Dissipative solitons which cannot be trapped

In this paper we study the behavior of dissipative solitons in systems with high order nonlinear dissipation and show how they cannot survive under the effect of trapping potentials both of rigid wall type or asymptotically increasing ones. This provides an striking example of a soliton which cannot be trapped and only survives to the action of a weak potential

Non-Equilibrium Dynamics and Weakly Broken Integrability

Motivated by dynamical experiments on cold atomic gases, we develop a quantum kinetic approach to weakly perturbed integrable models out of equilibrium. Using the exact matrix elements of the underlying integrable model we establish an analytical approach to real-time dynamics. The method addresses a broad range of timescales, from the intermediate regime of pre-thermalization to late-time thermalization. Predictions are given for the time-evolution of physical quantities, including effective temperatures and thermalization rates. The approach provides conceptual links between perturbed quantum many-body dynamics and classical Kolmogorov-Arnold-Moser (KAM) theory. In particular, we identify a family of perturbations which do not cause thermalization in the weakly perturbed regime.Comment: v4: Improved discussion of perturbed Lieb-Liniger model and interactions. 5+10 pages, 3+7 figures. v3: New discussion of perturbed Lieb-Liniger model, mentioned in text and new section in SM. 5+10 pages, 3+7 figures. v2: references added and discussion of nearly-integrable perturbations improved. 5+9 pages, 3+5 figure

Generation of the second-harmonic Bessel beams via nonlinear Bragg diffraction

We generate conical second-harmonic radiation by transverse excitation of a two-dimensional annular periodically-poled nonlinear photonic structure with a fundamental Gaussian beam. We show that these conical waves are the far-field images of the Bessel beams generated in a crystal by parametric frequency conversion assisted by nonlinear Bragg diffraction.Comment: 4 pages, 5 figures. submitte

Nonlinear optics with stationary pulses of light

We show that the recently demonstrated technique for generating stationary pulses of light [Nature {\bf 426}, 638 (2003)] can be extended to localize optical pulses in all three spatial dimensions in a resonant atomic medium. This method can be used to dramatically enhance the nonlinear interaction between weak optical pulses. In particular, we show that an efficient Kerr-like interaction between two pulses can be implemented as a sequence of several purely linear optical processes. The resulting process may enable coherent interactions between single photon pulses.Comment: 4 pages, 2 figure

A relativistic study of Bessel beams

We present a fully relativistic analysis of Bessel beams revealing some noteworthy features that are not explicit in the standard description. It is shown that there is a reference frame in which the field takes a particularly simple form, the wave appearing to rotate in circles. The concepts of polarization and angular momentum for Bessel beams is also reanalyzed.Comment: 11 pages, 2 fig

Superluminal Localized Solutions to the wave equation, in (vacuum or) dispersive media, for arbitrary frequencies and with adjustable bandwidth

In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in terms of the ordinary, so-called "X-shaped waves". Moeover, by the present formalism we obtain the first analytical localized Superluminal approximate solutions which represent beams propagating in dispersive media. Our solutions may find application in different fields, like optics, microwaves, radio waves, and so on. [PACS nos.: 03.50.De ; 41.20.Jb ; 83.50.Vr ; 62.30.+d ; 43.60.+d ; 91.30.Fn ; 04.30.Nk ; 42.25.Bs ; 46.40.Cd ; 52.35.Lv. Keywords: Wave equation; Wave propagation; Optics; Localized beams; Superluminal waves; Bessel beams; X-shaped waves; Acoustics; Mechanical waves; Dispersion compensation; Seismology; Geophysics; Gravitational Waves; Elementary particle physics].Comment: plain LaTeX file (16 pages), plus 9 figure

Tunable beam shaping with a phased array acousto-optic modulator

We demonstrate the generation of Bessel beams using an acousto-optic array based on a liquid filled cavity surrounded by a cylindrical multi-element ultrasound transducer array. Conversion of a Gaussian laser mode into a Bessel beam with tunable order and position is shown. Also higher-order Bessel beams up to the fourth order are successfully generated with experimental results very closely matching simulations

Adjusting bone mass for differences in projected bone area and other confounding variables: an allometric perspective.

The traditional method of assessing bone mineral density (BMD; given by bone mineral content [BMC] divided by projected bone area [Ap], BMD = BMC/Ap) has come under strong criticism by various authors. Their criticism being that the projected bone "area" (Ap) will systematically underestimate the skeletal bone "volume" of taller subjects. To reduce the confounding effects of bone size, an alternative ratio has been proposed called bone mineral apparent density [BMAD = BMC/(Ap)3/2]. However, bone size is not the only confounding variable associated with BMC. Others include age, sex, body size, and maturation. To assess the dimensional relationship between BMC and projected bone area, independent of other confounding variables, we proposed and fitted a proportional allometric model to the BMC data of the L2-L4 vertebrae from a previously published study. The projected bone area exponents were greater than unity for both boys (1.43) and girls (1.02), but only the boy's fitted exponent was not different from that predicted by geometric similarity (1.5). Based on these exponents, it is not clear whether bone mass acquisition increases in proportion to the projected bone area (Ap) or an estimate of projected bone volume (Ap)3/2. However, by adopting the proposed methods, the analysis will automatically adjust BMC for differences in projected bone size and other confounding variables for the particular population being studied. Hence, the necessity to speculate as to the theoretical value of the exponent of Ap, although interesting, becomes redundant

Nonlinear vortex light beams supported and stabilized by dissipation

We describe nonlinear Bessel vortex beams as localized and stationary solutions with embedded vorticity to the nonlinear Schr\"odinger equation with a dissipative term that accounts for the multi-photon absorption processes taking place at high enough powers in common optical media. In these beams, power and orbital angular momentum are permanently transferred to matter in the inner, nonlinear rings, at the same time that they are refueled by spiral inward currents of energy and angular momentum coming from the outer linear rings, acting as an intrinsic reservoir. Unlike vortex solitons and dissipative vortex solitons, the existence of these vortex beams does not critically depend on the precise form of the dispersive nonlinearities, as Kerr self-focusing or self-defocusing, and do not require a balancing gain. They have been shown to play a prominent role in "tubular" filamentation experiments with powerful, vortex-carrying Bessel beams, where they act as attractors in the beam propagation dynamics. Nonlinear Bessel vortex beams provide indeed a new solution to the problem of the stable propagation of ring-shaped vortex light beams in homogeneous self-focusing Kerr media. A stability analysis demonstrates that there exist nonlinear Bessel vortex beams with single or multiple vorticity that are stable against azimuthal breakup and collapse, and that the mechanism that renders these vortexes stable is dissipation. The stability properties of nonlinear Bessel vortex beams explain the experimental observations in the tubular filamentation experiments.Comment: Chapter of boo

Optical dipole traps and atomic waveguides based on Bessel light beams

We theoretically investigate the use of Bessel light beams generated using axicons for creating optical dipole traps for cold atoms and atomic waveguiding. Zeroth-order Bessel beams can be used to produce highly elongated dipole traps allowing for the study of one-dimensional trapped gases and realization of a Tonks gas of impentrable bosons. First-order Bessel beams are shown to be able to produce tight confined atomic waveguides over centimeter distances.Comment: 20 pages, 5 figures, to appear in Phys. Rev.