Using numerical methods, we construct families of vortical, quadrupole, and fundamental solitons in a two-dimensional (2D) nonlinear-Schrodinger/Gross-Pitaevskii equation Which models Bose-Einstein condensates (BECs) or photonic crystals. The equation includes the attractive or repulsive cubic nonlinearity and an anisotropic periodic potential. Two types of anisotropy are considered, accounted for by the difference in the strengths of the I D sublattices, or by a difference in their periods. The limit case of the quasi-1D optical lattice (OL), when one sublattice is missing, is included too. By means of systematic simulations, we identify stability limits for two species of vortex solitons and quadrupoles, of the rhombus and square types. In the attraction model, rhombic vortices and quadrupoles remain stable up to the limit case of the quasi-1D lattice. In the same model, finite stability limits are found for vortices and quadrupoles of the Square type, in terms of the anisotropy parameter. In the repulsion model, rhombic vortices and quadrupoles are stable in large parts of the first finite bandgap (FBG). Another species of partly stable anisotropic states is found in the second FBG, subfundamental dipoles, each squeezed into a single cell of the OL. Square-shaped quadrupoles are completely unstable in the repulsion model, while vortices of the same type are stable only in weakly anisotropic OL potentials.

Matter-wave vortices and solitons in anisotropic optical lattices

SALERNO, Mario
2009-01-01

Abstract

Using numerical methods, we construct families of vortical, quadrupole, and fundamental solitons in a two-dimensional (2D) nonlinear-Schrodinger/Gross-Pitaevskii equation Which models Bose-Einstein condensates (BECs) or photonic crystals. The equation includes the attractive or repulsive cubic nonlinearity and an anisotropic periodic potential. Two types of anisotropy are considered, accounted for by the difference in the strengths of the I D sublattices, or by a difference in their periods. The limit case of the quasi-1D optical lattice (OL), when one sublattice is missing, is included too. By means of systematic simulations, we identify stability limits for two species of vortex solitons and quadrupoles, of the rhombus and square types. In the attraction model, rhombic vortices and quadrupoles remain stable up to the limit case of the quasi-1D lattice. In the same model, finite stability limits are found for vortices and quadrupoles of the Square type, in terms of the anisotropy parameter. In the repulsion model, rhombic vortices and quadrupoles are stable in large parts of the first finite bandgap (FBG). Another species of partly stable anisotropic states is found in the second FBG, subfundamental dipoles, each squeezed into a single cell of the OL. Square-shaped quadrupoles are completely unstable in the repulsion model, while vortices of the same type are stable only in weakly anisotropic OL potentials.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/3018845
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 38
  • ???jsp.display-item.citation.isi??? 36
social impact