Optical pulse propagation in fibers with random dispersion

The propagation of optical pulses in two types of fibers with randomly varying dispersion is investigated. The first type refers to a uniform fiber dispersion superimposed by random modulations with a zero mean. The second type is the dispersion-managed fiber line with fluctuating parameters of the dispersion map. Application of the mean field method leads to the nonlinear Schr\"odinger equation (NLSE) with a dissipation term, expressed by a 4th order derivative of the wave envelope. The prediction of the mean field approach regarding the decay rate of a soliton is compared with that of the perturbation theory based on the Inverse Scattering Transform (IST). A good agreement between these two approaches is found. Possible ways of compensation of the radiative decay of solitons using the linear and nonlinear amplification are explored. Corresponding mean field equation coincides with the complex Swift-Hohenberg equation. The condition for the autosolitonic regime in propagation of optical pulses along a fiber line with fluctuating dispersion is derived and the existence of autosoliton (dissipative soliton) is confirmed by direct numerical simulation of the stochastic NLSE. The dynamics of solitons in optical communication systems with random dispersion-management is further studied applying the variational principle to the mean field NLSE, which results in a system of ODE's for soliton parameters. Extensive numerical simulations of the stochastic NLSE, mean field equation and corresponding set of ODE's are performed to verify the predictions of the developed theory.Comment: 17 pages, 7 eps figure

Excitations of a Bose-Einstein condensate in a one-dimensional optical lattice

We investigate the low-lying excitations of a stack of weakly-coupled two-dimensional Bose-Einstein condensates that is formed by a one-dimensional optical lattice. In particular, we calculate the dispersion relations of the monopole and quadrupole modes, both for the ground state as well as for the case in which the system contains a vortex along the direction of the lasers creating the optical lattice. Our variational approach enables us to determine analytically the dispersion relations for an arbitrary number of atoms in every two-dimensional condensate and for an arbitrary momentum. We also discuss the feasibility of experimentally observing our results.Comment: 16 pages, 5 figures, minor changes,accepted for publication in Phys. Rev.

Stability of dark solitons in a Bose-Einstein condensate trapped in an optical lattice

We investigate the stability of dark solitons (DSs) in an effectively one-dimensional Bose-Einstein condensate in the presence of the magnetic parabolic trap and an optical lattice (OL). The analysis is based on both the full Gross-Pitaevskii equation and its tight-binding approximation counterpart (discrete nonlinear Schr{\"o}dinger equation). We find that DSs are subject to weak instabilities with an onset of instability mainly governed by the period and amplitude of the OL. The instability, if present, sets in at large times and it is characterized by quasi-periodic oscillations of the DS about the minimum of the parabolic trap.Comment: Typo fixed in Eq. (1): cos^2 -> sin^

Coherent structures of Bose-Einstein condensates in optical lattices

We propose to employ the phenomenon of modulational instability in order to create regularly arranged localized excitations in arrays of Bose-Einstein condensates. These excitations are narrow tubes in 2D and small hollows in 3D arrays filled in with the condensed atoms of much greater density compared to surrounding array sites. As the regions with high atomic concentration develop due to the modulational instability, they can be preserved by increasing the strength of the optical lattice. Theoretical model, based on the multiple scale expansion, describes the main features of the phenomenon. Analytical predictions are confirmed by numerical simulations of the Gross-Pitaevskii equation. Keyword

Multidimensional solitons and vortices in periodic potentials

The existence of stable solitons and localized vortices in two- and three-dimensional (2D and 3D) media governed by the cubic nonlinear Schroedinger equation with a periodic potential is demonstrated by means of the variational approximation (VA) and in direct simulations. In the 2D case, multi-mode (hexagonal, triangular, and quasi periodic) potentials are considered (including search for vortex solitons in them), along with the usual square potential. In the 2D and 3D cases, low-dimensional (respectively quasi-1D and quasi-2D) potentials are considered too. Families of solitons include single- and multi-peaked ones. Solitons of the former type and their stability are well predicted by VA. Collisions of multidimensional solitons in a low dimensional periodic potential are also studied. Head-on collisions and in-phase solitons lead to their fusion into a collapsing pulse. Soliton colliding in adjacent lattice-.induced channels may form a bound state (BS), which then relaxes to a stable asymmetric form. An initial unstable soliton splits into a three-soliton BS. The results apply to Bose-Einstein condensates (BECs) in optical lattices (OLs), and to spatial or spatiotemporal solitons in layered optical media

Matter-wave solitons in radially periodic potentials

We investigate two-dimensional 2D states in Bose-Einstein condensates with self-attraction or selfrepulsion, trapped in an axially symmetric optical-lattice potential periodic along the radius. The states trapped both in the central potential well and in remote circular troughs are studied. In the repulsive mode, a new soliton species is found, in the form of radial gap solitons. The latter solitons are completely stable if they carry zero vorticity l=0, while with l0 they develop a weak azimuthal modulation, which makes them rotating patterns, that persist indefinitely long. In addition, annular gap solitons may support stable azimuthal darksoliton pairs on their crests. In remote troughs of the attractive model, stable localized states may assume a ringlike shape with weak azimuthal modulation, or shrink into solitons strongly localized in the azimuthal direction, which is explained in the framework of an averaged 1D equation with the cyclic azimuthal coordinate. Numerical simulations of the attractive model also reveal stable necklacelike patterns, built of several strongly localized peaks. Dynamics of strongly localized solitons circulating in the troughs is studied too. While the solitons with sufficiently small velocities are completely stable, fast solitons gradually decay, due to the leakage of matter into the adjacent trough, under the action of the centrifugal force. Investigation of head-on collisions between strongly localized solitons traveling in circular troughs shows that collisions between in-phase solitons in a common trough lead to collapse, while -out-of-phase solitons bounce many times, but eventually merge into a single one, without collapsing. In-phase solitons colliding in adjacent circular troughs also tend to merge into a single soliton

Modelling adiabatic N-soliton interactions and perturbations

We analyze a perturbed version of the complex Toda chain (CTC) in an attempt to describe the adiabatic N-soliton train interactions of the perturbed nonlinear Schrodinger equation. We study perturbations with weak quadratic and periodic external potentials analytically and numerically. The perturbed CTC adequately models the N-soliton train dynamics for both types of potentials. As an application of the developed theory, we consider the dynamics of a train of matter-wave solitons confined in a parabolic trap and an optical lattice

Cladding of stainless steel on carbon steel

The possibility of producing anticorrosion and wear resistant cladding from stainless steel onto tool and carbon steels by means of melting in high energy density light flux is demonstrated. Experiments are conducted in an installation with two arc xenon lamps of 10 kW power of each. Metallographic investigation of the interface shows the existence of high quality metallic bond between the clad and base material. The dilution of Ni and Cr is shown to depend on the melting time. A strong correlation between microstructure of produced cladding and treatment parameters - flux density and exposure time - is revealed