Exact bidirectional X-wave solutions in fiber Bragg gratings

We find exact solutions describing bidirectional pulses propagating in fiber Bragg gratings. They are derived by solving the coupled-mode theory equations and are expressed in terms of products of modified Bessel functions with algebraic functions. Depending on the values of the two free parameters the general bidirectional X-wave solution can also take the form of a unidirectional pulse. We analyze the symmetries and the asymptotic properties of the solutions and also discuss about additional waveforms that are obtained by interference of more than one solutions. Depending on their parameters such pulses can create a sharp focus with high contrast

Bessel-like optical beams with arbitrary trajectories

A method is proposed for generating Bessel-like optical beams with arbitrary trajectories in free space. The method involves phase-modulating an optical wavefront so that conical bundles of rays are formed whose apexes write a continuous focal curve with prespecified shape. These ray cones have circular bases on the input plane, thus their interference results in a Bessel-like transverse field profile that propagates along the specified trajectory with a remarkably invariant main lobe. Such beams can be useful as hybrids between nonaccelerating and accelerating optical waves that share diffraction-resisting and self-healing properties

Advanced trajectory engineering of diffraction-resisting laser beams

We introduce an analytical technique for engineering the trajectory of diffraction-resisting laser beams. The generated beams have a Bessel-like transverse field distribution and can be navigated along rather arbitrary curved paths in free space, thus being an advanced hybrid between accelerating and non-accelerating diffraction-free optical waves. The method involves phase-modulating the wavefront of a Gaussian laser beam to create a continuum of conical ray bundles whose apexes define a prespecified focal curve, along which a nearly perfect circular intensity lobe propagates without diffracting. Through extensive numerical simulations, we demonstrate the great flexibility in the design of a gamut of different beam trajectories. Propagation around obstructions and self-healing scenarios are also investigated. The proposed wave entities can be used extensively for light trajectory control in applications such as laser microfabrication, optical tweezers and curved plasma filamentation spectroscopy

Lattice solitons in Bose-Einstein condensates

We systematically study the properties of lattice solitons in Bose-Einstein condensates with either attractive or repulsive atom interactions. This is done, by exactly solving the mean-field Gross-Pitaevskii equation in the presence of a periodic potential. We find new families of lattice soliton solutions that are characterized by the position of the energy eigenvalue within the associated band structure. These include lattice solitons in condensates with either attractive or repulsive atom interactions that exist in finite or semi-infinite gaps, as well as nonlinear modes that exhibit atomic population cutoffs

Discrete Ginzburg-Landau solitons

We demonstrate that discrete solitons are possible in Ginzburg-Landau lattices. As a result of discreteness, we find that this system exhibits a host of features that have no counterpart whatsoever in either the continuous limit or in other conservative discrete models

Fourier mode dynamics for the nonlinear Schroedinger equation in one-dimensional bounded domains

We analyze the 1D focusing nonlinear Schr\"{o}dinger equation in a finite interval with homogeneous Dirichlet or Neumann boundary conditions. There are two main dynamics, the collapse which is very fast and a slow cascade of Fourier modes. For the cubic nonlinearity the calculations show no long term energy exchange between Fourier modes as opposed to higher nonlinearities. This slow dynamics is explained by fairly simple amplitude equations for the resonant Fourier modes. Their solutions are well behaved so filtering high frequencies prevents collapse. Finally these equations elucidate the unique role of the zero mode for the Neumann boundary conditions

Two-dimensional discrete Ginzburg-Landau solitons

We study the two-dimensional discrete Ginzburg-Landau equation. In the linear limit, the dispersion and gain curves as well as the diffraction pattern are determined analytically. In the nonlinear case, families of two-dimensional discrete solitons are found numerically as well as approximately in the high-confinement limit. The instability dynamics are analyzed by direct simulations

Multi-channel pulse dynamics in a stabilized Ginzburg-Landau system

We study the stability and interactions of chirped solitary pulses in a system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a group-velocity mismatch between them, where each CGL equation is stabilized by linearly coupling it to an additional linear dissipative equation. In the context of nonlinear fiber optics, the model describes transmission and collisions of pulses at different wavelengths in a dual-core fiber, in which the active core is furnished with bandwidth-limited gain, while the other, passive (lossy) one is necessary for stabilization of the solitary pulses. Complete and incomplete collisions of pulses in two channels in the cases of anomalous and normal dispersion in the active core are analyzed by means of perturbation theory and direct numerical simulations. It is demonstrated that the model may readily support fully stable pulses whose collisions are quasi-elastic, provided that the group-velocity difference between the two channels exceeds a critical value. In the case of quasi-elastic collisions, the temporal shift of pulses, predicted by the analytical approach, is in semi-quantitative agrement with direct numerical results in the case of anomalous dispersion (in the opposite case, the perturbation theory does not apply). We also consider a simultaneous collision between pulses in three channels, concluding that this collision remains quasi-elastic, and the pulses remain completely stable. Thus, the model may be a starting point for the design of a stabilized wavelength-division-multiplexed (WDM) transmission system.Comment: a text file in the revtex4 format, and 16 pdf files with figures. Physical Review E, in pres

An ultra-bright atom laser

We present a novel, ultra-bright atom-laser and ultra-cold thermal atom beam. Using rf-radiation we strongly couple the magnetic hyperfine levels of 87Rb atoms in a magnetically trapped Bose-Einstein condensate. At low rf-frequencies gravity opens a small hole in the trapping potenital and a well collimated, extremely bright atom laser emerges from just below the condensate. As opposed to traditional atom lasers based on weak coupling, this technique allows us to outcouple atoms at an arbitrarily large rate. We demonstrate an increase in flux per atom in the BEC by a factor of sixteen compared to the brightest quasi-continuous atom laser. Furthermore, we produce by two orders of magnitude the coldest thermal atom beam to date (200 nK).Comment: 20 pages, 9 figures, supplementary material online at http://www.bec.g