239 research outputs found
Gap-Townes solitons and localized excitations in low dimensional Bose Einstein condensates in optical lattices
We discuss localized ground states of Bose-Einstein condensates in optical
lattices with attractive and repulsive three-body interactions in the framework
of a quintic nonlinear Schr\"odinger equation which extends the
Gross-Pitaevskii equation to the one dimensional case. We use both a
variational method and a self-consistent approach to show the existence of
unstable localized excitations which are similar to Townes solitons of the
cubic nonlinear Schr\"odinger equation in two dimensions. These solutions are
shown to be located in the forbidden zones of the band structure, very close to
the band edges, separating decaying states from stable localized ones
(gap-solitons) fully characterizing their delocalizing transition. In this
context usual gap solitons appear as a mechanism for arresting collapse in low
dimensional BEC in optical lattices with attractive real three-body
interaction. The influence of the imaginary part of the three-body interaction,
leading to dissipative effects on gap solitons and the effect of atoms feeding
from the thermal cloud are also discussed. These results may be of interest for
both BEC in atomic chip and Tonks-Girardeau gas in optical lattices
Nonlinear polaritons in Bose-Einstein condensates in optical lattices
We study the interaction of a Bose-Einstein condensate in an optical lattice
with additional electromagnetic fields under Raman resonance condition. System
of evolution equations describing ultra-short optical pulse propagation and
photo-induced transport of cold atoms in optical lattice is derived. The steady
state solution of these equations was found. There are new kinds of polaritonic
solitary waves propagating.Comment: pdf-file, Reported on "IX International Readings on Quantum Optics",
12-17 October, St-Peterburg, Russi
Electromagnetic wave propagation in a nonlinear hyperbolic medium
The propagation of a quasi-harmonic electromagnetic wave in a bulk hyperbolic
dielectric metamaterial is considered. If the group velocities dispersion is
not taken into account, then wave propagation can be described either by the
hyperbolic nonlinear Schrodinger equation or by the hyperbolic Manakov
equations. It is shown that the region in the space of wave vectors in which
the modulation instability of a spatially homogeneous wave is possible is not
limited, in contrast to the case of ordinary media.Comment: 13 pages, no figures, it was submitted to Quantum Electronic
Solitary electromagnetic waves propagation in the asymmetric oppositely-directed coupler
We consider the electromagnetic waves propagating in the system of coupled
waveguides. One of the system components is a standard waveguide fabricated
from nonlinear medium having positive refraction and another component is a
waveguide produced from an artificial material having negative refraction. The
metamaterial constituting the second waveguide has linear characteristics and a
wave propagating in the waveguide of this type propagates in the direction
opposite to direction of energy flux. It is found that the coupled nonlinear
solitary waves propagating both in the same direction are exist in this
oppositely-directed coupler due to linear coupling between nonlinear positive
refractive waveguide and linear negative refractive waveguide. The
corresponding analytical solution is found and it is used for numerical
simulation to illustrate that the results of the solitary wave collisions are
sensible to the relative velocity of the colliding solitary waves.Comment: 9 pages,5 figure
Field Distribution into Binary Linear Waveguide Array
The binary (two-component) linear waveguide array that is formed either from identical waveguides but with alternating distances between adjacent waveguides, or waveguides with a positive refractive index, but having distinctions in the refractive index or the waveguide thickness. The exact solution of the coupled wave equations describing the field distribution over waveguides is found. These solutions describe the discrete diffraction in the model under consideration.
Keywords: coupled waveguides, binary array, discrete diffraction, generation function method
Spatial solitons under competing linear and nonlinear diffractions
We introduce a general model which augments the one-dimensional nonlinear
Schr\"{o}dinger (NLS) equation by nonlinear-diffraction terms competing with
the linear diffraction. The new terms contain two irreducible parameters and
admit a Hamiltonian representation in a form natural for optical media. The
equation serves as a model for spatial solitons near the supercollimation point
in nonlinear photonic crystals. In the framework of this model, a detailed
analysis of the fundamental solitary waves is reported, including the
variational approximation (VA), exact analytical results, and systematic
numerical computations. The Vakhitov-Kolokolov (VK) criterion is used to
precisely predict the stability border for the solitons, which is found in an
exact analytical form, along with the largest total power (norm) that the waves
may possess. Past a critical point, collapse effects are observed, caused by
suitable perturbations. Interactions between two identical parallel solitary
beams are explored by dint of direct numerical simulations. It is found that
in-phase solitons merge into robust or collapsing pulsons, depending on the
strength of the nonlinear diffraction
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