Search results for "WAVE TURBULENCE"

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…

Incoherent solitons and condensation processes

2006

International audience; We study the nonlinear interaction of partially incoherent nonlinear optical waves. We show that, in spite of the incoherence of the waves, coherent phase effects may play a relevant role during the propagation, in contrast with the usual wave turbulence description of the interaction. These nonlinear phase effects may lead the system to unexpected processes of self-organization, such as condensation, or incoherent soliton generation in instantaneous response nonlinear media. Such self-organization processes may be characterized by a reduction of the non-equilibrium entropy, which violates the Boltzmann's H-theorem of entropy growth inherent to the wave turbulence th…

Toward a wave turbulence formulation of statistical nonlinear optics

2012

International audience; During this last decade, several remarkable phenomena inherent to the nonlinear propagation of incoherent optical waves have been reported in the literature. This article is aimed at providing a generalized wave turbulence kinetic formulation of random nonlinear waves governed by the nonlinear Schrodinger equation in the presence of a nonlocal or a noninstantaneous nonlinear response function. Depending on the amount of nonlocal (noninstantaneous) nonlinear interaction and the amount of inhomogeneous (nonstationary) statistics of the incoherent wave, different types of kinetic equations are obtained. In the spatial domain, when the incoherent wave exhibits fluctuatio…

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…

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…

Optical Wave Turbulence in Fibers

2017

Wave-turbulence approach of supercontinuum generation: Influence of self-steepening and higher-order dispersion

2009

International audience; We analyze the influence of self-steepening and higher-order dispersion on the process of optical wave thermalization. This study is aimed at developing a thermodynamic formulation of supercontinuum generation in photonic crystal fibers. In the highly nonlinear regime of supercontinuum generation, the optical field exhibits a turbulent dynamics that may be described by the kinetic wave theory. In this respect, the phenomenon of spectral broadening inherent to supercontinuum generation may be interpreted as a natural process of thermalization, which is characterized by an irreversible evolution of the optical field toward a thermodynamic equilibrium state. The numeric…

Rogue waves, rational solitons and wave turbulence theory

2011

International audience; Considering a simple one dimensional nonlinear Schrödinger optical model, we study the existence of rogue wave events in the highly incoherent state of the system and compare them with the recently identified hierarchy of rational soliton solutions. We show that rogue waves can emerge in the genuine turbulent regime and that their coherent deterministic description provided by the rational soliton solutions is compatible with an accurate statistical description of the random wave provided by the wave turbulence theory. Furthermore, the simulations reveal that even in the weakly nonlinear regime, the nonlinearity can play a key role in the emergence of an individual r…

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…