Stability of narrow beams in bulk Kerr-type nonlinear media

We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As this equation is very cumbersome, we also study, in parallel to it, its simplified version which keeps the most essential term: the term which accounts for the {\it nonlinear diffraction}. The full equation additionally includes terms generated by a deviation from the paraxial approximation and by a longitudinal electric-field component in the beam. Solitary-wave stationary solutions to both the full and simplified equations are found, treating the terms which modify the nonlinear Schr\"{o}dinger equation as perturbations. Within the framework of the perturbative approach, a conserved power of the beam is obtained in an explicit form. It is found that the nonlinear diffraction affects stationary beams much stronger than nonparaxiality and longitudinal field. Stability of the beams is directly tested by simulating the simplified equation, with initial configurations taken as predicted by the perturbation theory. The numerically generated solitary beams are always stable and never start to collapse, although they display periodic internal vibrations, whose amplitude decreases with the increase of the beam power.Comment: 7 pages, 6 figures Accepted for publication in PR

Determination of the Carrier-Envelope Phase of Few-Cycle Laser Pulses with Terahertz-Emission Spectroscopy

The availability of few-cycle optical pulses opens a window to physical phenomena occurring on the attosecond time scale. In order to take full advantage of such pulses, it is crucial to measure and stabilise their carrier-envelope (CE) phase, i.e., the phase difference between the carrier wave and the envelope function. We introduce a novel approach to determine the CE phase by down-conversion of the laser light to the terahertz (THz) frequency range via plasma generation in ambient air, an isotropic medium where optical rectification (down-conversion) in the forward direction is only possible if the inversion symmetry is broken by electrical or optical means. We show that few-cycle pulses directly produce a spatial charge asymmetry in the plasma. The asymmetry, associated with THz emission, depends on the CE phase, which allows for a determination of the phase by measurement of the amplitude and polarity of the THz pulse

Ultrashort filaments of light in weakly-ionized, optically-transparent media

Modern laser sources nowadays deliver ultrashort light pulses reaching few cycles in duration, high energies beyond the Joule level and peak powers exceeding several terawatt (TW). When such pulses propagate through optically-transparent media, they first self-focus in space and grow in intensity, until they generate a tenuous plasma by photo-ionization. For free electron densities and beam intensities below their breakdown limits, these pulses evolve as self-guided objects, resulting from successive equilibria between the Kerr focusing process, the chromatic dispersion of the medium, and the defocusing action of the electron plasma. Discovered one decade ago, this self-channeling mechanism reveals a new physics, widely extending the frontiers of nonlinear optics. Implications include long-distance propagation of TW beams in the atmosphere, supercontinuum emission, pulse shortening as well as high-order harmonic generation. This review presents the landmarks of the 10-odd-year progress in this field. Particular emphasis is laid to the theoretical modeling of the propagation equations, whose physical ingredients are discussed from numerical simulations. Differences between femtosecond pulses propagating in gaseous or condensed materials are underlined. Attention is also paid to the multifilamentation instability of broad, powerful beams, breaking up the energy distribution into small-scale cells along the optical path. The robustness of the resulting filaments in adverse weathers, their large conical emission exploited for multipollutant remote sensing, nonlinear spectroscopy, and the possibility to guide electric discharges in air are finally addressed on the basis of experimental results.Comment: 50 pages, 38 figure

Measurement of the 8B solar neutrino flux in SNO+ with very low backgrounds

A measurement of the 8B solar neutrino flux has been made using a 69.2 kt-day dataset acquired with the SNO+ detector during its water commissioning phase. At energies above 6 MeV the dataset is an extremely pure sample of solar neutrino elastic scattering events, owing primarily to the detector’s deep location, allowing an accurate measurement with relatively little exposure. In that energy region the best fit background rate is 0.25+0.09−0.07  events/kt−day, significantly lower than the measured solar neutrino event rate in that energy range, which is 1.03+0.13−0.12  events/kt−day. Also using data below this threshold, down to 5 MeV, fits of the solar neutrino event direction yielded an observed flux of 2.53+0.31−0.28(stat)+0.13−0.10(syst)×106  cm−2 s−1, assuming no neutrino oscillations. This rate is consistent with matter enhanced neutrino oscillations and measurements from other experiments