13 research outputs found
Stable vortex and dipole vector solitons in a saturable nonlinear medium
We study both analytically and numerically the existence, uniqueness, and
stability of vortex and dipole vector solitons in a saturable nonlinear medium
in (2+1) dimensions. We construct perturbation series expansions for the vortex
and dipole vector solitons near the bifurcation point where the vortex and
dipole components are small. We show that both solutions uniquely bifurcate
from the same bifurcation point. We also prove that both vortex and dipole
vector solitons are linearly stable in the neighborhood of the bifurcation
point. Far from the bifurcation point, the family of vortex solitons becomes
linearly unstable via oscillatory instabilities, while the family of dipole
solitons remains stable in the entire domain of existence. In addition, we show
that an unstable vortex soliton breaks up either into a rotating dipole soliton
or into two rotating fundamental solitons.Comment: To appear in Phys. Rev.
Scattering of dipole-mode vector solitons: Theory and experiment
We study, both theoretically and experimentally, the scattering properties of
optical dipole-mode vector solitons - radially asymmetric composite
self-trapped optical beams. First, we analyze the soliton collisions in an
isotropic two-component model with a saturable nonlinearity and demonstrate
that in many cases the scattering dynamics of the dipole-mode solitons allows
us to classify them as ``molecules of light'' - extremely robust spatially
localized objects which survive a wide range of interactions and display many
properties of composite states with a rotational degree of freedom. Next, we
study the composite solitons in an anisotropic nonlinear model that describes
photorefractive nonlinearities, and also present a number of experimental
verifications of our analysis.Comment: 8 pages + 4 pages of figure
Interaction of two modulational instabilities in a semiconductor resonator
The interaction of two neighboring modulational instabilities in a coherently driven semiconductor cavity is investigated. First, an asymptotic reduction of the general equations is performed in the limit of a nearly vertical input-output characteristic. Next, a normal form is derived in the limit where the two instabilities are close to one other. An infinity of branches of periodic solutions are found to emerge from the unstable portion of the homogeneous branch. These branches have a nontrivial envelope in the bifurcation diagram that can either smoothly join the two instability points or form an isolated branch of solutions