Incoherent Dispersive Shocks in the Spectral Evolution of Random Waves

Garnier, Josselin; Xu, Gang; Trillo, Stefano; Picozzi, Antonio

doi:10.1103/physrevlett.111.113902

Cited by 47 publications

(61 citation statements)

References 62 publications

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“…The leading-order Burgers term in (16) is responsible for the development of a gradient catastrophe, which is subsequently regularized by the nonlinear dispersive term involving the Hilbert operator [7]. This prediction is confirmed by numerical simulations of the NLSE (1) with boundary conditions (2), which have been found in quantitative agreement with the MF-KE (5) and the reduced singular integro-differential MF-KE (16), as shown in Fig.…”

Section: Continuous Response Function: Spectral Shock Wavesupporting

confidence: 75%

“…4. As discussed in detail in [7], the dispersive shock wave reported here develops in the spectral evolution of the incoherent wave. It is thus of fundamental different nature than the conventional dispersive shocks that develop either in the spatial or the temporal domain from coherent disturbances, which have been experimentally observed in ion-acoustic waves [100], water surface gravity waves [101], and fiber optics [102], and have recently regained great interest in optics [103][104][105][106][107][108][109][110][111][112].…”

Section: Continuous Response Function: Spectral Shock Wavementioning

confidence: 99%

“…It was shown in Ref. [7] that the convolution operator is dominated by the behavior of the response function R(t) near by the origin t = 0. More specifically, it was shown in the Supplement of Ref.…”

Section: Stationary Statesmentioning

confidence: 99%

“…More specifically, it was shown in the Supplement of Ref. [7] that the convolution operator can be written in the fol- lowing form without approximations:…”

Section: Stationary Statesmentioning

confidence: 99%

“…The propagation of partially coherent nonlinear optical waves is a subject of growing interest in different fields of investigations, such as, e.g., supercontinuum (SC) generation [1,2], rogue waves [3][4][5][6], shock waves [7][8][9], nonlinear interferometry [10,11], or incoherent wave propagation in homogeneous [12][13][14][15][16], discrete [17], multimode [18,19] and single-mode fibers nearby the integrable limit [20][21][22]. From a different perspective, optical cavities and lasers offer an interesting experimental platform to study different regimes of optical turbulence [12,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Weak Langmuir optical turbulence in a fiber cavity

Garnier

Mussot

et al. 2016

Phys. Rev. A

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We study theoretically and numerically the dynamics of a passive optical fiber ring cavity pumped by a highly incoherent wave -an incoherently injected fiber laser. The theoretical analysis reveals that the turbulent dynamics of the cavity is dominated by the Raman effect. The forced-dissipative nature of the fiber cavity is responsible for a large diversity of turbulent behaviors: Besides nonequilibrium statistical stationary states, we report the formation of a periodic pattern of spectral incoherent solitons, or the formation of different types of spectral singularities, e.g., dispersive shock waves and incoherent spectral collapse behaviors. We derive a mean-field kinetic equation that describes in detail the different turbulent regimes of the cavity and whose structure is formally analogous to the weak Langmuir turbulence kinetic equation in the presence of forcing and damping. A quantitative agreement is obtained between the simulations of the nonlinear Schrödinger equation with cavity boundary conditions and those of the mean-field kinetic equation and the corresponding singular integro-differential reduction, without using adjustable parameters. We discuss the possible realization of a fiber cavity experimental set-up in which the theoretical predictions can be observed and studied.

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Section: Continuous Response Function: Spectral Shock Wavesupporting

confidence: 75%

Section: Continuous Response Function: Spectral Shock Wavementioning

confidence: 99%

Section: Stationary Statesmentioning

confidence: 99%

“…More specifically, it was shown in the Supplement of Ref. [7] that the convolution operator can be written in the fol- lowing form without approximations:…”

Section: Stationary Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Weak Langmuir optical turbulence in a fiber cavity

Garnier

Mussot

et al. 2016

Phys. Rev. A

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Time Asymmetric Quantum Mechanics and Shock Waves: Exploring the Irreversibility in Nonlinear Optics

et al. 2017

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The description of irreversible phenomena is a still debated topic in quantum mechanics. Still nowadays, there is no clear procedure to distinguish the coupling with external baths from the intrinsic irreversibility in isolated systems. In 1928 Gamow introduced states with exponentially decaying observables not belonging to the conventional Hilbert space. These states are named Gamow vectors, and they belong to rigged Hilbert spaces. This review summarizes the contemporary approach using Gamow vectors and rigged Hilbert space formalism as foundations of a generalized "time asymmetric" quantum mechanics. We study the irreversible propagation of specific wave packets and show that the topic is surprisingly related to the problem of irreversibility of shock waves in classical nonlinear evolution. We specifically consider the applications in the field of nonlinear optics. We show that it is possible to emulate irreversible quantum mechanical process by the nonlinear evolution of a laser beam and we provide experimental tests by the generation of dispersive shock waves in highly nonlocal regimes. We demonstrate experimentally the quantization of decay rates predicted by the time-asymmetric quantum mechanics. This work furnishes support to the idea of intrinsically irreversible wave propagation, and to novel tests of the foundations of quantum mechanics.

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Dispersive Shock Waves: From Water Waves to Nonlinear Optics

Conforti

Trillo

2016

Rogue and Shock Waves in Nonlinear Dispersive Media

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Rogue and dispersive shock waves are phenomena that occur in nonlinear dispersive media. They have been studied in different fields of physics, including ocean waves, nonlinear optics, Bose-Einstein condensates, plasma physics, etc. They are apparently very different phenomena; however, they are both characterised by the development of extremes: while the amplitude of a rogue wave reaches large values, shock waves develop extreme gradients. The presence of rogue and shock waves in an incoherent wave system drastically influences its statistical properties.During the last 15 years, the field of "rogue waves" has experienced a very quick development. The original motivation of the research was related mostly to the occasional measurement of extreme waves on the surface of the ocean and to the occurrence of various accidents caused by the impact of large amplitude waves on ships. Only more recently, it has been shown that extreme light fluctuations could be observed in an optical fibre; the research activity has now broadened up to the creation of a new field in its own.A rogue wave is the manifestation of a process of focussing of energy. One of the most accredited explanations of the formation of rogue waves (at least in an idealised case) is the modulational instability process by which a small perturbation of a plane wave can grow exponentially fast in time. This mechanism has been known from the late sixties, but only at the beginning of the new century, it has been associated to rogue waves. The nonlinear stages of the modulational instability are described by exact solutions of the nonlinear Schrödinger equation. Those solutions, named breathers, have been considered as the prototypes of rogue waves in the ocean.The development of an infinite gradient in finite time (gradient catastrophe) with consequent wave-breaking is probably a less baleful phenomenon, nonetheless of extreme nature. Mathematically, a classical shock wave is a discontinuous (weak) solution describing propagation beyond a breaking point where an infinite derivative develops. Starting from the last century, in several branches of physics, it has been recognised that the dissipation plays an important role in regularising the jump leading to physical shock waves characterised by strong but finite gradients. A completely different non-trivial dynamics may result when dispersion dominates. v vi Preface

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Incoherent Dispersive Shocks in the Spectral Evolution of Random Waves

Cited by 47 publications

References 62 publications

Weak Langmuir optical turbulence in a fiber cavity

Weak Langmuir optical turbulence in a fiber cavity

Time Asymmetric Quantum Mechanics and Shock Waves: Exploring the Irreversibility in Nonlinear Optics

Dispersive Shock Waves: From Water Waves to Nonlinear Optics

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