38 research outputs found
Two-dimensional gap solitons in elliptic-lattice potentials
We study two-dimensional (2D) matter-wave gap solitons trapped in an
elliptically deformed concentric lattice potential, within the framework of the
Gross-Pitaevskii equation (GPE) with self-attraction or self-repulsion. For a
fixed eccentricity of the lattice, soliton families are found in both the
repulsive and attractive models. In the former case, the analysis reveals two
kinds of gap solitons trapped in the first oval trough (the ring-shaped
potential minimum closest to the center): elliptic annular solitons (EASs), and
double solitons (DSs), which are formed by two tightly localized density peaks
located at diametrically opposite points of the trough, with zero phase
difference between them. With the decrease of the norm, the density
distribution in the EAS along the azimuthal direction changes from
nearly-uniform to double-peaked and, eventually, to the DS. In the attractive
model, there exist only DSs in the oval trough, while EASs are not found. All
such solitons without the angular momentum (l = 0) are fully stable. For l is
not equal to 0, vortical solitons - both EASs with a sufficiently large norm
(in the repulsive model) and DSs (in models with both signs of the
nonlinearity) - are quasi-stable, exhibiting rocking motion in the elliptic
trough (we consider the cases of l=1 and l=2). At smaller values of the norm,
the vortical annular solitons (in the repulsive model) are unstable. Stable
fundamental solitons trapped in the central potential well are investigated
too, in both the attractive and repulsive models, by means of the variational
approximation and numerical methods.Comment: Phys. Rev. A, in pres
Topologically enhanced nonlinear optical response of graphene nanoribbon heterojunctions
We study the nonlinear optical properties of heterojunctions made of graphene
nanoribbons (GNRs) consisting of two segments with either the same or different
topological properties. By utilizing a quantum mechanical approach that
incorporates distant-neighbor interactions, we demonstrate that the presence of
topological interface states significantly enhances the second- and third-order
nonlinear optical response of GNR heterojunctions that are created by merging
two topologically inequivalent GNRs. Specifically, GNR heterojunctions with
topological interface states display third-order harmonic hyperpolarizabilities
that are more than two orders of magnitude larger than those of their similarly
sized counterparts without topological interface states, whereas the
secondorder harmonic hyperpolarizabilities exhibit a more than ten-fold
contrast between heterojunctions with and without topological interface states.
Additionally, we find that the topological state at the interface between two
topologically distinct GNRs can induce a noticeable red-shift of the quantum
plasmon frequency of the heterojunctions. Our results reveal a general and
profound connection between the existence of topological states and an enhanced
nonlinear optical response of graphene nanostructures and possible other
photonic systems.Comment: 7 pages,5 figure
Stable surface solitons in truncated complex potentials
We show that surface solitons in the one-dimensional nonlinear Schr\"odinger
equation with truncated complex periodic potential can be stabilized by linear
homogeneous losses, which are necessary to balance gain in the near-surface
channel arising from the imaginary part of potential. Such solitons become
stable attractors when the strength of homogeneous losses acquires values from
a limited interval and they exist in focusing and defocusing media. The domains
of stability of surface solitons shrink with increase of the amplitude of
imaginary part of complex potential.Comment: 3 pages, 4 figures,accepted by Optics Letter
Generation of ring-shaped optical vortices in dissipative media by inhomogeneous effective diffusion
By means of systematic simulations we demonstrate generation of a variety of
ring-shaped optical vortices (OVs) from a two-dimensional input with embedded
vorticity, in a dissipative medium modeled by the cubic-quintic complex
Ginzburg-Landau equation with an inhomogeneous effective diffusion
(spatial-filtering) term, which is anisotropic in the transverse plane and
periodically modulated in the longitudinal direction. We show the generation of
stable square- and gear-shaped OVs, as well as tilted oval-shaped vortex rings,
and string-shaped bound states built of a central fundamental soliton and two
vortex satellites, or of three fundamental solitons. Their shape can be
adjusted by tuning the strength and modulation period of the inhomogeneous
diffusion. Stability domains of the generated OVs are identified by varying the
vorticity of the input and parameters of the inhomogeneous diffusion. The
results suggest a method to generate new types of ring-shaped OVs with
applications to the work with structured light.Comment: 24 pages, 5 figures; Nonlinear Dynamics, in pres