Propagation of intense laser pulses in air:

1
Filaments in air where the theory flourishes and
the understanding perishes
Two decades of studies on the
Propagation of intense laser pulses in air
a proliferation of theories
and a rarefaction of understanding
2
FILAMENTS IN AIR

1. A little history

2. Define filamentation
3. Experiments and theories for dummies
4. The new tools what do they bring?
5. Results with the new tools
5.1. IR filaments
5.2. UV filaments
6. New mysteries unveiled by the control of the
initial condition
Fluorescence --- Plasma --- Polarization
3
A little history
Once upon a time
A.Braun , G.Korn, X.Liu, D.Du, J.Squier and
G.Mourou, "Self-channeling of high-peak-power fs
laser pulses in air", Opt.Lett. 2073-75 (1994)
800 nm
X. M. Zhao, P. Rambo and J.-C. Diels, "Filamentati
on of Femtosecond UV Pulses in Air, QELS, 1995,
16 178 (QThD2), Baltimore, MA, (1995)
248 nm
16 years already! ?
4
And pre-history
Already a cold war between definition of
filaments in solids
Self-induced waveguide
Moving focus
Shen 1971, Phys. Rev. A
Akhmanov 1966, Sov Phys. JETP
Self-induced waveguides
do not exist, it is always a
moving focus (next slide)
Kerr focusing
5
y
Shens moving focus
A pulse represented by successive slices of
intensity
x
zct
By causality, the leading edge of the pulse
should always be a moving focus.
unless the material has been destroyed by the
leading part of the pulse.
a moving focus?
The trailing edge of the pulse
or the whole pulse energy trapped into a waveguide
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THE COLD WAR
1966 --- 1980s
Akhmanov 1966, Sov Phys. JETP
Shen 1971, Phys. Rev. A
Self-induced waveguides
Kerr focusing
do not exist, it is always a
moving focus (next slide)
Shen 1984, nonlinear optics and following editions
as optically nonlinear media"
Filaments do not exist
Filaments demonstrated with CW beams
More moving focus
Brodeur 1997, Optics Letters
7
Define filamentation in air!
Only uncontested point n n0 n2I
1) Moving focus
2) Self-induced waveguide balance between Kerr
lensing and plasma defocusing.
A. Couairon and A. Mysyrowicz. Physics Reports,
44149-189, 2007.
Dubietis, Gaisauskas, Tamosauskas, Di Trapani.
Phys. Rev. Lett., 92253903, 2004.
4) n(I) shows sign reversal at the intensities
typical of 800 nm filaments
Loriot, Hertz, Fauchet, Lavorel. Optics Express,
1713439, 2009
5) Filaments are continuously created from a
surrounding reservoir.
self-phase modulation, four-wave mixing,
self-steepening and pulse compression, third
harmonic generation, conical emission,
THz-generation, Raman, induced birefringence,
rotational revival, etc
8
What can the poor experimentalist do?
A dozen interwoven physical phenomena! The
theoreticians have mobbed the field like a pack
of doctors on a dying patient.
A mathematical MURI has been funded by the AFOSR
to tackle filamentation.
Instead of feeding complex experimental results
to theoricians,
create experiments that eliminate ambiguity and
multiple phenomena
After all, Blessed the feeble minded,
because the kingdom of heaven belongs to them
Create filaments from initial conditions that
eliminate some of the mechanisms
Long pulse filaments to eliminate ultrashort
pulse propagation effects
Low intensity filaments to eliminate higher order
nonlinear effects
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Filament experiments for dummies
Create filaments from initial conditions that
eliminate some of the mechanisms
1) Moving focus
2) Self-induced waveguide balance between Kerr
lensing and plasma defocusing.
4) n(I) shows sign reversal at the intensities
typical of 800 nm filaments
5) Filaments are continuously created from a
surrounding reservoir
Instead of starting from here
Start from there
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Filament experiments for dummies
Create filaments from initial conditions that
eliminate some of the mechanisms
There is nonlinear propagation in air prior to
the formation of a filament
What is the effect of the medium?
How does the observer
separate the phenomena caused by
preparationor filamentation?
For instance is the polarization of the filament
that of the input beam?
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Long pulse filaments
Theories for dummies
Neglect temporal dependence, and nonlinearities
gt than Kerr
Eigenvalue equation (normalized variables.
Solution of type
Townes soliton
2D nonlinear Schroedinger equation
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Scaling parameters
SOLUTION TOWNES SOLITON (Gaeta)
TOWNES Soliton as
Beam cleaner
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Theory for dummies
Dubietis, Di Trapani, Faccio leads to conical
like focusing and a Bessel beam PRL 92,
253903, 2004
Self-guided-channels
14
Balance between focalisation and de-focalisation
implies conical focalisation ? Bessel beam
4 wave mixing k-vector conservation leads to
supercontinuum?
15
Experiments for dummies
Create initial conditions that eliminate some
mechanisms
How to separate the two phases?
by turning off the nonlinearity
HOW?
The theoretician, by
a strike of a pen
setting all nonlinearities to zero
The experimentalist?
By putting the preparation phase in vacuum
Vacuum
?
Aerodynamic window
16
Experiments for dummies
Create initial conditions that eliminate some
mechanisms
Pressure Profile for the Aerodynamic Window
Atmospheric pressure
inlet
atmosphere
The only way to have a well defined initial
condition z 0
Vacuum
exhaust
Air compressor 8 kg\cm2 10 m3/min (150 dm3/s)
Vacuum
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The new tools
1. The Aerodynamic Window to create filaments ab
initio
2. A LINEAR attenuator for filaments
2.1. What does not work a thin quartz plate at
grazing incidence
2.2. What does work a thick coated plate at
grazing incidence
The results
To come
18
The new tools
2. A LINEAR attenuator for filaments
2.1. What does not work a thin quartz plate at
grazing incidence
89o
6 transmission 3GW in glass
zsf 1 mm
Pcr in glass is 2.5 MW
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The new tools
2. A LINEAR attenuator for filaments
2.2. What does work a thick coated plate at
grazing incidence
Coating for 355 nm, normal incidence
a
e
R
C C D
Rg
T lt .5x10-6 for 266 nm
20
The results with the new tools 1) IR filaments
Aerodynamic Window
f 3m
Vacuum chamber
10mJ 200fs
Coating for 1064nm
Compressed air
3 meters
Tlt 0.5 106 at 89 incidence
200mm
No axicon focusing, no moving focus, no
surrounding reservoir
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The results with the new tools 1) IR filaments
Single filaments generated without the
preparation phase survive over a longer distance
No axicon focusing, no moving focus, no
surrounding reservoir
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The results with the new tools 1) IR filaments
, no Loriot?
No axicon focusing, no moving focus, no
surrounding reservoir
Well defined initial condition ideal test case
for the Loriot model of n2
V.Loriot et al, Measurement of high order Kerr
refractive index
Optics Express, 1713439--13434, 2009
Kolesik, Mirell, Diels and Moloney, Optics
Lett., 35 36853687 (2010)
Standard n2
11mJ
9mJ
Loriot n2
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The results with the new tools 2) UV filaments
LOW POWER
C C D
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The results with the new tools 2) UV filaments
HIGH POWER
Dashed lines
4m
C C D
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FILAMENTS IN AIR

1. A little history

2. Define filamentation
3. Experiments/theories for dummies
4. The new tools what do they bring?
5. Results with the new tools
5.1. IR filaments
5.2. UV filaments
6. New mysteries unveiled by the control of the
initial condition
Fluorescence --- Plasma --- Polarization
26
New mysteries unveiled by the control of the
initial condition
a) Fluorescence
Aerodynamic Window
f 3m
Vacuum chamber
Compressed air
3 meters
27
New mysteries unveiled by the control of the
initial condition
a) Fluorescence
Emission spectrum near laser central wavelength
Filament prepared in vacuum
Filament prepared in air
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New mysteries unveiled by the control of the
initial condition
a) Fluorescence
Emission spectrum around 720 nm
Filament prepared in vacuum
Filament prepared in air
ZERO! No detectable emission,
as compared to
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A. Berstein to the rescue autocorrelations at
23 meters vs pulse energy
Color code
Zero Chirp, Initial Autocorrelation Pulsewidth
200fs
Representative Spectra
Temporal-Energy Mapping
Autocorrelation Lineouts
140 fs
0.5 mJ
1.7 ps
940
700
Wavelength (nm)
90 fs
2 mJ
1.7 ps
940
700
Wavelength (nm)
3.5 mJ
1.7 ps
940
700
Wavelength (nm)
1.1 ps
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Pre-filamentory pulse steepening, splitting, and
spectrum
at 4 meter from the source
A.C. Bernstein , Ph.D. Dissertation, UNM
(2004)
Conclusion a small pulse compression (2x) and a
spectral broadening consistent
with our recent observations.
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New mysteries unveiled by the control of the
initial condition
b) Plasma
Experiment on filaments conductivity
Compare preparation in vacuum or in air.
HV
100 kW
6 nF
22 W
Aerodynamic Window
f 3m
Vacuum chamber
Compressed air
3 meters
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New mysteries unveiled by the control of the
initial condition
b) Plasma
Experiment on filaments beakdown voltage
33
New mysteries unveiled by the control of the
initial condition
b) Plasma
Experiment on filaments conductivity
Linear polarization solid lines
Circular polarization dashed lines
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New mysteries unveiled by the control of the
initial condition
b) Plasma
Linear polarization solid lines
Fluorescence at 337 nm
Circular polarization dashed lines
air
Vacuum
or
air
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New mysteries unveiled by the control of the
initial condition
c) Plasma
Summary of the experiments
Preparation phase in vacuum versus preparation
phase in air

• For linear polarization, new spectrum generated
  in air, not in vacuum

• For linear polarization, the beam size is
  smaller in vacuum

• Linear polarization, spatial confinement over
  longer distance for vacuum preparation

• For linear polarization, the plasma is stronger
  in vacuum

• For circular polarization, no plasma, no
  fluorescence, no filament in vacuum

36
What my eminent theoretician colleagues say in
Self-focusing of circularly polarized beams
Gadi Fibich and Boaz Ilan
PHYSICAL REVIEW E 67, 036622 (2003)
Circularly polarized light leads to circularly
polarized filaments
Essential points of the theory non-paraxial, and
longitudinal component of E
Maxwells equation
Assumption no other nonlinearity than Kerr
(orientational electronic)
Result 1) No collapse 2) stable
propagation of circularly polarized filaments
37
What my eminent experimentalist colleagues say in
Above-mJ super-continuum generation using
polarization dependent filamentation in atoms and
molecules
Oscar Varela et al., Optics Express 173630 (2009)
(and Friday afternoon?)
This paper deals mostly with the generation of
filaments with 30 fs pulses
-- attempts to control the compression (to lt
3fs), multifilamentation, as well as
supercontinuum generation, by acting only on the
input state polarization (linear to
elliptical to circular)
The implication of interest in this contest is
Circularly polarized light leads to circularly
polarized filaments
38
And my most respected colleague Andre Mysyrowicz
answered the question (CLEO/QEL tutorial on
filaments, 2010)
Is there a difference between linear and circular
polarization?
by NO
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How do you explain the difference with my eminent
colleagues?
My old buddies from California to the rescue!
Evolution of circularly polarized light in a
Kerr medium
Close, Giuliano, Hellwarth, Hess, McClung and
Wagner
IEEE J. of Quantum Electronics, QE-2553 (1966)
Assumption molecular reorientation dominates
the Kerr effect
Their point circular polarization is unstable
and becomes linear.
40
Evolution of circularly polarized light in a Kerr
medium
Close, Giuliano, Hellwarth, Hess, McClung and
Wagner
IEEE J. of Quantum Electronics, QE-2553 (1966)
Amplitude of circularly polarized light
41
Evolution of circularly polarized light in a Kerr
medium
Close, Giuliano, Hellwarth, Hess, McClung and
Wagner
IEEE J. of Quantum Electronics, QE-2553 (1966)
Amplitude of circularly polarized light
42
Evolution of circularly polarized light in a Kerr
medium
Close, Giuliano, Hellwarth, Hess, McClung and
Wagner
Conclusion
Circular polarization is unstable in presence
of molecular re-orientation and leads to
(random) linear
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Wrapping it up who is wrong, who is right?
Their finding
Our case
200 fs
30 fs pulses
Varela et al
No orientational Kerr
Molecular orientation dominates
Gadi Fibich Boaz Ilan
between 10-5 and 10-3
between 0.1 and 0.01
Higher order than Kerr neglected
Higher order dominate at radii lt 250 mm
Circular
linear
Air
Close et al
Molecular re-orientation
Vacuum
?
44
Polarization dependence
where is the physical difference?
The answer is in the photon-electron momentum
transfer upon ionization.
Linear polarization electrons remain in the
vicinity of the ion
Average kinetic energy
Circular polarization The electrons drift away
Average kinetic energy
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Polarization dependence
where is the physical difference?
The answer is in the photon-electron momentum
transfer upon ionization.
There is also a longitudinal component of the
electron momentum
Partitioning of the linear photon momentum in
multiphoton ionization, arXiv1102.1881v1 physi
cs.optics 9 Feb 2011
46
where is the physical difference?
Polarization dependence
Some quotes from
Partitioning of the linear photon momentum in
multiphoton ionization, arXiv1102.1881v1 physi
cs.optics 9 Feb 2011
Circular and linear polarizations have very
difference kinetic energy distributions and this
affects the net longitudinal momentum of the
photoelectrons.
The momentum transfer to e- has been invoked to
account for THz generation in filaments This can
be augmented by using circular polarization and
longer wavelength.
Before rushing to applications, should it not be
wiser to investigate first
whether circularly polarized filaments do exist?
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Remarks The simulations cover only the range
over which we have NO measurement
The simulation indicates TOTAL ionization at the
entrance in air. This should be checked we have
to verify the ionization versus intensity
(fluorescence and conductivity.
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Simulation of Kolesik
Transients?? Are they accessible?
54
Simulation of Kolesik with our data
Why the difference in diameter?
55
Is the UV filament a true self induced channel?
Very low order nonlinearity, not conducive to
Bessel-beam
Very low diffraction, therefore low nonlinear
losses
(30mJ/m measured, negligible compared to the
trapped energy
The same comparative study has yet to be
performed
as with the IR filaments
56
Beam propagation
(1)
Solution of (1)
Gaussian fit
w 600 mm
P 500 MW
13.8 x Pcr
Same intensity Townes solution
Same width Townes solution
57
The results with the new tools 1) IR filaments
To generate filaments at 266 nm, with sub-ns, 1 J
pulses
Transverse resolution 20 mm
Compression and phase conjugation
LASER
4 ns, 3.5 J
58
Well defined initial condition ideal test case
for the Loriot model of n2
V.Loriot et al, Measurement of high order kerr
refractive index
Optics Express, 1713439--13434, 2009
59

1. The fundamental question what is the part of the

preparation phase and the light bullet
propagation.
Conical emission
We are not questioning the existence of conical
emission
In AIR, we are pondering whether the broad
spectrum is generated by the filament
or before the filament
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Fitting of the filament profile (solid line) to
the solution of
Parameters 1
1 Xin Miao Zhao et al., IEEE J. Quantum
Electron. 31, 599 (1995)
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Plasma and beam profile
-

HV
Aerodynamic Window
100kO
6nF
f 3m
Vacuum chamber
x
Compressed air
z
3 meters
A Breakdown voltage
B Conductivity (current)
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Launching the beam from air into vacuum
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Diffracting region
Axicon region
?
VACUUM
36 cm
AIR
Distance to lens z
Spot Size w
?
295
320
275
255
z
(cm)
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Spot Size w
255
320
275
295