Three-dimensional vortex solitons in quasi-two-dimensional lattices

Journal Article · Wed Aug 15 04:00:00 EDT 2007 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PHYSREVE.76.026604· OSTI ID:21076240

Leblond, Herve ^[1]; Malomed, Boris A ^[2]; Mihalache, Dumitru ^[3]

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1. Laboratoire POMA, UMR 6136, Universite d'Angers, 2 Bd Lavoisier, 49000 Angers (France)
2. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
3. Department of Theoretical Physics, Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest 077125 (Romania)

We consider the three-dimensional (3D) Gross-Pitaevskii or nonlinear Schroedinger equation with a quasi-2D square-lattice potential (which corresponds to the optical lattice trapping a self-attractive Bose-Einstein condensate, or, in some approximation, to a photonic-crystal fiber, in terms of nonlinear optics). Stable 3D solitons, with embedded vorticity S=1 and 2, are found by means of the variational approximation and in a numerical form. They are built, basically, as sets of four fundamental solitons forming a rhombus, with phase shifts {pi}S/2 between adjacent sites, and an empty site in the middle. The results demonstrate two species of stable 3D solitons, which were not studied before, viz., localized vortices ('spinning light bullets,' in terms of optics) with S>1, and vortex solitons (with any S{ne}0) supported by a lattice in the 3D space. Typical scenarios of instability development (collapse or decay) of unstable localized vortices are identified too.

• OSTI ID: 21076240
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 2 Vol. 76; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BOSE-EINSTEIN CONDENSATION
CRYSTALS
NONLINEAR OPTICS
NONLINEAR PROBLEMS
PHASE SHIFT
SCHROEDINGER EQUATION
SOLITONS
TETRAGONAL LATTICES
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
VARIATIONAL METHODS