Nonlinear spatiotemporal photonics in bundled arrays of waveguides,

Date du colloque : 11/2010International audienc

Stable vortex solitons in the Ginzburg-Landau model of a two-dimensional lasing medium with a transverse grating

We introduce a two-dimensional model of a laser cavity based on the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity and a lattice potential accounting for the transverse grating. A remarkable fact is that localized vortices, built as sets of four peaks pinned to the periodic potential, may be stable without the unphysical diffusion term, which was necessary for the stabilization in previously studied models. The vortices are chiefly considered in the onsite (rhombic) form, but the stabilization of offsite vortices (square-shaped ones) and quadrupoles is demonstrated too. Stability regions for the rhombic vortices and fundamental solitons are identified in the model’s parameter space, and scenarios of the evolution of unstable vortices are described. An essential result is a minimum strength of the lattice potential which is necessary to stabilize the vortices. The stability border is also identified in the case of the self-focusing quintic term in the underlying model, which suggests a possibility of the supercritical collapse. Beyond this border, the stationary vortex turns into a vortical breather, which is subsequently replaced by a dipolar breather and eventually by a single-peak breather

Progressive motion of an ac-driven kink in an annular damped system

A novel dynamical effect is presented: systematic drift of a topological soliton in ac-driven weakly damped systems with periodic boundary conditions. The effect is demonstrated in detail for a long annular Josephson junction. Unlike earlier considered cases of the ac-driven motion of fluxons (kinks), in the present case the long junction is_spatially uniform_. Numerical simulations reveal that progressive motion of the fluxon commences if the amplitude of the ac drive exceeds a threshold value. The direction of the motion is randomly selected by initial conditions, and a strong hysteresis is observed. An analytical approach to the problem is based on consideration of the interaction between plasma waves emitted by the fluxon under the action of the ac drive and the fluxon itself, after the waves complete round trip in the annular junction. The analysis predicts instability of the zero-average-velocity state of the fluxon interacting with its own radiation tails, provided that the drive's amplitude exceeds an explicitly found threshold. The predicted threshold amplitude strongly depends on the phase shift gained by the wave after the round trip. A very similar dependence is found in the simulations, testifying to the relevance of the analytical consideration.Comment: revtex text file and five eps figure files. Physical Review E, in pres

On the Origin of Traveling Pulses in Bistable Systems

The interaction between a pair of Bloch fronts forming a traveling domain in a bistable medium is studied. A parameter range beyond the nonequilibrium Ising-Bloch bifurcation is found where traveling domains collapse. Only beyond a second threshold the repulsive front interactions become strong enough to balance attractive interactions and asymmetries in front speeds, and form stable traveling pulses. The analysis is carried out for the forced complex Ginzburg-Landau equation. Similar qualitative behavior is found in the bistable FitzHugh-Nagumo model.Comment: 5 pages, RevTeX. Aric Hagberg: http://t7.lanl.gov/People/Aric/; Ehud Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm

Radiation linewidth of a long Josephson junction in the flux-flow regime

Theoretical model for the radiation linewidth in a multi-fluxon state of a long Josephson junction is presented. Starting from the perturbed sine-Gordon model with the temperature dependent noise term, we develop a collective coordinate approach which allows to calculate the finite radiation linewidth due to excitation of the internal degrees of freedom in the moving fluxon chain. At low fluxon density, the radiation linewidth is expected to be substantially larger than that of a lumped Josephson oscillator. With increasing the fluxon density, a crossover to a much smaller linewidth corresponding to the lumped oscillator limit is predicted.Comment: 11 pages LaTeX, to appear in Phys Rev

Linearly Coupled Bose-Einstein Condensates: From Rabi Oscillations and Quasi-Periodic Solutions to Oscillating Domain Walls and Spiral Waves

In this paper, an exact unitary transformation is examined that allows for the construction of solutions of coupled nonlinear Schr{\"o}dinger equations with additional linear field coupling, from solutions of the problem where this linear coupling is absent. The most general case where the transformation is applicable is identified. We then focus on the most important special case, namely the well-known Manakov system, which is known to be relevant for applications in Bose-Einstein condensates consisting of different hyperfine states of $^{87}$Rb. In essence, the transformation constitutes a distributed, nonlinear as well as multi-component generalization of the Rabi oscillations between two-level atomic systems. It is used here to derive a host of periodic and quasi-periodic solutions including temporally oscillating domain walls and spiral waves.Comment: 6 pages, 4 figures, Phys. Rev. A (in press

Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation

We report results of collisions between coaxial vortex solitons with topological charges ±S in the complex cubic-quintic Ginzburg-Landau equation. With the increase of the collision momentum, merger of the vortices into one or two dipole or quadrupole clusters of fundamental solitons (for S=1 and 2, respectively) is followed by the appearance of pairs of counter-rotating “unfinished vortices,” in combination with a soliton cluster or without it. Finally, the collisions become elastic. The clusters generated by the collisions are very robust, while the “unfinished vortices,” eventually split into soliton pairs