68 research outputs found
Higher-order nonlinear modes and bifurcation phenomena due to degenerate parametric four-wave mixing
We demonstrate that weak parametric interaction of a fundamental beam with
its third harmonic field in Kerr media gives rise to a rich variety of families
of non-fundamental (multi-humped) solitary waves. Making a comprehensive
comparison between bifurcation phenomena for these families in bulk media and
planar waveguides, we discover two novel types of soliton bifurcations and
other interesting findings. The later includes (i) multi-humped solitary waves
without even or odd symmetry and (ii) multi-humped solitary waves with large
separation between their humps which, however, may not be viewed as bound
states of several distinct one-humped solitons.Comment: 9 pages, 17 figures, submitted to Phys. Rev.
Model of position-dynamic structure of river basins
In this work, we have presented semi automated means of modeling of position-dynamic structure (PDS) of river basins’ landscapes with application of geo-informational systems (GIS). Results of modeling were tested on the basin of one of headwaters. The structure of the model includes landscape lines, layers, sub-regions and regions. The model takes into account conditions of formation of landscape’s PDS in mountain and plain parts of river basinsyesБелгородский государственный университе
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.
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
Statistical characteristics of formation and evolution of structure in the universe
An approximate statistical description of the formation and evolution of
structure of the universe based on the Zel'dovich theory of gravitational
instability is proposed. It is found that the evolution of DM structure shows
features of self-similarity and the main structure characteristics can be
expressed through the parameters of initial power spectrum and cosmological
model. For the CDM-like power spectrum and suitable parameters of the
cosmological model the effective matter compression reaches the observed scales
20 -- 25Mpc with the typical mean separation of
wall-like elements 50 -- 70Mpc. This description can be
directly applied to the deep pencil beam galactic surveys and absorption
spectra of quasars. For larger 3D catalogs and simulations it can be applied to
results obtained with the core-sampling analysis.
It is shown that the interaction of large and small scale perturbations
modulates the creation rate of early Zel'dovich pancakes and generates bias on
the SLSS scale. For suitable parameters of the cosmological model and reheating
process this bias can essentially improve the characteristics of simulated
structure of the universe.
The models with give the best description of the
observed structure parameters. The influence of low mass "warm" dark matter
particles, such as a massive neutrino, will extend the acceptable range of
and .Comment: 20pages, 7 figures, MNRAS in pres
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
Three-dimensional quantum solitons with parametric coupling
We consider the quantum field theory of two bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium, this corresponds to the process of second-harmonic generation (via chi((2)) nonlinearity) modified by the chi((3)) nonlinearity. The quantum solitons or energy eigenstates (bound-state solutions) are obtained exactly in the simplest case of two-particle binding, in one, two, and three space dimensions. We also investigate three-particle binding in one space dimension. The results indicate that the exact quantum solitons of this field theory have a singular, pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. To estimate the physically accessible radii and binding energies of the bound states, we impose a momentum cutoff on the nonlinear couplings. In the case of nonlinear optical interactions, the resulting radii and binding energies of these photonic particlelike excitations in highly nonlinear parametric media appear to be close to physically observable values
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