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

Hervé Leblond1, Boris A. Malomed2, and Dumitru Mihalache3

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

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Phys. Rev. E 76, 026604 – Published 17 August, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.026604

Abstract

We consider the three-dimensional (3D) Gross-Pitaevskii or nonlinear Schrödinger 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 πS∕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≠0) supported by a lattice in the 3D space. Typical scenarios of instability development (collapse or decay) of unstable localized vortices are identified too.

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Phys. Rev. E 76, 026604– Published 17 August, 2007
  • Received 12 June 2006

© 2007 American Physical Society

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