Intense light propagation in air

1
Intense optical pulses at UV wavelength

Alejandro Aceves University of New Mexico,
Department of Mathematics and Statistics in
collaboration with A, Sukhinin and Olivier
Chalus, Jean-Claude Diels, UNM Department of
Physics and Astronomy
6th ICIAM Meeting, Zurich Switzerland, July 2007
Work funded by ARO grant W911NF-06-1-0024
2
Recent work

• S. Skupin and L. Berge, Physica D 220, pp. 14-30
  (2006), (numerical)
• Moloney et.al, Phys. Rev E, 72016618 (numerical,
  looking at instabilities of CW solutions, pulse
  splitting)
• Many authors have studied singular collapse
  phenomena
• Fibich, Papanicolau, Developed modulation theory
  to study perturbed NLSE at critical values of
  dimension/nonlinearity
• A. Braun et.al, Opt. Lett 20, pp 73-75 (1994)
  (experimental, short pulses at 755nm)
• J.C. Diels et. al., QELS proceedings (1995)
  (experimental verification of UV filamentation
  for femtosecond pulses)

3
Background and Motivation

• There have been several experiments which confirm
  the self-filamentation
• of femtosecond laser beams. Almost all in the IR
  regime.
• It is possible, for example, to control the path
  of the discharge of
• electrical charge by creating a suitable
  filament. The discharge will
• follow the pass of the filament instead of a
  random pass.
• In air, the laser beam size remains relatively of
  the same size after
• a propagation distance of hundreds of meters up
  into the normally
• cloudy and damp atmospheric conditions.
• Gain a complete understanding of the
  filamentation of intense UV
• picosecond pulses in air. On the theoretical
  side, the interest is to find
• stationary solutions of the modeling equations
  and determine their stability.
• Thus we expect we will give insight to the
  experimental conditions for
• propagation in long distances.

4

• The discharge is triggered
• by the laser filament

(B) There is no filament which bring a random
pass between the electrodes.
5
Applications
Light Detection and Ranging(LIDAR)
Directed Energy
Remote Diagnostics
Laser guide stars
Laser Induced Lightening
6
Formation of a filament
High power pulses self-focus during their
propagation through air due to the nonlinear
index of refraction. At some critical power this
self-focusing can overcome diffraction and
possibly lead to a collapse of the beam. Short
pulses of high peak intensity create their own
plasma due to multi-photon ionization of air.
When the laser intensity exceeds the threshold
of multiphoton ionization, the produced plasma
will defocus the beam. If the self-focusing is
balanced by multiphoton ionization defocusing, a
stable filament can form.
7
Aerodynamic window
CCD Filters
Vacuum
UV Beam
8


Filament array in air
Figure. Setup of the Aerodynamic window, Focus
of the beam into the vacuum then propagation of
the filament in atmospheric pressure
The possible propagation of filament is dependent
on input power. Most of the energy loss occurs in
the formation of the filament. The propagation of
the filament once formed, is practically
lossless. If we match the shape of the intensity
at the input we can minimize loss of energy in
the filament as it propagates in Aerodynamic
window.
9
Equation for the plasma
The number of electrons
in the medium is the function of time
Jens Schwarz and J.C. Diels,2001
and the intensity of the beam
where
is the third order multiphoton ionization
coefficient,
the electron-positive-ion recombination
coefficient
the electron oxygen attachment coefficient
third order multi-photon ionization coefficient
atom density at sea level
10
Wave Equation for the electric field
The change of index
due to the electron plasma can be expressed
In terms of intensity
the electron-ion collision frequency
the laser frequency
the plasma frequency
11
Reduced equation for the model
The model to be considered is an unidirected beam
described by an envelope approximation that leads
to the following equation
where the second and third terms on the
right-hand side describe the second and third
order nonlinearities of the propagation
which respectively introduce the focusing and
defocusing phenomena
Let
12
Dimensionless equations
(1)
(2)
where
C1 1.155, C2 3.5405, C3 1.62 10-4, C4
1.3 10-4, C5 1.5 10-4
13
Search of the stationary solution
14
becomes a nonlinear eigenvalue problem
Equation for
is an eigenvalue and
where
Our approach is a continuation method beginning
from the A member of the Townes soliton family
of 2D NLSE which is also the solution of our
model if
boundary conditions
15
Numerical Approach
for
Near r equal to zero we have
16
where
Using the continuation method along with Newtons
method we can find the solution
17
Results (relevant to the experimental realization)
18

19
(No Transcript)
20
vs
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
Profile at 1.5m propagation
25
Profile at 2m propagation
26
Immediate future work
1. Stability analysis.
Helpful is stability with CW case as it will give
us some insight of the
full Linear stability analysis.
2. Modulation theory.
3. Full
simulation. (see the buildup of the plasma
leading towards steady state)