Condensation of Classical Nonlinear Waves

Connaughton, Colm; Josserand, Christophe; Picozzi, Antonio; Pomeau, Yves; Rica, Sergio

doi:10.1103/physrevlett.95.263901

Cited by 191 publications

(289 citation statements)

References 26 publications

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“…On the contrary, when increasing H, modes at any point in the structure can sustain oscillations at any frequency, and as they are all coupled, they synchronize, resulting in large-scale coherent emission. This process is to be compared with other forms of recently reported examples of condensation processes in nonlinear optics, [29][30][31] and extends previously reported investigations to the spatial domain. 28 To provide a model for the reported phenomena, we describe the electric field E as a mode superposition written as…”

Section: Resultssupporting

confidence: 64%

Non-locality and collective emission in disordered lasing resonators

2013

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Random lasing is observed in optically active resonators in the presence of disorder. As the optical cavities involved are open, the modes are coupled, and energy may pour from one state to another provided that they are spatially overlapping. Although the electromagnetic modes are spatially localized, our system may be actively switched to a collective state, presenting a novel form of non-locality revealed by a high degree of spectral correlation between the light emissions collected at distant positions. In a nutshell, light may be stored in a disordered nonlinear structure in different fashions that strongly differ in their spatial properties. This effect is experimentally demonstrated and theoretically explained in titania clusters embedded in a dye, and it provides clear evidence of a transition to a multimodal collective emission involving the entire spatial extent of the disordered system. Our results can be used to develop a novel type of miniaturized, actively controlled all-optical chip.

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Section: Resultssupporting

confidence: 64%

Non-locality and collective emission in disordered lasing resonators

2013

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“…The dynamics acquires an irreversible character by spatial or temporal coarse-graining [134]. This can be mapped to a Boltzmann equation that yields an irreversible evolution where the system thermalizes to an equilibrium state with Rayleigh-Jeans statistics [41,135]. Figure 19 shows the density profile and its resolution into condensate and thermal density, before (left panels) and after (right panels) GPe evolution.…”

Section: Slow Thermalization Of the Initial Statementioning

confidence: 99%

Comparison between microscopic methods for finite-temperature Bose gases

et al. 2011

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We analyze the equilibrium properties of a weakly interacting, trapped quasi-one-dimensional Bose gas at finite temperatures and compare different theoretical approaches. We focus in particular on two stochastic theories: a number-conserving Bogoliubov (ncB) approach and a stochastic GrossPitaevskii equation (sGPe) that have been extensively used in numerical simulations. Equilibrium properties like density profiles, correlation functions, and the condensate statistics are compared to predictions based upon a number of alternative theories. We find that due to thermal phase fluctuations, and the corresponding condensate depletion, the ncB approach loses its validity at relatively low temperatures. This can be attributed to the change in the Bogoliubov spectrum, as the condensate gets thermally depleted, and to large fluctuations beyond perturbation theory. Although the two stochastic theories are built on different thermodynamic ensembles (ncB: canonical, sGPe: grandcanonical), they yield the correct condensate statistics in a large BEC (strong enough particle interactions). For smaller systems, the sGPe results are prone to anomalously large number fluctuations, well-known for the grand-canonical, ideal Bose gas. Based on the comparison of the above theories to the modified Popov approach, we propose a simple procedure for approximately extracting the Penrose-Onsager condensate from first-and second-order correlation functions that is computationally convenient. This also clarifies the link between condensate and quasi-condensate in the Popov theory of low-dimensional systems.

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“…Therefore one expects, assuming a constant injection of wave action in the injecting domain around k i , the formation of such spectrum in finite time. This situation is in fact similar to the self-similar formation of a condensate of weakly classical nonlinear waves [11,12,14,31] and we shall characterize quantitatively this selfsimilar dynamics. To do that, we compute the characteristic length scale involved in the self-similar process, via the negative moments (typically n ≤ −2 later on) of the spectral distribution [1]:…”

Section: Signature Of a Finite-time Singularitymentioning

confidence: 68%

Self-similar formation of an inverse cascade in vibrating elastic plates

2015

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The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the framework of wave turbulence for elastic plates, we present substantial evidence of the existence of a time dependent inverse cascade, opening up the possibility of self organization for a larger class of systems. This inverse cascade transports the spectral density of the amplitude of the waves from short up to large scales, increasing the distribution of long waves despite the short wave fluctuations. This dynamics appears to be self-similar and possesses a power law behavior in the short wavelength limit which is significantly different from the exponent obtained via a Kolmogorov dimensional analysis argument. Finally, we show explicitly a tendency to build a long wave coherent structure in finite time.

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Condensation of Classical Nonlinear Waves

Cited by 191 publications

References 26 publications

Non-locality and collective emission in disordered lasing resonators

Non-locality and collective emission in disordered lasing resonators

Comparison between microscopic methods for finite-temperature Bose gases

Self-similar formation of an inverse cascade in vibrating elastic plates

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