Stable azimuthal stationary state in quintic nonlinear optical media

Quiroga-Teixeiro, M.; Michinel, Humberto

doi:10.1364/josab.14.002004

Cited by 266 publications

(217 citation statements)

References 14 publications

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“…In the first direct simulations of 2D solitons with spin 1 in the CQ model, reported in the pioneer work [34], it was found that they are robust, provided that their energy is not too small [34]. Later analysis, based on the computation of linear-stability eigenvalues, demonstrated that some of the spinning 2D solitons considered in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Later analysis, based on the computation of linear-stability eigenvalues, demonstrated that some of the spinning 2D solitons considered in Ref. [34] are subject to a weak azimuthal instability. Nonetheless, in another part of their existence region, where they have a very large energy, the solitons with spin s = 1 and s = 2 were confirmed to be stable in the 2D CQ model [35] (see also Ref.…”

Section: Introductionmentioning

confidence: 99%

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Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

et al. 2002

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We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, give rise to completely localized spatiotemporal solitons (vortex tori) with vorticity s = 1. There is no threshold necessary for the existence of these solitons. They are found to be stable if their energy exceeds a certain critical value, so that the stability domain occupies about 10 % of the existence region of the solitons. On the contrary to spatial vortex solitons in the same model, the spatiotemporal ones with s = 2 are never stable. These results might open the way for experimental observation of spinning three-dimensional solitons in optical media.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

et al. 2002

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“…A later analysis, based on the computation of linear-stability eigenvalues, demonstrated that some of the spinning 2D solitons considered in Ref. [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).…”

mentioning

confidence: 96%

“…In the first simulations of 2D solitons with spin 1 in the CQ model, it was found that they propagated in a stable way, provided that their energy is not too small [26]. A later analysis, based on the computation of linear-stability eigenvalues, demonstrated that some of the spinning 2D solitons considered in Ref.…”

mentioning

confidence: 98%

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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“…quadratic-cubic nonlinearities [5,6]. Nevertheless, such models are very challenging to implement in practice, as they would require very large light intensities where the higher-order nonlinearities are typically accompanied by additional dominant processes, like multi-photon absorption [7].…”

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confidence: 99%

Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices

2005

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Stable ring vortex solitons, featuring a bright-shape, appear to be very rare in nature.However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice. We find the families of vortex lattice solitons and reveal their salient properties, including the conditions required for their stability. We show that the higher the soliton topological charge, the deeper the lattice modulation necessary for stabilization.PACS numbers: 42.65.Tg, 42.65.Jx, 42.65.Wi Vortex solitons with a bright shape, i.e., screw topological phase dislocations embedded in a localized ring-shaped beam, might exist in different systems with focusing nonlinearities [1]. However, such solitons realize higher-order, excited states of the corresponding nonlinear systems; therefore they tend to be highly prone to azimuthal modulational instabilities that lead to their spontaneous self-destruction into vorticityless solitons [2]. This process has been observed experimentally in different settings [3], with the orbital angular momentum associated to the input vorticity being carried away by the soliton fragments that fly off the original ring. Homogeneous defocusing nonlinear media can support stable vortex solitons, but those have the form of dark-shaped beams, i.e., dislocations that seat on a background which extents to infinity along the transverse direction [4]. Localized, stable ring-vortex solitons in homogeneous media are only known to exist in models with competing cubic-quintic, or 1

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Stable azimuthal stationary state in quintic nonlinear optical media

Cited by 266 publications

References 14 publications

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

Stable Spinning Optical Solitons in Three Dimensions

Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices

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