210 research outputs found
Symmetric Itinerary Sets
We consider a one parameter family of dynamical systems W :[0, 1] -> [0, 1]
constructed from a pair of monotone increasing diffeomorphisms Wsub(i), such
that Wsub(i)(inverse): [0, 1] -> [0, 1], (i = 0, 1). We characterise the set of
symbolic itineraries of W using an attractor of an iterated closed relation,in
the terminology of McGehee, and prove that there is a member of the family for
which is symmetrical
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
Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media
We demonstrate the existence of stable three-dimensional spatiotemporal
solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental
(nonspinning) STSs forming one-parameter families are stable if their
propagation constant exceeds a certain critical value, that is inversely
proportional to the range of nonlocality of nonlinear response. All spinning
three-dimensional STSs are found to be unstable.Comment: 14 pages, 6 figures, accepted to PRE, Rapid Communication
Spatiotemporal discrete multicolor solitons
We have found various families of two-dimensional spatiotemporal solitons in
quadratically nonlinear waveguide arrays. The families of unstaggered odd, even
and twisted stationary solutions are thoroughly characterized and their
stability against perturbations is investigated. We show that the twisted and
even solutions display instability, while most of the odd solitons show
remarkable stability upon evolution.Comment: 18 pages,7 figures. To appear in Physical Review
Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation
We report results of collisions between coaxial vortex solitons with topological charges ±S in the complex cubic-quintic Ginzburg-Landau equation. With the increase of the collision momentum, merger of the vortices into one or two dipole or quadrupole clusters of fundamental solitons (for S=1 and 2, respectively) is followed by the appearance of pairs of counter-rotating “unfinished vortices,” in combination with a soliton cluster or without it. Finally, the collisions become elastic. The clusters generated by the collisions are very robust, while the “unfinished vortices,” eventually split into soliton pairs
Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities
We show that the quadratic interaction of fundamental and second harmonics in
a bulk dispersive medium, combined with self-defocusing cubic nonlinearity,
give rise to completely localized spatiotemporal solitons (vortex tori) with
vorticity s=1. There is no threshold necessary for the existence of these
solitons. They are found to be stable against small perturbations if their
energy exceeds a certain critical value, so that the stability domain occupies
about 10% of the existence region of the solitons. We also demonstrate that the
s=1 solitons are stable against very strong perturbations initially added to
them. However, on the contrary to spatial vortex solitons in the same model,
the spatiotemporal solitons with s=2 are never stable.Comment: latex text, 10 ps and 2 jpg figures; Physical Review E, in pres
Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media
We demonstrate that two-dimensional two-component bright solitons of an
annular shape, carrying vorticities in the components, may be
stable in media with the cubic-quintic nonlinearity, including the
\textit{hidden-vorticity} (HV) solitons of the type , whose net
vorticity is zero. Stability regions for the vortices of both types
are identified for , 2, and 3, by dint of the calculation of stability
eigenvalues, and in direct simulations. A novel feature found in the study of
the HV solitons is that their stability intervals never reach the (cutoff)
point at which the bright vortex carries over into a dark one, hence dark HV
solitons can never be stable, contrarily to the bright ones. In addition to the
well-known symmetry-breaking (\textit{external}) instability, which splits the
ring soliton into a set of fragments flying away in tangential directions, we
report two new scenarios of the development of weak instabilities specific to
the HV solitons. One features \textit{charge flipping}, with the two components
exchanging the angular momentum and periodically reversing the sign of their
spins. The composite soliton does not split in this case, therefore we identify
such instability as an \textit{intrinsic} one. Eventually, the soliton splits,
as weak radiation loss drives it across the border of the ordinary strong
(external) instability. Another scenario proceeds through separation of the
vortex cores in the two components, each individual core moving toward the
outer edge of the annular soliton. After expulsion of the cores, there remains
a zero-vorticity breather with persistent internal vibrations.Comment: 10 pages, 11 figure
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
Polarization conversion spectroscopy of hybrid modes
Enhanced polarization conversion in reflection for the Otto and Kretschmann
configurations is introduced as a new method for hybrid-mode spectroscopy.
Polarization conversion in reflection appears when hybrid-modes are excited in
a guiding structure composed of at least one anisotropic media. In contrast to
a dark dip, in this case modes are associated to a peak in the converted
reflectance spectrum, increasing the detection sensitivity and avoiding
confusion with reflection dips associated with other processes as can be
transmission.Comment: 4 pages, 4 figure
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