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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17834–17851

Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type

Thawatchai Mayteevarunyoo, Boris A. Malomed, and Athikom Roeksabutr  »View Author Affiliations


Optics Express, Vol. 19, Issue 18, pp. 17834-17851 (2011)
http://dx.doi.org/10.1364/OE.19.017834


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Abstract

Solitons in the model of nonlinear photonic crystals with the transverse structure based on two-dimensional (2D) quadratic- or rhombic-shaped Kronig-Penney (KP) lattices are studied by means of numerical methods. The model can also applies to a Bose-Einstein condensate (BEC) trapped in a superposition of linear and nonlinear 2D periodic potentials. The analysis is chiefly presented for the self-repulsive nonlinearity, which gives rise to several species of stable fundamental gap solitons, dipoles, four-peak complexes, and vortices in two finite bandgaps of the underlying spectrum. Stable solitons with complex shapes are found, in particular, in the second bandgap of the KP lattice with the rhombic structure. The stability of the localized modes is analyzed in terms of eigenvalues of small perturbations, and tested in direct simulations. Depending on the value of the KP’s duty cycle (DC, i.e., the ratio of the void’s width to the lattice period), an internal stability boundary for the solitons and vortices may exist inside of the first bandgap. Otherwise, the families of the localized modes are entirely stable or unstable in the bandgaps. With the self-attractive nonlinearity, only unstable solitons and vortices are found in the semi-infinite gap.

© 2011 OSA

OCIS Codes
(020.1475) Atomic and molecular physics : Bose-Einstein condensates
(060.5295) Fiber optics and optical communications : Photonic crystal fibers
(050.5298) Diffraction and gratings : Photonic crystals
(190.6135) Nonlinear optics : Spatial solitons

ToC Category:
Photonic Crystals

History
Original Manuscript: August 5, 2011
Revised Manuscript: August 13, 2011
Manuscript Accepted: August 14, 2011
Published: August 25, 2011

Citation
Thawatchai Mayteevarunyoo, Boris A. Malomed, and Athikom Roeksabutr, "Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type," Opt. Express 19, 17834-17851 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17834


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