Search results for "Wave turbulence"
showing 10 items of 15 documents
Condensation of classical nonlinear waves
2005
We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schr\"odinger equation as a representative model. We formulate a thermodynamic description of the condensation process by using a wave turbulence theory with ultraviolet cut-off. In 3 dimensions the equilibrium state undergoes a phase transition for sufficiently low energy density, while no transition occurs in 2 dimensions, in analogy with standard Bose-Einstein condensation in quantum systems. Numerical simulations show that the thermodynamic limit is reached for systems with $16^3$ computational modes and greater. On the basis of a modified wave tu…
Introduction to Wave Turbulence Formalisms for Incoherent Optical Waves
2016
We provide an introduction to different wave turbulence formalisms describing the propagation of partially incoherent optical waves in nonlinear media. We consider the nonlinear Schrodinger equation as a representative model accounting for a nonlocal or a noninstantaneous nonlinearity, as well as higher-order dispersion effects. We discuss the wave turbulence kinetic equation describing, e.g., wave condensation or wave thermalization through supercontinuum generation; the Vlasov formalism describing incoherent modulational instabilities and the formation of large scale incoherent localized structures in analogy with long-range gravitational systems; and the weak Langmuir turbulence formalis…
MR2997965 (Review) 37D45 Viana, R. L.; Lopes, S. R.; Szezech, J.D., Jr.; Caldas, I. L. Synchronization of chaos and the transition to wave turbulence…
2013
In this paper the authors analyze the onset of the wave turbulence in the spatially extended threewave interacting model by using the concept of synchronization. In order to work with a set of ordinary differential equations, they make a pseudo-spectral decomposition of the wave field and identify the onset of wave turbulence as the excitation of spatial modes in the presence of underlying temporally chaotic dynamics. Each spatial point is regarded as a nonlinear oscillator and the onset of wave turbulence is the point where the oscillators lose phase synchronization. The authors use an extremely sensitive complex-order parameter to estimate the threshold of weak turbulence and perform a Ly…
Wave dynamics and turbulence in multimode optical systems
2021
The subject of this thesis essentially focuses on the experimental and theoretical study of optical turbulence in different types of nonlinear media. The first part of the manuscript is devoted to the study of thermalization and condensation of optical waves during their propagation in graded-index multimode fibers. The analysis based on the wave turbulence theory reveals that the disorder inherent to light propagation in an optical fiber induces a significant acceleration of the process of optical thermalization, which can clarify the mechanism of certain regimes of spatial beam cleaning recently reported in the literature. We show experimentally that the optical field relaxes during its p…
Optical Wave Turbulence in Fibers
2017
Classical wave thermalisation in chaotic multimode optical fibre
2023
Thermodynamic approach of supercontinuum generation
2009
International audience; This paper is aimed at providing an overview on recent theoretical and experimental works in which a thermodynamic description of the incoherent regime of supercontinuum generation has been formulated. On the basis of the wave turbulence theory, we show that this highly nonlinear and quasi-continuous-wave regime of supercontinuum generation is characterized by two different phenomena. (i) A process of optical wave thermalization ruled by the four-wave mixing effects: The spectral broadening inherent to supercontinuum generation is shown to result from the natural tendency of the optical field to reach its thermodynamic equilibrium state, i. e., the state of maximum n…
Wave turbulence in integrable systems: nonlinear propagation of incoherent optical waves in single-mode fibers.
2011
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…
Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics
2014
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…
Rogue wave description: Rational solitons and wave turbulence theory
2012
We show that rogue waves can emerge from optical turbulence and that their coherent deterministic description provided by the rational solutions is compatible with the statistical description provided by the wave turbulence theory.