2,739 research outputs found
Mixed perturbative expansion: the validity of a model for the cascading
A new type of perturbative expansion is built in order to give a rigorous
derivation and to clarify the range of validity of some commonly used model
equations.
This model describes the evolution of the modulation of two short and
localized pulses, fundamental and second harmonic, propagating together in a
bulk uniaxial crystal with non-vanishing second order susceptibility
and interacting through the nonlinear effect known as ``cascading'' in
nonlinear optics.
The perturbative method mixes a multi-scale expansion with a power series
expansion of the susceptibility, and must be carefully adapted to the physical
situation. It allows the determination of the physical conditions under which
the model is valid: the order of magnitude of the walk-off, phase-mismatch,and
anisotropy must have determined values.Comment: arxiv version is already officia
Stabilization of vortex beams in Kerr media by nonlinear absorption
We elaborate a new solution for the problem of stable propagation of
transversely localized vortex beams in homogeneous optical media with
self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are
stabilized against azimuthal breakup and collapse by multiphoton absorption,
while the respective power loss is offset by the radial influx of the power
from an intrinsic reservoir. A linear stability analysis and direct numerical
simulations reveal a region of stability of these vortices. Beams with multiple
vorticities have their stability regions too. These beams can then form robust
tubular filaments in transparent dielectrics as common as air, water and
optical glasses at sufficiently high intensities. We also show that the
tubular, rotating and speckle-like filamentation regimes, previously observed
in experiments with axicon-generated Bessel beams, can be explained as
manifestations of the stability or instability of a specific nonlinear
Bessel-vortex state, which is fully identified.Comment: Physical Review A, in press, 9 pages, 6 figure
Building patterns by traveling vortices and dipoles in periodic dissipative media
We analyze pattern-formation scenarios in the two-dimensional (2D) complex
Ginzburg-Landau (CGL) equation with the cubic-quintic (CQ) nonlinearity and a
cellular potential. The equation models laser cavities with built-in gratings,
which are used to stabilize 2D patterns. The pattern-building process is
initiated by kicking a localized compound mode, in the form of a dipole,
quadrupole, or vortex which is composed of four local peaks. The hopping motion
of the kicked mode through the cellular structure leads to the generation of
various extended patterns pinned by the structure. In the ring-shaped system,
the persisting freely moving dipole hits the stationary pattern from the
opposite side, giving rise to several dynamical regimes, with the pinned
multi-soliton chain playing the role of the Newton's cradle (NC)
Pattern formation by kicked solitons in the two-dimensionnal Ginzburg-Landau medium with a transverse grating
We consider the kick-induced mobility of two-dimensional (2D) fundamental
dissipative solitons in models of lasing media based on the 2D complex
Ginzburg-Landau (CGL) equation including a spatially periodic potential
(transverse grating). The depinning threshold is identified by means of
systematic simulations, and described by means of an analytical approximation,
depending on the orientation of the kick. Various pattern-formation scenarios
are found above the threshold. Most typically, the soliton, hopping between
potential cells, leaves arrayed patterns of different sizes in its wake. In the
laser cavity, this effect may be used as a mechanism for selective pattern
formation controlled by the tilt of the seed beam. Freely moving solitons
feature two distinct values of the established velocity. Elastic and inelastic
collisions between free solitons and pinned arrayed patterns are studied too.Comment: 15 pages, 20 figures (with 41 sub-figures
Anyons, group theory and planar physics
Relativistic and nonrelativistic anyons are described in a unified formalism
by means of the coadjoint orbits of the symmetry groups in the free case as
well as when there is an interaction with a constant electromagnetic field. To
deal with interactions we introduce the extended Poincar\'e and Galilei Maxwell
groups.Comment: 22 pages, journal reference added, bibliography update
Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets
The dimensional reduction of the three-dimensional fermion-Chern-Simons model
(related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either
the static, fixed--chirality sector of our non-relativistic spinor-Chern-Simons
model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the
plane.Comment: 4 pages, Plain Tex, no figure
The influence of twin boundaries on the Flux Line Lattice structure in YBaCuO: a study by Small Angle Neutron Scattering
The influence of Twin Boundaries (TB) on the Flux Line Lattice(FLL) structure
was investigated by Small Angle Neutron Scattering (SANS). YBaCuO single
crystals possessing different TB densities were studied. The SANS experiments
show that the TB strongly modify the structure of the FLL. The flux lines
meander as soon as the magnetic field makes an angle with the TB direction.
According to the value of this angle but also to the ratio of the flux lines
density over the TB density, one observes that the FLL exhibits two different
unit cells in the plane perpendicular to the magnetic field. One is the
classical hexagonal and anisotropic cell while the other is affected by an
additional deformation induced by the TB. We discuss a possible relation
between this deformation and the increase of the critical current usually
observed in heavily twinned samples.Comment: accepted for publication in Phys Rev
Lorentz Transformation from Symmetry of Reference Principle
The Lorentz Transformation is traditionally derived requiring the Principle
of Relativity and light-speed universality. While the latter can be relaxed,
the Principle of Relativity is seen as core to the transformation. The present
letter relaxes both statements to the weaker, Symmetry of Reference Principle.
Thus the resulting Lorentz transformation and its consequences (time
dilatation, length contraction) are, in turn, effects of how we manage space
and time.Comment: 2 page
(In)finite extensions of algebras from their Inonu-Wigner contractions
The way to obtain massive non-relativistic states from the Poincare algebra
is twofold. First, following Inonu and Wigner the Poincare algebra has to be
contracted to the Galilean one. Second, the Galilean algebra is to be extended
to include the central mass operator. We show that the central extension might
be properly encoded in the non-relativistic contraction. In fact, any
Inonu-Wigner contraction of one algebra to another, corresponds to an infinite
tower of abelian extensions of the latter. The proposed method is
straightforward and holds for both central and non-central extensions. Apart
from the Bargmann (non-zero mass) extension of the Galilean algebra, our list
of examples includes the Weyl algebra obtained from an extension of the
contracted SO(3) algebra, the Carrollian (ultra-relativistic) contraction of
the Poincare algebra, the exotic Newton-Hooke algebra and some others. The
paper is dedicated to the memory of Laurent Houart (1967-2011).Comment: 7 pages, revtex style; v2: Minor corrections, references added; v3:
Typos correcte
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