Stable Spatiotemporal Solitons in Bessel Optical Lattices

Mihalache, Dumitru; Mazilu, Dumitru; Lederer, F.; Malomed, Boris A.; Kartashov, Yaroslav V.; Crasovan, L.-C.; Torner, Lluís

doi:10.1103/physrevlett.95.023902

Cited by 126 publications

(68 citation statements)

References 41 publications

(29 reference statements)

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“…hence one can boost solitons (20) and cnoidal waves (21) to a (formally) arbitrary velocity by means of transformation (25). In fact, the velocity is not arbitrary because the factor exp (ivy/4) also must satisfy the periodic b.c., which leads to a quantization condition, v = 4n/r 0 , with n = 0, ±1, ±2, ... .…”

Section: Note That Eq (18) Features the Galilean Invariance: If A(ymentioning

confidence: 99%

“…[42] and [43], respectively). Accordingly, parameter H in solutions (21), (22) is not continuous, but rather takes discrete values selected by matching the b.c. to the periodicity of cn 2 ,…”

Section: Ring-shaped Solitons a Analytical Approachmentioning

confidence: 99%

“…The low-dimensional OL can also be implemented as a radial (axially symmetric) lattice in both 2D [13]- [19] and 3D [21] settings. In both cases, stable solitons in the selfattractive medium were predicted, in the form of a spot trapped either at the central potential well, or (in the 2D case) in a radial potential trough (additionally, the so-called azimuthons were predicted as azimuthally periodic deformations of vortices in the uniform 2D medium [22]; however, they are unstable in the case of the cubic nonlinearity).…”

Section: Introductionmentioning

confidence: 99%

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Matter-wave solitons in radially periodic potentials

2006

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We investigate two-dimensional (2D) states of Bose-Einstein condensates (BEC) with selfattraction or self-repulsion, trapped in an axially symmetric optical-lattice potential periodic along the radius. Unlike previously studied 2D models with Bessel lattices, no localized states exist in the linear limit of the present model, hence all localized states are truly nonlinear ones. We consider the states trapped in the central potential well, and in remote circular troughs. In both cases, a new species, in the form of radial gap solitons, are found in the repulsive model (the gap soliton trapped in a circular trough may additionally support stable dark-soliton pairs). In remote troughs, stable localized states may assume a ring-like shape, or shrink into strongly localized solitons. The existence of stable annular states, both azimuthally uniform and weakly modulated ones, is corroborated by simulations of the corresponding Gross-Pitaevskii equation. Dynamics of strongly localized solitons circulating in the troughs is also studied. While the solitons with sufficiently small velocities are stable, fast solitons gradually decay, due to the leakage of matter into the adjacent trough under the action of the centrifugal force. Collisions between solitons are investigated too. Head-on collisions of in-phase solitons lead to the collapse; π-out of phase solitons bounce many times, but eventually merge into a single soliton without collapsing.

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Section: Note That Eq (18) Features the Galilean Invariance: If A(ymentioning

confidence: 99%

Section: Ring-shaped Solitons a Analytical Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Matter-wave solitons in radially periodic potentials

2006

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“…In addition to the node- duced in Ref. [20] where a cubic-quintic nonlocal nonlinearity was considered with a nonlinear contribution to the refractive index depending also the quadratic power of the light intensity.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of dipole solitons in nonlocal nonlinear media

Kartashov

Torner

2008

Phys. Rev. A

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We address the stabilization of dipole solitons in nonlocal nonlinear materials by two different approaches. First, we study the properties of such solitons in thermal nonlinear media, where the refractive index landscapes induced by laser beams strongly depend on the boundary conditions and on the sample geometry. We show how the sample geometry impacts the stability of higherorder solitons in thermal nonlinear media and reveal that dipole solitons can be made dynamically stable in rectangular geometries in contrast to their counterparts in thermal samples with square cross-section. Second, we discuss the impact of the saturation of the nonlocal nonlinear response on the properties of multipole solitons. We find that the saturable response also stabilizes dipole solitons even in symmetric geometries, provided that the input power exceeds a critical value.

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“…Optical lattices (OLs), i.e., periodic potentials induced by laser beams illuminating the experimental field, is a versatile tool in the studies of ultracold quantum gases [5][6][7][8][9][10][11]. In particular, matter-wave solitons of the gap type, i.e., those whose chemical potential falls into a bandgap of the linear spectrum induced by the OL, were predicted [5] and created [6] in BECs with repulsive interactions between atoms.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional gap solitons in elliptic-lattice potentials

Malomed

2010

Phys. Rev. A

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We study two-dimensional (2D) matter-wave gap solitons trapped in an elliptically deformed concentric lattice potential, within the framework of the Gross-Pitaevskii equation (GPE) with self-attraction or self-repulsion. For a fixed eccentricity of the lattice, soliton families are found in both the repulsive and attractive models. In the former case, the analysis reveals two kinds of gap solitons trapped in the first oval trough (the ring-shaped potential minimum closest to the center):elliptic annular solitons (EASs), and double solitons (DSs), which are formed by two tightly localized density peaks located at diametrically opposite points of the trough, with zero phase difference between them. With the decrease of the norm, the density distribution in the EAS along the azimuthal direction changes from nearly-uniform to double-peaked and, eventually, to the DS.

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Stable Spatiotemporal Solitons in Bessel Optical Lattices

Cited by 126 publications

References 41 publications

Matter-wave solitons in radially periodic potentials

Matter-wave solitons in radially periodic potentials

Stabilization of dipole solitons in nonlocal nonlinear media

Two-dimensional gap solitons in elliptic-lattice potentials

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