96 research outputs found
Polychromatic solitons in a quadratic medium
We introduce the simplest model to describe parametric interactions in a
quadratically nonlinear optical medium with the fundamental harmonic containing
two components with (slightly) different carrier frequencies [which is a direct
analog of wavelength-division multiplexed (WDM) models, well known in media
with cubic nonlinearity]. The model takes a closed form with three different
second-harmonic components, and it is formulated in the spatial domain. We
demonstrate that the model supports both polychromatic solitons (PCSs), with
all the components present in them, and two types of mutually orthogonal simple
solitons, both types being stable in a broad parametric region. An essential
peculiarity of PCS is that its power is much smaller than that of a simple
(usual) soliton (taken at the same values of control parameters), which may be
an advantage for experimental generation of PCSs. Collisions between the
orthogonal simple solitons are simulated in detail, leading to the conclusion
that the collisions are strongly inelastic, converting the simple solitons into
polychromatic ones, and generating one or two additional PCSs. A collision
velocity at which the inelastic effects are strongest is identified, and it is
demonstrated that the collision may be used as a basis to design a simple
all-optical XOR logic gate.Comment: 9 pages, 8 figures, accepted to Phys. Rev.
Dipole-Mode Vector Solitons
We find a new type of optical vector soliton that originates from trapping of
a dipole mode by a soliton-induced waveguide. These solitons, which appear as a
consequence of the vector nature of the two component system, are more stable
than the previously found optical vortex-mode solitons and represent a new type
of extremely robust nonlinear vector structure.Comment: Four pages with five eps figure
Soliton Interactions in Perturbed Nonlinear Schroedinger Equations
We use multiscale perturbation theory in conjunction with the inverse
scattering transform to study the interaction of a number of solitons of the
cubic nonlinear Schroedinger equation under the influence of a small correction
to the nonlinear potential. We assume that the solitons are all moving with the
same velocity at the initial instant; this maximizes the effect each soliton
has on the others as a consequence of the perturbation. Over the long time
scales that we consider, the amplitudes of the solitons remain fixed, while
their center of mass coordinates obey Newton's equations with a force law for
which we present an integral formula. For the interaction of two solitons with
a quintic perturbation term we present more details since symmetries -- one
related to the form of the perturbation and one related to the small number of
particles involved -- allow the problem to be reduced to a one-dimensional one
with a single parameter, an effective mass. The main results include
calculations of the binding energy and oscillation frequency of nearby solitons
in the stable case when the perturbation is an attractive correction to the
potential and of the asymptotic "ejection" velocity in the unstable case.
Numerical experiments illustrate the accuracy of the perturbative calculations
and indicate their range of validity.Comment: 28 pages, 7 figures, Submitted to Phys Rev E Revised: 21 pages, 6
figures, To appear in Phys Rev E (many displayed equations moved inline to
shorten manuscript
Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries
We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys.
JETP {\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves
in the nonlinear Schr\"oedinger equation (NLS) can be generalised for models
with two phase symmetries. MI of three-wave parametric spatial solitons due to
group velocity dispersion (GVD) is investigated as a typical example of such
models. We reveal a new branch of neck instability, which dominates the usual
snake type MI found for normal GVD. The resultant nonlinear evolution is
thereby qualitatively different from cases with only a single phase symmetry.Comment: 4 pages with figure
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
We review the latest progress and properties of the families of bright and
dark one-dimensional periodic waves propagating in saturable Kerr-type and
quadratic nonlinear media. We show how saturation of the nonlinear response
results in appearance of stability (instability) bands in focusing (defocusing)
medium, which is in sharp contrast with the properties of periodic waves in
Kerr media. One of the key results discovered is the stabilization of
multicolor periodic waves in quadratic media. In particular, dark-type waves
are shown to be metastable, while bright-type waves are completely stable in a
broad range of energy flows and material parameters. This yields the first
known example of completely stable periodic wave patterns propagating in
conservative uniform media supporting bright solitons. Such results open the
way to the experimental observation of the corresponding self-sustained
periodic wave patterns.Comment: 29 pages, 10 figure
Modulational instability in periodic quadratic nonlinear materials
We investigate the modulational instability of plane waves in quadratic
nonlinear materials with linear and nonlinear quasi-phase-matching gratings.
Exact Floquet calculations, confirmed by numerical simulations, show that the
periodicity can drastically alter the gain spectrum but never completely
removes the instability. The low-frequency part of the gain spectrum is
accurately predicted by an averaged theory and disappears for certain gratings.
The high-frequency part is related to the inherent gain of the homogeneous
non-phase-matched material and is a consistent spectral feature.Comment: 4 pages, 7 figures corrected minor misprint
STOCHASTIC DYNAMICS OF LARGE-SCALE INFLATION IN DE~SITTER SPACE
In this paper we derive exact quantum Langevin equations for stochastic
dynamics of large-scale inflation in de~Sitter space. These quantum Langevin
equations are the equivalent of the Wigner equation and are described by a
system of stochastic differential equations. We present a formula for the
calculation of the expectation value of a quantum operator whose Weyl symbol is
a function of the large-scale inflation scalar field and its time derivative.
The unique solution is obtained for the Cauchy problem for the Wigner equation
for large-scale inflation. The stationary solution for the Wigner equation is
found for an arbitrary potential. It is shown that the large-scale inflation
scalar field in de Sitter space behaves as a quantum one-dimensional
dissipative system, which supports the earlier results. But the analogy with a
one-dimensional model of the quantum linearly damped anharmonic oscillator is
not complete: the difference arises from the new time dependent commutation
relation for the large-scale field and its time derivative. It is found that,
for the large-scale inflation scalar field the large time asymptotics is equal
to the `classical limit'. For the large time limit the quantum Langevin
equations are just the classical stochastic Langevin equations (only the
stationary state is defined by the quantum field theory).Comment: 21 pages RevTex preprint styl
Observation of dipole-mode vector solitons
We report on the first experimental observation of a novel type of optical
vector soliton, a {\em dipole-mode soliton}, recently predicted theoretically.
We show that these vector solitons can be generated in a photorefractive medium
employing two different processes: a phase imprinting, and a symmetry-breaking
instability of a vortex-mode vector soliton. The experimental results display
remarkable agreement with the theory, and confirm the robust nature of these
radially asymmetric two-component solitary waves.Comment: 4 pages, 8 figures; pictures in the PRL version are better qualit
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
Ultrashort filaments of light in weakly-ionized, optically-transparent media
Modern laser sources nowadays deliver ultrashort light pulses reaching few
cycles in duration, high energies beyond the Joule level and peak powers
exceeding several terawatt (TW). When such pulses propagate through
optically-transparent media, they first self-focus in space and grow in
intensity, until they generate a tenuous plasma by photo-ionization. For free
electron densities and beam intensities below their breakdown limits, these
pulses evolve as self-guided objects, resulting from successive equilibria
between the Kerr focusing process, the chromatic dispersion of the medium, and
the defocusing action of the electron plasma. Discovered one decade ago, this
self-channeling mechanism reveals a new physics, widely extending the frontiers
of nonlinear optics. Implications include long-distance propagation of TW beams
in the atmosphere, supercontinuum emission, pulse shortening as well as
high-order harmonic generation. This review presents the landmarks of the
10-odd-year progress in this field. Particular emphasis is laid to the
theoretical modeling of the propagation equations, whose physical ingredients
are discussed from numerical simulations. Differences between femtosecond
pulses propagating in gaseous or condensed materials are underlined. Attention
is also paid to the multifilamentation instability of broad, powerful beams,
breaking up the energy distribution into small-scale cells along the optical
path. The robustness of the resulting filaments in adverse weathers, their
large conical emission exploited for multipollutant remote sensing, nonlinear
spectroscopy, and the possibility to guide electric discharges in air are
finally addressed on the basis of experimental results.Comment: 50 pages, 38 figure
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