Stabilized vortices in layered Kerr media

Montesinos, Gaspar D.; Pérez-Garcı́a, Vı́ctor M.; Michinel, Humberto; Salgueiro, José R.

doi:10.1103/physreve.71.036624

Cited by 10 publications

(14 citation statements)

References 29 publications

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“…For the vortex solitons with S ≥ 1, the numerical analysis reveals an internal stability boundary, β stability (S) < β collapse (S), the vortices being stable at β < β stability (S), see Table 1. In the interval of β stability (S) < β < β collapse (S), they are broken by azimuthal perturbations into rotating necklace-shaped clusters of fragments, which resembles the initial stage of the instability development of localized vortices in usual models; however, unlike those models [244][245][246] The stability boundary, β stability (S), can be found in an approximate analytical form too [85]. To this end, the wave function of an azimuthally perturbed vortex ring is approximated by…”

Section: B Basic Results For Vortex Solitonsmentioning

confidence: 99%

(INVITED) Vortex solitons: Old results and new perspectives

Malomed

2019

Physica D: Nonlinear Phenomena

176

115

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A comparative review is given of some well-known and some recent results obtained in studies of two-and three-dimensional (2D and 3D) solitons, with emphasis on states carrying embedded vorticity. Physical realizations of multidimensional solitons in atomic Bose-Einstein condensates (BECs) and nonlinear optics are briefly discussed too. Unlike 1D solitons, which are typically stable, 2D and 3D ones are vulnerable to instabilities induced by the occurrence of the critical and supercritical collapse, respectively, in the 2D and 3D models with the cubic self-focusing nonlinearity. Vortex solitons are subject to a still stronger splitting instability. For this reason, a central problem is looking for physical settings in which 2D and 3D solitons may be stabilized. The review addresses in detail two well-established topics, viz., the stabilization of vortex solitons by means of competing nonlinearities, or by trapping potentials (harmonic-oscillator and spatially-periodic ones). The former topic includes a new addition, closely related to the recent breakthrough, viz., the prediction and creation of robust quantum droplets. Two other topics included in the review outline new schemes which were recently elaborated for the creation of stable vortical solitons in BEC. One scheme relies on the use of the spin-orbit coupling (SOC) in binary condensates with cubic intrinsic attraction, making it possible to predict stable 2D and 3D solitons, which couple or mix components with vorticities S = 0 and ±1 (semi-vortices (SVs) or mixed modes (MMs), respectively). In this system, the situation is drastically different in the 2D and 3D geometries. In 2D, the SOC helps to create a ground state (GS, which does not exist otherwise), represented by stable SV or MM solitons, whose norm falls below the threshold value at which the critical collapse sets in. In the 3D geometry, the supercritical collapse does not allow one to create a GS, but metastable solitons of the SV and MM types can be constructed. Another new scheme makes it possible to create stable 2D vortex-ring solitons with arbitrarily high S in a binary BEC with components coupled by microwave radiation. Some other topics are addressed briefly, such as vortex solitons in dissipative media, and attempts to create vortex solitons in experiments.List of acronyms: 1D -one-dimensional; 2D -two dimensional; 3D -three-dimensional; BEC -Bose-Einstein condensate; CGLE -complex Ginzburg-Landau equation; CQ -cubic-quintic (nonlinearity), FF -fundamental frequency; GPE -Gross-Pitaevskii equation; GS -ground state; GVD -group-velocity dispersion; HO -harmonic oscillator (potential); HV -hidden vorticity; LHY -Lee-Huang-Yang (correction to the mean-field dynamics of BEC); MF -mean field; MM -mixed mode; NLSE -nonlinear Schrödinger equation; OL -optical lattice; PT -parity-time (symmetry); QD -quantum droplet; SH -second harmonic; SOC -spin-orbit coupling; SV -semi-vortex; TF -Thomas-Fermi (approximation); TS -Townes' soliton; VA -variational approximation; VAV -vortex-antivortex (composit...

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Section: B Basic Results For Vortex Solitonsmentioning

confidence: 99%

(INVITED) Vortex solitons: Old results and new perspectives

Malomed

2019

Physica D: Nonlinear Phenomena

176

115

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“…These include the use of competing (cubicquintic [13]- [15] or quadratic-cubic [16]) nonlinearities, trapping configurations [17], and, as demonstrated experimentally [18] and theoretically [19], periodic lattice potentials. The stabilization may be enhanced by "management" techniques, i.e., periodic alternation of the sign of the nonlinear term [20]. Another possibility for the stabilization is provided by the use of nonlocal nonlinearity [21].…”

mentioning

confidence: 99%

Soliton Gyroscopes in Media with Spatially Growing Repulsive Nonlinearity

et al. 2014

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We find that the recently introduced model of self-trapping supported by a spatially growing strength of a repulsive nonlinearity gives rise to robust vortex-soliton tori, i.e., three-dimensional vortex solitons, with topological charges S≥1. The family with S=1 is completely stable, while the one with S=2 has alternating regions of stability and instability. The families are nearly exactly reproduced in an analytical form by the Thomas-Fermi approximation. Unstable states with S=2 and 3 split into persistently rotating pairs or triangles of unitary vortices. Application of a moderate torque to the vortex torus initiates a persistent precession mode, with the torus' axle moving along a conical surface. A strong torque heavily deforms the vortex solitons, but, nonetheless, they restore themselves with the axle oriented according to the vectorial addition of angular momenta.

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“…On the other hand, in a recent work [129] it was demonstrated that a two-component (vectorial) generalization of the present model may support stable existence, in the course of very long time, of compound solitons in which one component is arranged as a (partly incoherent) fundamental soliton, while the other one carries vorticity.…”

Section: Direct Numerical Resultsmentioning

confidence: 48%

Soliton Management in Periodic Systems

Malomed¹

2006

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Stabilized vortices in layered Kerr media

Cited by 10 publications

References 29 publications

(INVITED) Vortex solitons: Old results and new perspectives

(INVITED) Vortex solitons: Old results and new perspectives

Soliton Gyroscopes in Media with Spatially Growing Repulsive Nonlinearity

Soliton Management in Periodic Systems

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