Cubic-quintic solitons in the checkerboard potential

Journal Article · Sat Dec 15 04:00:00 EST 2007 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.76.066604· OSTI ID:21101966

Driben, Rodislav; Zyss, Joseph ^[1]; Malomed, Boris A; Gubeskys, Arthur ^[2]

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1. Laboratoire de Photonique Quantique et Moleculaire, CNRS, Ecole Normale Superieure de Cachan, UMR 8537, 94235 Cachan (France)
2. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

We introduce a two-dimensional (2D) model which combines a checkerboard potential, alias the Kronig-Penney (KP) lattice, with the self-focusing cubic and self-defocusing quintic nonlinear terms. The beam-splitting mechanism and soliton multistability are explored in this setting, following the recently considered 1D version of the model. Families of single- and multi-peak solitons (in particular, five- and nine-peak species naturally emerge in the 2D setting) are found in the semi-infinite gap, with both branches of bistable families being robust against perturbations. For single-peak solitons, the variational approximation (VA) is developed, providing for a qualitatively correct description of the transition from monostability to the bistability. 2D solitons found in finite band gaps are unstable. Also constructed are two different species of stable vortex solitons, arranged as four-peak patterns ('oblique' and 'straight' ones). Unlike them, compact 'crater-shaped' vortices are unstable, transforming themselves into randomly walking fundamental beams.

• OSTI ID: 21101966
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print) Journal Issue: 6 Vol. 76; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BEAM SPLITTING
FOCUSING
NONLINEAR PROBLEMS
OPTICAL MODELS
PERTURBATION THEORY
POTENTIALS
TWO-DIMENSIONAL CALCULATIONS
VARIATIONAL METHODS