Stability of two-dimensional spatial solitons in nonlocal nonlinear media

Skupin, Stefan; Bang, Ole; Edmundson, D.; Królikowski, Wiesław

doi:10.1103/physreve.73.066603

Cited by 185 publications

(160 citation statements)

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“…Starting in the stable power regime, dissipation makes the nonlinear mode "glide down" the family branch until it reaches powers in the unstable regime. Figure 3(c) confirms this property by comparing maximal intensity and FWHM obtained upon propagation with values found from exact numerical solution of the conservative problem using the method described in [8]. The solid lines are obtained upon propagation, which explains the small oscillations in the curves.…”

Section: (A)supporting

confidence: 69%

“…In the conservative system (χ ′′ 0 = χ ′′ nl = 0) all modes we tried (ground state, single charged vortex, dipole, double charged vortex) turned out to be stable if the power P = I(r)dr, is high enough. At least for the latter two modes this is quite remarkable, since they are known to be unstable (or only stable in a small power window) for other nonlocal models [8,19,20]. We attribute this enhanced stabilization to the combination of nonlocality and nonlinear saturation.…”

mentioning

confidence: 81%

“…However, in many real physical systems the nonlinear response is spatially nonlocal which means that the refractive index depends on the beam intensity in the neighborhood of each spatial point. This can be phenomenologically expressed as n(r) = dr ′ K(r, r ′ )I(r ′ ), where the response kernel K depends on the particular model of nonlocality [4].It has been shown that nonlocality drastically affects the stationary structure and dynamics of spatial solitons, leading to such effects as collapse arrest of high intensity beams and stabilization of otherwise unstable complex solitonic structures [5,6,7,8]. Nonlocality is often the consequence of transport processes which include atom or heat diffusion in atomic vapors [9], plasma [10] and thermal media [11], or charge drift in photorefractive crystals [12].…”

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confidence: 99%

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Nonlocal Stabilization of Nonlinear Beams in a Self-Focusing Atomic Vapor

2007

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We show that ballistic transport of optically excited atoms in an atomic vapor provides a nonlocal nonlinearity which stabilizes the propagation of vortex beams and higher order modes in the presence of a self-focusing nonlinearity. Numerical experiments demonstrate stable propagation of lowest and higher order vortices over a hundred diffraction lengths, before dissipation leads to decay of these structures.PACS numbers: 42.65. Tg,42.65.Sf, The propagation and dynamics of localized nonlinear waves is a subject of great interest in a range of physical settings stretching from nonlinear optics to plasmas and ultracold atomic gases [1,2]. The structure and stability of nonlinear optical modes is determined by the interplay of the radiation field with the functional form of the material nonlinearity [3]. In the case of optical beams the nonlinear response can be described in terms of the induced change in the refractive index n which is often approximated as a local function of the wave intensity, i.e. n(r) = n(I(r)). However, in many real physical systems the nonlinear response is spatially nonlocal which means that the refractive index depends on the beam intensity in the neighborhood of each spatial point. This can be phenomenologically expressed as n(r) = dr ′ K(r, r ′ )I(r ′ ), where the response kernel K depends on the particular model of nonlocality [4].It has been shown that nonlocality drastically affects the stationary structure and dynamics of spatial solitons, leading to such effects as collapse arrest of high intensity beams and stabilization of otherwise unstable complex solitonic structures [5,6,7,8]. Nonlocality is often the consequence of transport processes which include atom or heat diffusion in atomic vapors [9], plasma [10] and thermal media [11], or charge drift in photorefractive crystals [12]. In addition long range interactions are responsible for a nonlocal response in liquid crystals [13] or dipolar Bose Einstein condensates [14].Hot atomic vapors are an important and widely used nonlinear medium. The nonlocal nonlinear response of atomic vapors has previously only been associated with state dependent transport of ground state atoms which possess a multilevel structure [9]. In this letter we introduce a new and significant mechanism of nonlocality in atomic vapors which is provided by the ballistic transport of excited atoms and is important even for the simplest case of an idealized two-level atom. We show using parameters representative of beam propagation in Rubidium vapor that ballistic transport plays a dramatic role leading to stabilization of otherwise unstable vortex modes in the presence of a self-focusing nonlinearity.Prior to introducing a model for the nonlocal character of the refractive index we first recall the main features of beam propagation in a hot atomic vapor. We consider a scalar traveling wave E = E(x,y,z) 2 e ı(kz−ωt) + c.c. For all parameters of interest the refractive index is n ≃ 1 so the wave intensity is I ≃ ǫ0c 2 |E| 2 . In the slowly varying envelope approx...

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Section: (A)supporting

confidence: 69%

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confidence: 81%

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confidence: 99%

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Nonlocal Stabilization of Nonlinear Beams in a Self-Focusing Atomic Vapor

2007

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“…In contrast to the linear vortex phase, the phase of the azimuthon is a staircaselike nonlinear function of the polar angle. Various kinds of azimuthons have been shown to be stable in media with a nonlocal nonlinear response [7,8,9,10,11].The aim of this Brief Report is to present nonrotating multisoliton (in particular, dipole and quadrupole) and rotating multisoliton (azimuthon) structures in the 2D BEC with attraction and study their stability by a linear stability analysis. We show that, in the presence of a confining potential, stable azimuthons also exist for a medium with a local cubic attractive nonlinearity.…”

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confidence: 99%

Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates

Lashkin

2008

Phys. Rev. A

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We present spatially localized nonrotating and rotating (azimuthon) multisolitons in the twodimensional (2D) ("pancake-shaped configuration") Bose-Einstein condensate (BEC) with attractive interaction. By means of a linear stability analysis, we investigate the stability of these structures and show that rotating dipole solitons are stable provided that the number of atoms is small enough. The results were confirmed by direct numerical simulations of the 2D Gross-Pitaevskii equation.PACS numbers: 03.75. Lm, 05.30.Jp, 05.45.Yv Localized coherent structures, such as fundamental solitons, vortices, nonrotating and rotating multisolitons are universal objects which appear in many nonlinear physical systems [1], and, in particular, in Bose-Einstein condensates (BEC's). Stability of these nonlinear structures is one of the most important questions because of its direct connection with the possibility of experimental observation of solitons and vortices.Detailed investigations of the stability of localized vortices in an effectively two-dimensional (2D) trapped BEC with a negative scattering length (attractive interaction) were performed in Ref.[2] and later extended to the three-dimensional case [3] (see also Ref. [4]). While vortex solitons in attractive BEC are strongly unstable in free space, the presence of the trapping potential results in existence of stable vortices provided that the number of particles does not exceed a threshold value [2,4,5].Recently, a novel class of 2D spatially localized vortices with a spatially modulated phase, the so called azimuthons, was introduced in Ref. [6]. Azimuthons represent intermediate states between the radially symmetric vortices and rotating soliton clusters. In contrast to the linear vortex phase, the phase of the azimuthon is a staircaselike nonlinear function of the polar angle. Various kinds of azimuthons have been shown to be stable in media with a nonlocal nonlinear response [7,8,9,10,11].The aim of this Brief Report is to present nonrotating multisoliton (in particular, dipole and quadrupole) and rotating multisoliton (azimuthon) structures in the 2D BEC with attraction and study their stability by a linear stability analysis. We show that, in the presence of a confining potential, stable azimuthons also exist for a medium with a local cubic attractive nonlinearity. Results of the linear stability analysis were confirmed by direct numerical simulations of the azimuthon dynamics.We consider a condensate which is loaded in an axisymmetric with respect to the (x, y) plane harmonic trap, and tightly confined in the z direction. The dynamics of the condensate is described by the Gross-Pitaevskii equation * Electronic address: vlashkin@kinr.kiev.uawhere Ψ(r, t) is the condensate wave function, a ≷ 0 is the s-wave scattering length. We assume that the axial confinement frequency Ω z is much larger than the radial one Ω r (the pancake configuration). Then, the 3D equation (1) can be reduced to an effective GPE in two dimensions [2] (for a detailed discussion of the appl...

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“…For example, it may promote the modulational instability in self-defocusing media or can arrest wave collapse in multidimensional self-focusing media. Furthermore, nonlocal nonlinearity may affect soliton interactions as well as may support the formation of stable localized structures [13]. It is thus of interest to investigate the modulational instability as well as the localization of wave packets in strongly coupled relativistically degenerate plasmas.…”

Section: Introductionmentioning

confidence: 99%

Stability and evolution of wave packets in strongly coupled degenerate plasmas

Misra

Shukła

2012

Phys. Rev. E

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We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature associated with their strong coupling, whereas that of electrons is provided by the relativistic degeneracy pressure. Using a multiple scale technique, a (3+1)-dimensional coupled set of nonlinear Schrödinger-like equations with nonlocal nonlinearity is derived from a generalized viscoelastic hydrodynamic model. These coupled equations, which govern the dynamics of wave packets, are used to study the oblique modulational instability of a Stoke's wave train to a small plane wave perturbation. We show that the wave packets, though stable to the parallel modulation, becomes unstable against oblique modulations. In contrast to the long-wavelength carrier modes, the wave packets with short-wavelengths are shown to be stable in the weakly relativistic case, whereas they can be stable or unstable in the ultra-relativistic limit. Numerical simulation of the coupled equations reveals that a steady state solution of the wave amplitude exists together with the formation of a localized structure in (2+1) dimensions. However, in the (3+1)-dimensional evolution, a Gaussian wave beam self-focuses after interaction and blows up in a finite time. The latter is, however, arrested when the dispersion predominates over the nonlinearities. This occurs when the Coulomb coupling strength is higher or a choice of obliqueness of modulation, or a wavelength of excitation is different. Possible application of our results to the interior as well as in an outer mantle of white dwarfs are discussed.

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Stability of two-dimensional spatial solitons in nonlocal nonlinear media

Cited by 185 publications

References 43 publications

Nonlocal Stabilization of Nonlinear Beams in a Self-Focusing Atomic Vapor

Nonlocal Stabilization of Nonlinear Beams in a Self-Focusing Atomic Vapor

Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates

Stability and evolution of wave packets in strongly coupled degenerate plasmas

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