36 research outputs found
Predictions of ultra-harmonic oscillations in coupled arrays of limit cycle oscillators
Coupled distinct arrays of nonlinear oscillators have been shown to have a
regime of high frequency, or ultra-harmonic, oscillations that are at multiples
of the natural frequency of individual oscillators. The coupled array
architectures generate an in-phase high-frequency state by coupling with an
array in an anti-phase state. The underlying mechanism for the creation and
stability of the ultra-harmonic oscillations is analyzed. A class of
inter-array coupling is shown to create a stable, in-phase oscillation having
frequency that increases linearly with the number of oscillators, but with an
amplitude that stays fairly constant. The analysis of the theory is illustrated
by numerical simulation of coupled arrays of Stuart-Landau limit cycle
oscillators.Comment: 24 pages, 9 figures, accepted to Phys. Rev. E, in pres
Complete chaotic synchronization in mutually coupled time-delay systems
Complete chaotic synchronization of end lasers has been observed in a line of
mutually coupled, time-delayed system of three lasers, with no direct
communication between the end lasers. The present paper uses ideas from
generalized synchronization to explain the complete synchronization in the
presence of long coupling delays, applied to a model of mutually coupled
semiconductor lasers in a line. These ideas significantly simplify the analysis
by casting the stability in terms of the local dynamics of each laser. The
variational equations near the synchronization manifold are analyzed, and used
to derive the synchronization condition that is a function of the parameters.
The results explain and predict the dependence of synchronization on various
parameters, such as time-delays, strength of coupling and dissipation. The
ideas can be applied to understand complete synchronization in other chaotic
systems with coupling delays and no direct communication between synchronized
sub-systems.Comment: 22 pages, 6 figure
Probing the longitudinal momentum spread of the electron wave packet at the tunnel exit
We present an ellipticity resolved study of momentum distributions arising
from strong-field ionization of Helium at constant intensity. The influence of
the ion potential on the departing electron is considered within a
semi-classical model consisting of an initial tunneling step and subsequent
classical propagation. We find that the momentum distribution can be explained
by the presence of a longitudinal momentum spread of the electron at the exit
from the tunnel. Our combined experimental and theoretical study provides an
estimate of this momentum spread
Wannier-Bloch approach to localization in high harmonics generation in solids
Emission of high-order harmonics from solids provides a new avenue in
attosecond science. On one hand, it allows to investigate fundamental processes
of the non-linear response of electrons driven by a strong laser pulse in a
periodic crystal lattice. On the other hand, it opens new paths toward
efficient attosecond pulse generation, novel imaging of electronic wave
functions, and enhancement of high-order harmonic generation (HHG) intensity. A
key feature of HHG in a solid (as compared to the well-understood phenomena of
HHG in an atomic gas) is the delocalization of the process, whereby an electron
ionized from one site in the periodic lattice may recombine with any other.
Here, we develop an analytic model, based on the localized Wannier wave
functions in the valence band and delocalized Bloch functions in the conduction
band. This Wannier-Bloch approach assesses the contributions of individual
lattice sites to the HHG process, and hence addresses precisely the question of
localization of harmonic emission in solids. We apply this model to investigate
HHG in a ZnO crystal for two different orientations, corresponding to wider and
narrower valence and conduction bands, respectively. Interestingly, for
narrower bands, the HHG process shows significant localization, similar to
harmonic generation in atoms. For all cases, the delocalized contributions to
HHG emission are highest near the band-gap energy. Our results pave the way to
controlling localized contributions to HHG in a solid crystal, with hard to
overestimate implications for the emerging area of atto-nanoscience
Extraction of higher-order nonlinear electronic response to strong field excitation in solids using high harmonic generation
State-of-the-art experiments employ strong ultrafast optical fields to study
the nonlinear response of electrons in solids on an attosecond time-scale.
Notably, a recent experiment retrieved a 3rd order nonlinear susceptibility by
comparing the nonlinear response induced by a strong laser field to a linear
response induced by the otherwise identical weak field. In parallel,
experiments have demonstrated high harmonic generation (HHG) in solids, a
highly nonlinear process that until recently had only been observed in gases.
The highly nonlinear nature of HHG has the potential to extract even higher
order nonlinear susceptibility terms, and thereby characterize the entire
response of the electronic system to strong field excitation. However, up till
now, such characterization has been elusive due to a lack of direct
correspondence between high harmonics and nonlinear susceptibilities. Here, we
demonstrate a regime where such correspondence can be clearly made, extracting
nonlinear susceptibilities (7th, 9th, and 11th) from sapphire of the same order
as the measured high harmonics. The extracted high order susceptibilities show
angular-resolved periodicities arising from variation in the band structure
with crystal orientation. Nonlinear susceptibilities are key to ultrafast
lightwave driven optoelectronics, allowing petahertz scaling manipulation of
the signal. Our results open a door to multi-channel signal processing,
controlled by laser polarization