192 research outputs found
Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials
Complex Ginzburg-Landau (CGL) models of laser media (with the cubic-quintic
nonlinearity) do not contain an effective diffusion term, which makes all
vortex solitons unstable in these models. Recently, it has been demonstrated
that the addition of a two-dimensional periodic potential, which may be induced
by a transverse grating in the laser cavity, to the CGL equation stabilizes
compound (four-peak) vortices, but the most fundamental "crater-shaped"
vortices (CSVs), alias vortex rings, which are, essentially, squeezed into a
single cell of the potential, have not been found before in a stable form. In
this work we report families of stable compact CSVs with vorticity S=1 in the
CGL model with the external potential of two different types: an axisymmetric
parabolic trap, and the periodic potential. In both cases, we identify
stability region for the CSVs and for the fundamental solitons (S=0). Those
CSVs which are unstable in the axisymmetric potential break up into robust
dipoles. All the vortices with S=2 are unstable, splitting into tripoles.
Stability regions for the dipoles and tripoles are identified too. The periodic
potential cannot stabilize CSVs with S>=2 either; instead, families of stable
compact square-shaped quadrupoles are found
Symmetry breaking and manipulation of nonlinear optical modes in an asymmetric double-channel waveguide
We study light-beam propagation in a nonlinear coupler with an asymmetric
double-channel waveguide and derive various analytical forms of optical modes.
The results show that the symmetry-preserving modes in a symmetric
double-channel waveguide are deformed due to the asymmetry of the two-channel
waveguide, yet such a coupler supports the symmetry-breaking modes. The
dispersion relations reveal that the system with self-focusing nonlinear
response supports the degenerate modes, while for self-defocusingmedium the
degenerate modes do not exist. Furthermore, nonlinear manipulation is
investigated by launching optical modes supported in double-channel waveguide
into a nonlinear uniform medium.Comment: 10 page
Analysis of an atom laser based on the spatial control of the scattering length
In this paper we analyze atom lasers based on the spatial modulation of the
scattering length of a Bose-Einstein Condensate. We demonstrate, through
numerical simulations and approximate analytical methods, the controllable
emission of matter-wave bursts and study the dependence of the process on the
spatial dependence of the scattering length along the axis of emission. We also
study the role of an additional modulation of the scattering length in time.Comment: Submitted to Phys. Rev.
The Sasa-Satsuma higher order nonlinear Schrodinger equation and its bilinearization and multi-soliton solutions
Higher order and multicomponent generalizations of the nonlinear Schrodinger
equation are important in various applications, e.g., in optics. One of these
equations, the integrable Sasa-Satsuma equation, has particularly interesting
soliton solutions. Unfortunately the construction of multi-soliton solutions to
this equation presents difficulties due to its complicated bilinearization. We
discuss briefly some previous attempts and then give the correct
bilinearization based on the interpretation of the Sasa-Satsuma equation as a
reduction of the three-component Kadomtsev-Petvishvili hierarchy. In the
process we also get bilinearizations and multi-soliton formulae for a two
component generalization of the Sasa-Satsuma equation (the
Yajima-Oikawa-Tasgal-Potasek model), and for a (2+1)-dimensional
generalization.Comment: 13 pages in RevTex, added reference
Dark-Soliton Timing Jitter Caused By Fluctuations In Initial Pulse-Shape
The dark-soliton timing jitters caused by fluctuations in either the soliton initial phase angle or the background amplitude when such a soliton propagates in a monomode optical fiber under the influence of the stimulated Raman scattering are investigated and compared with those that exist when the stimulated Raman scattering is not present. In addition, it is demonstrated that in the presence of the stimulated Raman scattering, there exists a distance at which, for the negative soliton initial phase angle, the dark-soliton timing jitter caused by fluctuations in the background amplitude becomes zero
Elliptic Vortices in Composite Mathieu Lattices
We address the elliptically shaped vortex solitons in defocusing nonlinear
media imprinted with a composite Mathieu lattice. Elliptic vortices feature
anisotropic patterns both in intensity and phase, and can only exist when their
energy flow exceed some certain threshold. Single-charged elliptic vortices are
found to arise via bifurcation from dipole modes, which, to the best of our
knowledge is the first example in the context of optics studies of symmetry
breaking bifurcations for the phase dislocations of different dimensionalities.
Higher-order elliptic vortices with topological charge could exhibit spatially
separated single-charged phase singularities, leading to their stabilization.
The salient features of reported elliptic vortices qualitatively hold for other
elliptic shaped confining potentials.Comment: 22 pages, 5 figures, to appear in Phys. Rev.
Light bullets in quadratic media with normal dispersion at the second harmonic
Stable two- and three-dimensional spatiotemporal solitons (STSs) in
second-harmonic-generating media are found in the case of normal dispersion at
the second harmonic (SH). This result, surprising from the theoretical
viewpoint, opens a way for experimental realization of STSs. An analytical
estimate for the existence of STSs is derived, and full results, including a
complete stability diagram, are obtained in a numerical form. STSs withstand
not only the normal SH dispersion, but also finite walk-off between the
harmonics, and readily self-trap from a Gaussian pulse launched at the
fundamental frequency.Comment: 4 pages, 5 figures, accepted to Phys. Rev. Let
Stable spinning optical solitons in three dimensions
We introduce spatiotemporal spinning solitons (vortex tori) of the
three-dimensional nonlinear Schrodinger equation with focusing cubic and
defocusing quintic nonlinearities. The first ever found completely stable
spatiotemporal vortex solitons are demonstrated. A general conclusion is that
stable spinning solitons are possible as a result of competition between
focusing and defocusing nonlinearities.Comment: 4 pages, 6 figures, accepted to Phys. Rev. Let
Subwavelength Plasmonic Lattice Solitons in Arrays of Metallic Nanowires
We predict theoretically that stable subwavelength plasmonic lattice solitons
(PLSs) are formed in arrays of metallic nanowires embedded in a nonlinear
medium. The tight confinement of the guiding modes of the metallic nanowires,
combined with the strong nonlinearity induced by the enhanced field at the
metal surface, provide the main physical mechanisms for balancing the wave
diffraction and the formation of PLSs. As the conditions required for the
formation of PLSs are satisfied in a variety of plasmonic systems, we expect
these nonlinear modes to have important applications to subwavelength
nanophotonics. In particular, we show that the subwavelength PLSs can be used
to optically manipulate with nanometer accuracy the power flow in ultracompact
photonic systems.Comment: 4 pages, 5 figure
Semi-discrete solitons in arrayed waveguide structures with Kerr nonlinearity
We construct families of optical semi-discrete composite solitons (SDCSs),
with one or two independent propagation constants, supported by a planar slab
waveguide, XPM-coupled to a periodic array of stripes. Both structures feature
the cubic nonlinearity and support intrinsic modes with mutually orthogonal
polarizations. We report three species of SDCSs, odd, even, and twisted ones,
the first type being stable. Transverse motion of phase-tilted solitons, with
potential applications to beam steering, is considered too.Comment: 6 pages, 9 figure
- …