66 research outputs found
Numerical validation of the Complex Swift-Hohenberg equation for lasers
Order parameter equations, such as the complex Swift-Hohenberg (CSH)
equation, offer a simplified and universal description that hold close to an
instability threshold. The universality of the description refers to the fact
that the same kind of instability produces the same order parameter equation.
In the case of lasers, the instability usually corresponds to the emitting
threshold, and the CSH equation can be obtained from the Maxwell-Bloch (MB)
equations for a class C laser with small detuning. In this paper we numerically
check the validity of the CSH equation as an approximation of the MB equations,
taking into account that its terms are of different asymptotic order, and that,
despite of having been systematically overlooked in the literature, this fact
is essential in order to correctly capture the weakly nonlinear dynamics of the
MB. The approximate distance to threshold range for which the CSH equation
holds is also estimated.Comment: submitted to European Journal of Physic
Fluctuations and correlations in hexagonal optical patterns
We analyze the influence of noise in transverse hexagonal patterns in
nonlinear Kerr cavities. The near field fluctuations are determined by the
neutrally stable Goldstone modes associated to translational invariance and by
the weakly damped soft modes. However these modes do not contribute to the far
field intensity fluctuations which are dominated by damped perturbations with
the same wave vectors than the pattern. We find strong correlations between the
intensity fluctuations of any arbitrary pair of wave vectors of the pattern.
Correlation between pairs forming 120 degrees is larger than between pairs
forming 180 degrees, contrary to what a naive interpretation of emission in
terms of twin photons would suggest.Comment: 10 pages, 13 figure
Spatiotemporal Chaos, Localized Structures and Synchronization in the Vector Complex Ginzburg-Landau Equation
We study the spatiotemporal dynamics, in one and two spatial dimensions, of
two complex fields which are the two components of a vector field satisfying a
vector form of the complex Ginzburg-Landau equation. We find synchronization
and generalized synchronization of the spatiotemporally chaotic dynamics. The
two kinds of synchronization can coexist simultaneously in different regions of
the space, and they are mediated by localized structures. A quantitative
characterization of the degree of synchronization is given in terms of mutual
information measures.Comment: 6 pages, using bifchaos.sty (included). 7 figures. Related material,
including higher quality figures, could be found at
http://www.imedea.uib.es/PhysDept/publicationsDB/date.html . To appear in
International Journal of Bifurcation and Chaos (1999
Diffusion-Limited Coalescence with Finite Reaction Rates in One Dimension
We study the diffusion-limited process in one dimension, with
finite reaction rates. We develop an approximation scheme based on the method
of Inter-Particle Distribution Functions (IPDF), which was formerly used for
the exact solution of the same process with infinite reaction rate. The
approximation becomes exact in the very early time regime (or the
reaction-controlled limit) and in the long time (diffusion-controlled)
asymptotic limit. For the intermediate time regime, we obtain a simple
interpolative behavior between these two limits. We also study the coalescence
process (with finite reaction rates) with the back reaction , and in
the presence of particle input. In each of these cases the system reaches a
non-trivial steady state with a finite concentration of particles. Theoretical
predictions for the concentration time dependence and for the IPDF are compared
to computer simulations. P. A. C. S. Numbers: 82.20.Mj 02.50.+s 05.40.+j
05.70.LnComment: 13 pages (and 4 figures), plain TeX, SISSA-94-0
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
Dynamics of localized structures in vector waves
Dynamical properties of topological defects in a twodimensional complex
vector field are considered. These objects naturally arise in the study of
polarized transverse light waves. Dynamics is modeled by a Vector Complex
Ginzburg-Landau Equation with parameter values appropriate for linearly
polarized laser emission. Creation and annihilation processes, and
selforganization of defects in lattice structures, are described. We find
"glassy" configurations dominated by vectorial defects and a melting process
associated to topological-charge unbinding.Comment: 4 pages, 5 figures included in the text. To appear in Phys. Rev.
Lett. (2000). Related material at http://www.imedea.uib.es/Nonlinear and
http://www.imedea.uib.es/Photonics . In this new version, Fig. 3 has been
replaced by a better on
Spatial correlations in hexagons generated via a Kerr nonlinearity
We consider the hexagonal pattern forming in the cross-section of an optical
beam produced by a Kerr cavity, and we study the quantum correlations
characterizing this structure. By using arguments related to the symmetry
broken by the pattern formation, we identify a complete scenario of six-mode
entanglement. Five independent phase quadratures combinations, connecting the
hexagonal modes, are shown to exhibit sub-shot-noise fluctuations. By means of
a non-linear quantum calculation technique, quantum correlations among the mode
photon numbers are demonstrated and calculated.Comment: ReVTeX file, 20 pages, 7 eps figure
- …