53 research outputs found
Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices
The nonlinear lattice---a new and nonlinear class of periodic
potentials---was recently introduced to generate various nonlinear localized
modes. Several attempts failed to stabilize two-dimensional (2D) solitons
against their intrinsic critical collapse in Kerr media. Here, we provide a
possibility for supporting 2D matter-wave solitons and vortices in an extended
setting---the cubic and quintic model---by introducing another nonlinear
lattice whose period is controllable and can be different from its cubic
counterpart, to its quintic nonlinearity, therefore making a fully `nonlinear
quasi-crystal'.
A variational approximation based on Gaussian ansatz is developed for the
fundamental solitons and in particular, their stability exactly follows the
inverted \textit{Vakhitov-Kolokolov} stability criterion, whereas the vortex
solitons are only studied by means of numerical methods. Stability regions for
two types of localized mode---the fundamental and vortex solitons---are
provided. A noteworthy feature of the localized solutions is that the vortex
solitons are stable only when the period of the quintic nonlinear lattice is
the same as the cubic one or when the quintic nonlinearity is constant, while
the stable fundamental solitons can be created under looser conditions. Our
physical setting (cubic-quintic model) is in the framework of the
Gross-Pitaevskii equation (GPE) or nonlinear Schr\"{o}dinger equation, the
predicted localized modes thus may be implemented in Bose-Einstein condensates
and nonlinear optical media with tunable cubic and quintic nonlinearities.Comment: 8 pages,7 figures, Frontiers of Physics (In Press
Three-dimensional topological solitons in PT-symmetric optical lattices
We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both fundamental and vortex-carrying soliton states. The imaginary part of the lattice induces internal currents in the solitons that strongly affect their domains of existence and stability. The domain of stability for fundamental solitons can extend nearly up to the PT-symmetry breaking point, where the linear lattice spectrum becomes complex. Vortex solitons feature spatially asymmetric profiles in the PT-symmetric lattices, but they are found to still exist as stable states within narrow regions. Our results provide the first example of continuous families of stable three-dimensional propagating solitons supported by complex potentials.Peer ReviewedPostprint (published version
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