Theory of optical dispersive shock waves in photorefractive media

El, Gennady; Gammal, A.; Khamis, Eduardo Georges; Kraenkel, Roberto André; Камчатнов, А. М.

doi:10.1103/physreva.76.053813

Cited by 89 publications

(140 citation statements)

References 39 publications

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“…In this section, El's method 150 will be used for the higher order NLS equation (9) as the leading and trailing edge equations can be solved exactly in this low intensity limit. It should be noted that El's method has been applied to similar higher order NLS equations in previous work [18,36]. The higher order NLS equation (8) differs from that used in this previous work only in the scaling of the cubic and quintic nonlinear terms due to the colloid constitutive relation (2).…”

Section: Dam Break Solutionmentioning

confidence: 96%

“…This is an NLS equation with a fifth order nonlinearity correction, which has been extensively studied [18,36,45]. It can be set in the standard form…”

Section: Low Light Intensity Limitmentioning

confidence: 99%

“…In the context of fluid flow, undular bores have been observed, studied and modelled in the atmosphere [7,8,9], on the continental shelf in the internal tide [10], 20 in stratified fluids [11], in magma flow in geophysics [12, 13,14], in Fermi gases [15] and BoseEinstein condensates [16]. Of relevance to the present work, there have been experimental and theoretical studies of DSWs in nonlinear optical media such as photorefractive crystals [17,18,19], nonlinear optical fibres [20,21,22] and nonlinear thermal optical media [23,24]. While the terms DSW and undular bore refer to the same phenomenon and, in principle, are interchangeable, the 25 first term will be used in the present work.…”

Section: Introductionmentioning

confidence: 99%

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Optical dispersive shock waves in defocusing colloidal media

Marchant

Smyth

2017

Physica D: Nonlinear Phenomena

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The propagation of an optical dispersive shock wave, generated from a jump discontinuity in light intensity, in a defocusing colloidal medium is analysed. The equations governing nonlinear light propagation in a colloidal medium consist of a nonlinear Schrödinger equation for the beam and an algebraic equation for the medium response. In the limit of low light intensity, these equations reduce to a perturbed higher order nonlinear Schrödinger equation. Solutions for the leading and trailing edges of the colloidal dispersive shock wave are found using modulation theory. This is done for both the perturbed nonlinear Schrödinger equation and the full colloid equations for arbitrary light intensity. These results are compared with numerical solutions of the colloid equations. AbstractThe propagation of an optical dispersive shock wave, generated from a jump discontinuity in light intensity, in a defocussing colloidal medium is analysed. The equations governing nonlinear light propagation in a colloidal medium consist of a nonlinear Schrödinger equation for the beam and an algebraic equation for the medium response. In the limit of low light intensity, these equations reduce to a perturbed higher order nonlinear Schrödinger equation. Solutions for the leading and trailing edges of the colloidal dispersive shock wave are found using modulation theory. This is done for both the perturbed nonlinear Schrödinger equation and the full colloid equations for arbitrary light intensity. These results are compared with numerical solutions of the colloid equations.

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Section: Dam Break Solutionmentioning

confidence: 96%

“…This is an NLS equation with a fifth order nonlinearity correction, which has been extensively studied [18,36,45]. It can be set in the standard form…”

Section: Low Light Intensity Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optical dispersive shock waves in defocusing colloidal media

Marchant

Smyth

2017

Physica D: Nonlinear Phenomena

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“…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]. Coherent dispersive shocks and their stationary analogues have shown to play a role also in passive cavity configurations [113][114][115], where one can envisage that they can impact the generation of combs in the normal dispersion regime [116,117].…”

Section: Continuous Response Function: Spectral Shock Wavementioning

confidence: 99%

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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“…For example, in experiment [4] with photo-refractive material the saturation of nonlinearity is quite essential and the corresponding theory of DSWs was developed in Ref. [9]. In fiber optics, one needs to take into account such effects as dissipation, higher-order dispersion, intra-pulse Raman scattering and self-steepening (see, e.g., [10]).…”

Section: Introductionmentioning

confidence: 99%

Riemann problem for the photon fluid: Self-steepening effects

Ivanov

Камчатнов

2017

Phys. Rev. A

Self Cite

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We consider the Riemann problem of evolution of initial discontinuities for the photon fluid propagating in a normal dispersion fiber with account of self-steepening effects. The dynamics of light field is described by the nonlinear Schrödinger (NLS) equation with self-steepening term appearing due to retardation of the fiber material response to variations of the electromagnetic signal. It is shown that evolution dynamics in this case is much richer than that for the NLS equation. Complete classification of possible wave structures is given for all possible jump conditions at the discontinuity.

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Theory of optical dispersive shock waves in photorefractive media

Cited by 89 publications

References 39 publications

Optical dispersive shock waves in defocusing colloidal media

Optical dispersive shock waves in defocusing colloidal media

Weak Langmuir optical turbulence in a fiber cavity

Riemann problem for the photon fluid: Self-steepening effects

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