65 research outputs found
Analytical solution of the optimal laser control problem in two-level systems
The optimal control of two-level systems by time-dependent laser fields is
studied using a variational theory. We obtain, for the first time, general
analytical expressions for the optimal pulse shapes leading to global
maximization or minimization of different physical quantities. We present
solutions which reproduce and improve previous numerical results.Comment: 12 pages, 2 figure
Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential
We address a two-dimensional nonlinear elliptic problem with a
finite-amplitude periodic potential. For a class of separable symmetric
potentials, we study the bifurcation of the first band gap in the spectrum of
the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to
describe this bifurcation. The coupled-mode equations are derived by the
rigorous analysis based on the Fourier--Bloch decomposition and the Implicit
Function Theorem in the space of bounded continuous functions vanishing at
infinity. Persistence of reversible localized solutions, called gap solitons,
beyond the coupled-mode equations is proved under a non-degeneracy assumption
on the kernel of the linearization operator. Various branches of reversible
localized solutions are classified numerically in the framework of the
coupled-mode equations and convergence of the approximation error is verified.
Error estimates on the time-dependent solutions of the Gross--Pitaevskii
equation and the coupled-mode equations are obtained for a finite-time
interval.Comment: 32 pages, 16 figure
Nonlinear localized waves in a periodic medium
We analyze the existence and stability of nonlinear localized waves in a
periodic medium described by the Kronig-Penney model with a nonlinear defect.
We demonstrate the existence of a novel type of stable nonlinear band-gap
localized states, and also reveal an important physical mechanism of the
oscillatory wave instabilities associated with the band-gap resonances.Comment: 4 pages, 5 figure
Self-trapping and stable localized modes in nonlinear photonic crystals
We predict the existence of stable nonlinear localized modes near the band
edge of a two-dimensional reduced-symmetry photonic crystal with a Kerr
nonlinearity. Employing the technique based on the Green function, we reveal a
physical mechanism of the mode stabilization associated with the effective
nonlinear dispersion and long-range interaction in the photonic crystals.Comment: 4 pages (RevTex) with 5 figures (EPS
On negative higher-order Kerr effect and filamentation
As a contribution to the ongoing controversy about the role of higher-order
Kerr effect (HOKE) in laser filamentation, we first provide thorough details
about the protocol that has been employed to infer the HOKE indices from the
experiment. Next, we discuss potential sources of artifact in the experimental
measurements of these terms and show that neither the value of the observed
birefringence, nor its inversion, nor the intensity at which it is observed,
appear to be flawed. Furthermore, we argue that, independently on our values,
the principle of including HOKE is straightforward. Due to the different
temporal and spectral dynamics, the respective efficiency of defocusing by the
plasma and by the HOKE is expected to depend substantially on both incident
wavelength and pulse duration. The discussion should therefore focus on
defining the conditions where each filamentation regime dominates.Comment: 22 pages, 11 figures. Submitted to Laser physics as proceedings of
the Laser Physics 2010 conferenc
Stable spinning optical solitons in three dimensions
We introduce spatiotemporal spinning solitons (vortex tori) of the
three-dimensional nonlinear Schrodinger equation with focusing cubic and
defocusing quintic nonlinearities. The first ever found completely stable
spatiotemporal vortex solitons are demonstrated. A general conclusion is that
stable spinning solitons are possible as a result of competition between
focusing and defocusing nonlinearities.Comment: 4 pages, 6 figures, accepted to Phys. Rev. Let
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
Third-harmonic generation and self-channeling in air using high-power femtosecond laser pulses
It is shown, both theoretically and experimentally, that during laser pulse filamentation in air an intense ultrashort third- harmonic pulse is generated forming a two-colored filament. The third-harmonic pulse maintains both its peak intensity and energy over distances much longer than the characteristic coherence length. We argue that this is due to a nonlinear phase-locking mechanism between the two pulses in the filament and is independent of the initial material wave-vector mismatch. A rich spatiotemporal propagation dynamics of the third-harmonic pulse is predicted. Potential applications of this phenomenon to other parametric processes are discussed
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