Stability of spinning ring solitons of the cubic–quintic nonlinear Schrödinger equation

Towers, Isaac; Buryak, Alexander V.; Sammut, R.A.; Malomed, Boris A.; Crasovan, L.-C.; Mihalache, Dumitru

doi:10.1016/s0375-9601(01)00565-5

Cited by 104 publications

(64 citation statements)

References 18 publications

(48 reference statements)

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“…8(c). Vortex solitons with integer topological charge m can be looked for as E(r, φ) = E 0 (r)e imφ , where (r, φ) are polar coordinates with the origin at the pivot of the vortex [40,43,[45][46][47][48]. The fundamental 2D soliton corresponds to m = 0, with the maximum at the origin.…”

Section: Two-dimensional Self-localized Solutions: Stripes Fundammentioning

confidence: 99%

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

et al. 2011

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We use the cubic complex Ginzburg-Landau equation coupled to a dissipative linear equation as a model of lasers with an external frequency-selective feedback. It is known that the feedback can stabilize the one-dimensional (1D) self-localized mode. We aim to extend the analysis to 2D stripe-shaped and vortex solitons. The radius of the vortices increases linearly with their topological charge, m, therefore the flat-stripe soliton may be interpreted as the vortex with m = ∞, while vortex solitons can be realized as stripes bent into rings. The results for the vortex solitons are applicable to a broad class of physical systems. There is a qualitative agreement between our results and those recently reported for models with saturable nonlinearity.

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Section: Two-dimensional Self-localized Solutions: Stripes Fundammentioning

confidence: 99%

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

et al. 2011

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“…[26] are subject to a weak azimuthal instability. Nonetheless, in another part of their existence region, with very large energies, solitons with spin s = 1 and s = 2 were confirmed to be truly stable in the 2D CQ model [27] (all the solitons with s ≥ 3 are unstable).…”

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confidence: 96%

“…The relative width of the stability region is κ (3D) offset − κ st /κ (3D) offset ≈ 0.2. However, there is no stability region for 3D solitons with s = 2, in contrast to the 2D vortex solitons in the CQ model [27]. In the case when a spinning soliton is unstable, its instability is oscillatory; the corresponding frequency, Imλ, is of the same order of magnitude as Reλ at the maximum-instability point (see Fig.…”

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confidence: 97%

Stable Spinning Optical Solitons in Three Dimensions

et al. 2002

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We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schrödinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.Optical solitons (spatial, temporal, or spatiotemporal) are self-trapped light beams or pulses that are supported by a balance between diffraction and/or dispersion and various nonlinearities. They are ubiquitous objects in optical media [1] [3,7], quadratically nonlinear (χ (2) ) [2,8], and graded-index Kerr media [9]. While a fully localized STS in three dimensions (3D) has not yet been found in an experiment, 2D ones were observed in a bulk χ (2) medium [10]. The interplay of spatio-temporal coupling and nonlinearity may also play an important role in self-defocusing media [11].Spinning (vortex) solitons are also possible in optical media. Starting with the works [12], both delocalized ("dark") and localized ("bright") optical vortices in 2D were investigated [13,14,15]. In the 3D case they take the shape of a torus ("doughnut") [16,17]. However, the only previously known physical model which could support stable 3D vortex solitons is the Skyrme model [18], which has recently found a new important application to Bose-Einstein condensates (BEC) [19]. Our objective in this paper is to identify fundamental models of the nonlinear-Schrödinger (NLS) type in 3D that give rise to stable spinning solitons, as NLS models are much simpler and closer to more experimental situations, having applications to optics, BEC, plasmas, etc. (see below).For bright vortex solitons stability is a major issue as, unlike their zero-spin counterparts, the spinning solitons are prone to destabilization by azimuthal perturbations. In 2D models with χ (2) and saturable nonlinearities an azimuthal instability was revealed by simulations [14] and observed experimentally [15]. As a result, a soliton with spin 1 splits into two or three fragments, each being a moving zero-spin soliton. Simulations of the 3D spinning STS in the χ (2) model also demonstrates its instability-induced splitting into separating zero-spin solitons [17]. Nevertheless, the χ (2) nonlinearity acting in combination with the self-defocusing Kerr (χ (3) ) nonlinearity, gives rise to the first examples of stable spinning (ring-shaped) 2D solitons with spin s = 1 and 2 [20]. It should be stressed that all the 2D spinning solitons actually represent static spatial beams; on the contrary, 3D solitons are moving spatiotemporal ones, which are localized not only in the transverse plane, but also in the propagation coordinate, see below.A model which may support stable spinning solitons in 3D is the one with a cubic-quintic (CQ) nonlinearity, which (in terms of optics) assumes a nonlinear correction to the medium's refractive index in the form δn = n 2 I − n 4 I 2 , I being the lig...

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“…In nonlinear optics, vortex solitons are associated with the phase dislocations (or phase singularities) carried by the nondiffracting optical beams [5], and share many common properties with the vortices observed in other systems, e.g., superfluids and Bose-Einstein condensates [6,7]. In a homogeneous medium, stable vortex solitons were proposed to exist in the so-called cubic-quintic or other similar nonlinear media, for example, combination of χ (2) and χ (3) nonlinear media, based on competing self-focusing and self-defocusing nonlinearities [8][9][10][11]. However, the experimental realization of vortex solitons in such media is hard, as the requirement of very high energy flow of light usually excites other higher-order nonlinearities, which may be dominant and suppress the occurrence of competing nonlinearities.…”

Section: Introductionmentioning

confidence: 99%