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1.
Phys Rev Lett ; 129(6): 063901, 2022 Aug 05.
Artigo em Inglês | MEDLINE | ID: mdl-36018655

RESUMO

We address the problem of thermalization in the presence of a time-dependent disorder in the framework of the nonlinear Schrödinger (or Gross-Pitaevskii) equation with a random potential. The thermalization to the Rayleigh-Jeans distribution is driven by the nonlinearity. On the other hand, the structural disorder is responsible for a relaxation toward the homogeneous equilibrium distribution (particle equipartition), which thus inhibits thermalization (energy equipartition). On the basis of the wave turbulence theory, we derive a kinetic equation that accounts for the presence of strong disorder. The theory unveils the interplay of disorder and nonlinearity. It unexpectedly reveals that a nonequilibrium process of condensation and thermalization can take place in the regime where disorder effects dominate over nonlinear effects. We validate the theory by numerical simulations of the nonlinear Schrödinger equation and the derived kinetic equation, which are found in quantitative agreement without using any adjustable parameter. Experiments realized in multimode optical fibers with an applied external stress evidence the process of thermalization in the presence of strong disorder.

2.
Phys Rev E ; 104(5-1): 054205, 2021 Nov.
Artigo em Inglês | MEDLINE | ID: mdl-34942767

RESUMO

The long-term behavior of a modulationally unstable conservative nonintegrable system is known to be characterized by the soliton turbulence self-organization process. We consider this problem in the presence of a long-range interaction in the framework of the Schrödinger-Poisson (or Newton-Schrödinger) equation accounting for the gravitational interaction. By increasing the amount of nonlinearity, the system self-organizes into a large-scale incoherent localized structure that contains "hidden" coherent soliton states: The solitons can hardly be identified in the usual spatial or spectral domains, but their existence can be unveiled in the phase-space representation (spectrogram). We develop a theoretical approach that provides the coupled description of the coherent soliton component [governed by the Schrödinger-Poisson equation (SPE)] and of the incoherent structure [governed by a wave turbulence Vlasov-Poisson equation (WT-VPE)]. We demonstrate theoretically and numerically that the incoherent structure introduces an effective trapping potential that stabilizes the hidden coherent soliton and we show that the incoherent structure belongs to a family of stationary solutions of the WT-VPE. The analysis reveals that the incoherent structure evolves in the strongly nonlinear regime and that it is characterized by a compactly supported spectral shape. By relating the analytical properties of the hidden soliton to those of the stationary incoherent structure, we clarify the quantum-to-classical (i.e., SPE-to-VPE) correspondence in the limit ℏ/m→0: The hidden soliton appears as the latest residual quantum correction preceding the classical limit described by the VPE. This study is of potential interest for self-gravitating Boson models of fuzzy dark matter. Although we focus our paper on the Schrödinger-Poisson equation, we show that the regime of hidden solitons stabilized by an incoherent structure is general for long-range wave systems featured by an algebraic decay of the interacting potential. This work should stimulate nonlinear optics experiments in highly nonlocal nonlinear (thermal) media that mimic the long-range nature of gravitational interactions.

3.
Phys Rev Lett ; 127(1): 014101, 2021 Jul 02.
Artigo em Inglês | MEDLINE | ID: mdl-34270296

RESUMO

We consider the problem of the formation of soliton states from a modulationally unstable initial condition in the framework of the Schrödinger-Poisson (or Newton-Schrödinger) equation accounting for gravitational interactions. We unveil a previously unrecognized regime: By increasing the nonlinearity, the system self-organizes into an incoherent localized structure that contains "hidden" coherent soliton states. The solitons are hidden in the sense that they are fully immersed in random wave fluctuations: The radius of the soliton is much larger than the correlation radius of the incoherent fluctuations, while its peak amplitude is of the same order of such fluctuations. Accordingly, the solitons can hardly be identified in the usual spatial or spectral domains, while their existence is clearly unveiled in the phase-space representation. Our multiscale theory based on coupled coherent-incoherent wave turbulence formalisms reveals that the hidden solitons are stabilized and trapped by the incoherent localized structure. Furthermore, hidden binary soliton systems are identified numerically and described theoretically. The regime of hidden solitons is of potential interest for self-gravitating Boson models of "fuzzy" dark matter. It also sheds new light on the quantum-to-classical correspondence with gravitational interactions. The hidden solitons can be observed in nonlocal nonlinear optics experiments through the measurement of the spatial spectrogram.

4.
Phys Rev Lett ; 122(12): 123902, 2019 Mar 29.
Artigo em Inglês | MEDLINE | ID: mdl-30978031

RESUMO

Classical nonlinear waves exhibit a phenomenon of condensation that results from the natural irreversible process of thermalization, in analogy with the quantum Bose-Einstein condensation. Wave condensation originates in the divergence of the thermodynamic equilibrium Rayleigh-Jeans distribution, which is responsible for the macroscopic population of the fundamental mode of the system. However, achieving complete thermalization and condensation of incoherent waves through nonlinear optical propagation is known to require prohibitive large interaction lengths. Here, we derive a discrete kinetic equation describing the nonequilibrium evolution of the random wave in the presence of a structural disorder of the medium. Our theory reveals that a weak disorder accelerates the rate of thermalization and condensation by several order of magnitudes. Such a counterintuitive dramatic acceleration of condensation can provide a natural explanation for the recently discovered phenomenon of optical beam self-cleaning. Our experiments in multimode optical fibers report the observation of the transition from an incoherent thermal distribution to wave condensation, with a condensate fraction of up to 60% in the fundamental mode of the waveguide trapping potential.

5.
Phys Rev Lett ; 120(5): 055301, 2018 Feb 02.
Artigo em Inglês | MEDLINE | ID: mdl-29481198

RESUMO

The nonlinear Schrödinger equation, used to describe the dynamics of quantum fluids, is known to be valid not only for massive particles but also for the propagation of light in a nonlinear medium, predicting condensation of classical waves. Here we report on the initial evolution of random waves with Gaussian statistics using atomic vapors as an efficient two dimensional nonlinear medium. Experimental and theoretical analysis of near field images reveal a phenomenon of nonequilibrium precondensation, characterized by a fast relaxation towards a precondensate fraction of up to 75%. Such precondensation is in contrast to complete thermalization to the Rayleigh-Jeans equilibrium distribution, requiring prohibitive long interaction lengths.

6.
Opt Lett ; 39(14): 4192-5, 2014 Jul 15.
Artigo em Inglês | MEDLINE | ID: mdl-25121684

RESUMO

Spectral incoherent solitons (SIS) refer to an incoherent solitonic structure that only can be identified in the frequency domain and which is sustained by noninstantaneous Raman-like nonlinearities. We provide a generalized formulation of SIS by considering the generalized nonlinear Schrödinger equation. We show that nonlinear dispersive effects (e.g., self-steepening) dramatically affect the structure of SIS, in particular by significantly decelerating their spectral velocity in frequency space. The wave turbulence description of the problem reveals an underlying self-organization process: the soliton trajectory in frequency space is selected in such a way that it allows the system to self-organize into a stationary SIS state.

7.
Opt Lett ; 39(3): 590-3, 2014 Feb 01.
Artigo em Inglês | MEDLINE | ID: mdl-24487873

RESUMO

We study the interaction of temporal incoherent solitons sustained by a highly noninstantaneous (Raman-like) nonlinear response. The incoherent solitons exhibit a nonmutual interaction, which can be either attractive or repulsive depending on their relative initial distance. The analysis reveals that incoherent solitons exhibit a long-range interaction in frequency space, which is in contrast with the expected spectral short-range interaction described by the usual approach based on the Raman-like spectral gain curve. Both phenomena of anomalous interaction and spectral long-range behavior of incoherent solitons are described in detail by a long-range Vlasov equation.

8.
Opt Lett ; 38(16): 2972-5, 2013 Aug 15.
Artigo em Inglês | MEDLINE | ID: mdl-24104624

RESUMO

We study the influence of a constant background noise on the dynamics of spectral incoherent solitons, which are incoherent structures sustained by a noninstantaneous (Raman-like) nonlinearity. As the level of the noise background increases, the incoherent wave enters a novel nonlinear regime characterized by oscillatory dynamics of the incoherent spectrum, which develop within a spectral cone during the propagation. In contrast to the conventional Raman-like spectral red shift, such incoherent spectral dynamics can be characterized by a significant spectral blue shift. On the basis of the kinetic wave theory, we derive explicit analytical expressions of these incoherent oscillatory spectral dynamics.

9.
Phys Rev Lett ; 111(11): 113902, 2013 Sep 13.
Artigo em Inglês | MEDLINE | ID: mdl-24074088

RESUMO

We predict theoretically and numerically the existence of incoherent dispersive shock waves. They manifest themselves as an unstable singular behavior of the spectrum of incoherent waves that evolve in a noninstantaneous nonlinear environment. This phenomenon of "spectral wave breaking" develops in the weakly nonlinear regime of the random wave. We elaborate a general theoretical formulation of these incoherent objects on the basis of a weakly nonlinear statistical approach: a family of singular integro-differential kinetic equations is derived, which provides a detailed deterministic description of the incoherent dispersive shock wave phenomenon.

10.
Phys Rev Lett ; 107(23): 233901, 2011 Dec 02.
Artigo em Inglês | MEDLINE | ID: mdl-22182089

RESUMO

The long-term behavior of a modulationally unstable nonintegrable system is known to be characterized by the soliton turbulence self-organization process: It is thermodynamically advantageous for the system to generate a large-scale coherent soliton in order to reach the ("most disordered") equilibrium state. We show that this universal process of self-organization breaks down in the presence of a highly nonlocal nonlinear response. A wave turbulence approach based on a Vlasov-like kinetic equation reveals the existence of an incoherent soliton turbulence process: It is advantageous for the system to self-organize into a large-scale, spatially localized, incoherent soliton structure.

11.
Opt Lett ; 36(20): 4038-40, 2011 Oct 15.
Artigo em Inglês | MEDLINE | ID: mdl-22002378

RESUMO

We consider the counterpropagating interaction of a signal and a pump beam in a spun fiber and in a randomly birefringent fiber, the latter being relevant to optical telecommunication systems. On the basis of a geometrical analysis of the Hamiltonian singularities of the system, we provide a complete understanding of the phenomenon of polarization attraction in these two systems, which allows to achieve a control of the polarization state of the signal beam by adjusting the polarization of the pump. In spun fibers, all polarization states of the signal beam are attracted toward a specific line of polarization states on the Poincaré sphere, whose characteristics are determined by the polarization state of the injected backward pump. In randomly birefringent telecommunication fibers, we show that an unpolarized signal beam can be repolarized into any particular polarization state, without loss of energy.

12.
Opt Express ; 19(18): 17852-63, 2011 Aug 29.
Artigo em Inglês | MEDLINE | ID: mdl-21935152

RESUMO

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 ultimately reaches a steady state. The kinetic approach allows us to derive an analytical expression of the damped oscillations, which is found in agreement with the numerical simulations of both the NLS and kinetic equations. We report the experimental observation of this peculiar relaxation process of the integrable NLS equation.

13.
Phys Rev Lett ; 104(5): 054101, 2010 Feb 05.
Artigo em Inglês | MEDLINE | ID: mdl-20366765

RESUMO

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.

14.
Opt Express ; 17(9): 7392-406, 2009 Apr 27.
Artigo em Inglês | MEDLINE | ID: mdl-19399118

RESUMO

We report an experimental, numerical and theoretical study of the incoherent regime of supercontinuum generation in a two zero-dispersion wavelengths fiber. By using a simple experimental setup, we show that the phenomenon of spectral broadening inherent to supercontinuum generation can be described as a thermalization process, which is characterized by an irreversible evolution of the optical field towards a thermal equilibrium state. In particular, the thermodynamic equilibrium spectrum predicted by the kinetic wave theory is characterized by a double peak structure, which has been found in quantitative agreement with the numerical simulations without adjustable parameters. We also confirm that stimulated Raman scattering leads to the generation of an incoherent structure in the normal dispersion regime which is reminiscent of a spectral incoherent soliton.


Assuntos
Tecnologia de Fibra Óptica/métodos , Modelos Teóricos , Análise Espectral Raman/métodos , Simulação por Computador , Luz , Fótons , Espalhamento de Radiação , Temperatura
15.
Opt Lett ; 33(23): 2833-5, 2008 Dec 01.
Artigo em Inglês | MEDLINE | ID: mdl-19037442

RESUMO

We consider the incoherent nonlinear regime of the supercontinuum generation process in optical fibers. We show that, under certain conditions, the phenomenon of spectral broadening inherent to the supercontinuum generation may be described by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the supercontinuum generation process may be regarded as a thermalization process, which is characterized by an irreversible evolution of the optical field toward a thermodynamic equilibrium state, i.e., the state of maximum nonequilibrium entropy.

16.
Phys Rev Lett ; 101(9): 093901, 2008 Aug 29.
Artigo em Inglês | MEDLINE | ID: mdl-18851612

RESUMO

We show both theoretically and experimentally in an optical fiber system that a noninstantaneous nonlinear environment supports the existence of spectral incoherent solitons. Contrary to conventional solitons, spectral incoherent solitons do not exhibit a confinement in the spatiotemporal domain, but exclusively in the frequency domain. The theory reveals that the causality condition inherent to the nonlinear response function is the key property underlying the existence of spectral incoherent solitons. These solitons constitute nonequilibrium stable states of the incoherent field and are shown to be robust with respect to binary collisions.

17.
Opt Express ; 16(22): 17171-85, 2008 Oct 27.
Artigo em Inglês | MEDLINE | ID: mdl-18957998

RESUMO

We analyze theoretically the polarization properties of a partially coherent optical field that propagates in a nonlinear Kerr medium. We consider the standard model of two resonantly coupled nonlinear Schrödinger equations, which account for a wave-vector mismatch between the orthogonal polarization components. We show that such a phase-mismatch is responsible for the existence of a spontaneous repolarization process of the partially incoherent optical field during its nonlinear propagation. The repolarization process is characterized by an irreversible evolution of the unpolarized beam towards a highly polarized state, without any loss of energy. This unexpected result contrasts with the commonly accepted idea that an optical field undergoes a depolarization process under nonlinear evolution. The repolarization effect can be described in details by simple thermodynamic arguments based on the kinetic wave theory: It is shown to result from the natural tendency of the optical field to approach its thermal equilibrium state. The theory then reveals that it is thermodynamically advantageous for the optical field to evolve towards a highly polarized state, because this permits the optical field to reach the ???most disordered state???, i.e., the state of maximum (nonequilibrium) entropy. The theory is in quantitative agreement with the numerical simulations, without adjustable parameters. The physics underlying the reversible property of the repolarization process is briefly discussed in analogy with the celebrated Joule???s experiment of free expansion of a gas. Besides its fundamental interest, the repolarization effect may be exploited to achieve complete polarization of unpolarized incoherent light without loss of energy.

18.
Opt Express ; 15(14): 9063-83, 2007 Jul 09.
Artigo em Inglês | MEDLINE | ID: mdl-19547246

RESUMO

Focus Serial: Frontiers of Nonlinear Optics

This concise review is aimed at providing an introduction to the kinetic theory of partially coherent optical waves propagating in nonlinear media. The subject of incoherent nonlinear optics received a renewed interest since the first experimental demonstration of incoherent solitons in slowly responding photorefractive crystals. Several theories have been successfully developed to provide a detailed description of the novel dynamical features inherent to partially coherent nonlinear optical waves. However, such theories leave unanswered the following important question: Which is the long term (spatiotemporal) evolution of a partially incoherent optical field propagating in a nonlinear medium? In complete analogy with kinetic gas theory, one may expect that the incoherent field may evolve, owing to nonlinearity, towards a thermodynamic equilibrium state. Weak-turbulence theory is shown to describe the essential properties of this irreversible process of thermal wave relaxation to equilibrium. Precisely, the theory describes an irreversible evolution of the spectrum of the field towards a thermodynamic equilibrium state. The irreversible behavior is expressed through the H-theorem of entropy growth, whose origin is analogous to the celebrated Boltzmann's H-theorem of kinetic gas theory. It is shown that thermal wave relaxation to equilibrium may be characterized by the existence of a genuine condensation process, whose thermodynamic properties are analogous to those of Bose-Einstein condensation, despite the fact that the considered optical wave is completely classical. In spite of the formal reversibility of optical wave propagation, the condensation process occurs by means of an irreversible evolution of the field towards a homogeneous plane-wave (condensate) with small-scale fluctuations superimposed (uncondensed particles), which store the information necessary for the reversible propagation. As a remarkable result, an increase of entropy ("disorder") in the optical field requires the generation of a coherent structure (plane-wave). We show that, beyond the standard thermodynamic limit, wave condensation also occurs in two spatial dimensions. The numerical simulations are in quantitative agreement with the kinetic wave theory, without any adjustable parameter.

19.
Phys Rev Lett ; 97(3): 033902, 2006 Jul 21.
Artigo em Inglês | MEDLINE | ID: mdl-16907501

RESUMO

We show both theoretically and experimentally in an optical fiber system that a set of incoherent nonlinear waves irreversibly evolves to a specific equilibrium state, in which the individual wave packets propagate with identical group velocities. This intriguing process of velocity locking can be explained in detail by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the selection of the velocity-locked state is shown to result from the natural tendency of the isolated wave system to approach the state that maximizes the nonequilibrium entropy.

20.
Phys Rev Lett ; 96(1): 013905, 2006 Jan 13.
Artigo em Inglês | MEDLINE | ID: mdl-16486457

RESUMO

We show that a conservative system of a pair of coupled incoherent nonlinear waves exhibits huge oscillations of coherence, which are characterized by a recurrent transfer of noise fluctuations between the coupled waves. This sustained oscillatory behavior is in contradiction with the expected irreversible evolution towards equilibrium. As a consequence, the process of coherence transfer is characterized by a reduction of nonequilibrium entropy, which violates the H theorem of entropy growth inherent to the kinetic theory.

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