## Two-dimensional intraband solitons in lattice potentials with local defects and self-focusing nonlinearity |

JOSA B, Vol. 30, Issue 7, pp. 1786-1793 (2013)

http://dx.doi.org/10.1364/JOSAB.30.001786

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### Abstract

It is commonly known that stable bright solitons in periodic potentials, which represent gratings in photonics/plasmonics, or optical lattices in quantum gases, exist either in the spectral semi-infinite gap (SIG) or in finite bandgaps. Using numerical methods, we demonstrate that, under the action of the cubic self-focusing nonlinearity, defects in the form of “holes” in two-dimensional (2D) lattices support continuous families of 2D solitons *embedded* into the first two Bloch bands of the respective linear spectrum, where solitons normally do not exist. The two families of the *embedded defect solitons* (EDSs) are found to be continuously linked by the branch of *gap defect solitons* (GDSs) populating the first finite bandgap. Further, the EDS branch traversing the first band links the GDS family with the branch of regular defect-supported solitons populating the SIG. Thus, we construct a continuous chain of regular, embedded, and gap-mode solitons (“superfamily”) threading the entire bandgap structure considered here. The EDSs are stable in the first Bloch band, and partly stable in the second. They exist with the norm exceeding a minimum value; hence they do not originate from linear defect modes. Further, we demonstrate that double, triple, and quadruple lattice defects support stable dipole-mode solitons and vortices.

© 2013 Optical Society of America

**OCIS Codes**

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(350.7420) Other areas of optics : Waves

(020.1475) Atomic and molecular physics : Bose-Einstein condensates

(230.5298) Optical devices : Photonic crystals

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: January 3, 2013

Revised Manuscript: March 28, 2013

Manuscript Accepted: May 6, 2013

Published: June 5, 2013

**Citation**

Jianhua Zeng and Boris A. Malomed, "Two-dimensional intraband solitons in lattice potentials with local defects and self-focusing nonlinearity," J. Opt. Soc. Am. B **30**, 1786-1793 (2013)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-7-1786

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