catastrophic process of coherence degradation characterized by a virtually unlimited spectral broadening of the waves. This effect is described by self-similar solutions of the kinetic equations inherent to the wave turbulence theory.

Temporal Dynamics of Incoherent Nonlinear Waves

We review different formalisms describing incoherent waves: the wave turbulence kinetic equation, the Vlasov equation in analogy with Gravitation, the weak Langmuir turbulence equation describing spectral solitons and incoherent dispersive shocks.

Thermalization of random nonlinear waves: Application to optical waves

International audience

Thermalization and condensation in an incoherently pumped passive optical cavity

International audience; We study theoretically and numerically the condensation and the thermalization of classical optical waves in an incoherently pumped passive Kerr cavity. We show that the dynamics of the cavity exhibits a turbulent behavior that can be described by the wave turbulence theory. A mean-field kinetic equation is derived, which reveals that, in its high finesse regime, the cavity behaves essentially as a conservative Hamiltonian system. In particular, the intracavity turbulent field is shown to relax adiabatically toward a thermodynamic equilibrium state of energy equipartition. As a consequence of this effect of wave thermalization, the incoherent optical field undergoes …

Influence of third-order dispersion on the propagation of incoherent light in optical fibers

International audience; We study the influence of third-order dispersion effects on the propagation of an incoherent nonlinear wave in an optical fiber system. The wave spectrum is shown to exhibit a highly asymmetric deformation characterized by a lateral spectral shoulder and the subsequent formation of an unexpected constant spectral pedestal. A kinetic approach to the problem reveals the existence of an invariant that explains in detail the essential properties of such asymmetric spectral evolution of the wave.