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Discrete reduced-symmetry solitons and second-band vortices in two-dimensional nonlinear waveguide arrays

Magnus Johansson1,2,3,*, Andrey A. Sukhorukov1,†, and Yuri S. Kivshar1,‡

  • 1Nonlinear Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory 0200, Australia
  • 2Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden
  • 3School of Pure and Applied Natural Sciences, University of Kalmar, SE-391 82 Kalmar, Sweden

  • *Electronic address: mjn@ifm.liu.se; http://people.ifm.liu.se/majoh
  • †Electronic address: ans124@physics.anu.edu.au; http://physics.anu.edu.au/nonlinear
  • ‡Electronic address: ysk124@physics.anu.edu.au; http://physics.anu.edu.au/nonlinear
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Phys. Rev. E 80, 046604 – Published 15 October, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.046604

Abstract

Considering a two-dimensional lattice of weakly coupled waveguides, where each waveguide may carry two orthogonal modes of dipolar character, we present a nonlinear discrete vector model for the study of Kerr optical solitons with profiles having a reduced symmetry relative to the underlying lattice. We describe analytically and numerically existence and stability properties of such states in square and triangular lattices and also reveal directional mobility properties of two-dimensional gap solitons which were recently observed in experiment. The model also describes one-site peaked discrete vortices corresponding to experimentally observed “second-band” vortex lattice solitons, for which oscillatory instabilities are predicted. We also introduce a concept of “rotational Peierls-Nabarro barrier” characterizing the minimum energy needed for rotation of stable dipole modes and compare numerically translational and rotational energy barriers in regimes of good mobility.

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Phys. Rev. E 80, 046604– Published 15 October, 2009
  • Received 26 May 2009

© 2009 American Physical Society

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