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Pulse Channeling Movie :::
The observation of long distance apparently self-guided pulses in
air at GW peak powers has attracted much recent interest.
The physical mechanism underlying this phenomenon
has still to be uncovered in detail.
Early discussions centered on the idea of a quasi-stable propagation
which is a result of a balance between self-focusing (SF) and
the defocusing effect of the electron plasma generated
by multi-photon ionization (MPI).
On the other hand, Brodeur et. al. suggested the moving focus
model to explain the features of the filaments observed in their
experiments.
Recently, Lange et al. argued in favour of the pulse self-guiding
stabilized by plasma defocusing. They presented results of anomalous
long-range pulse propagation in a focusing geometry. The pulse
propagated beyond the linear focus,
a fact they advanced as evidence against the moving focus picture.
We present numerical simulations of nonlinear pulse propagation in air
to elucidate the physical mechanism of the phenomenon.
Our comprehensive model for propagation in air includes the effects
of SF (Kerr and cubic Raman-type nonlinearity), MPI, avalanche
ionization, group velocity dispersion GVD), and absorption and
defocusing due to the generated electron density.
Although our present simulations suffer from the lack of detailed
material parameters for air, and hence detailed validation against
current experiments, it was clear that they do not yield results
remotely resembling the simple self-guiding picture.
Instead a very dynamic picture emerges of long distance propagation in
which pulses form, are absorbed, and subsequently are replenished by
new pulses, thereby creating the illusion of one pulse, of energy
much less than the input, which is self-guided. The new emerging
pulses gain their energy from the outer and trailing parts of the
pulse which can have enough power to self-focus.
This picture holds as we increase the incident power,
even though the length of the ``channel'' does not change drastically.
We will show that although the maximum intensity stabilizes
over roughly a Rayleigh range of the initial collimated pulse, in
agreement with the moving focus model of Brodeur et. al.,
the evolution of the pulse is very dynamic, involving
the development of a leading edge pulse which subsequently decays
and is replaced by a new pulse.
The dynamic picture does not change if we use a focusing geometry in
our
simulations. In this case we also observe the ``channel'' beyond the
linear focus which can be explained within our ``replenishment
scenario'': After the first ``collapse'' event occurs, the
peripheral portion of the collapsing pulse can have enough power to
reinitiate self-focusing,
but the position of such a nonlinear focus is now shifted
further along the propagation direction by
the effect of plasma defocusing of the already generated plasma.
There is also a potential link between the spatial ring formation
predicted in the present work and the conical emission observed in
recent experiments. Our dynamic replenishment picture implies that
such conical emission would appear to originate at relatively
localized places along the ``channel'' if connected with the plasma
generation. Conical emission can also be due to the four wave mixing
in the presence of GVD.
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