Transcript moloney

Ultra-intense Laser Pulse Propagation
in Gaseous and Condensed Media
Jerome V Moloney and Miroslav Kolesik
Arizona Center for Mathematical Sciences
Overview of Talk
• Why envelope equations don’t work
• Rigorous bi-directional pulse propagator
• Collapse regularization in ultrafast nonlinear optics
• Some real world examples – novel beams
• ACMS Terawatt femtosecond laser laboratory
Maxwell’s Equations
Phenomenology
• Long distance propagation
• Ultrafast waveforms
• Electromagnetic shocks
• Spectral broadening
Direct solution of Maxwell’s equation not feasible!
Breakdown of SVEA – Third Harmonic Generation in Air
Spectrally narrow slowly-varying
envelopes at  and 3
Classic two envelope model fails!
• Waves with the same frequency propagate with different
phase and group velocities
• Decomposition into two envelope contribution not unique
Which envelope at
this frequency?
Full Scalar Bidirectional UPPE Model
Exact linear dispersion
Unidirectional Maxwell - Scalar UPPE
Unidirectional Pulse Propagating Equation (z-UPPE)
Plasma-related current
Accurate chromatic dispersion
Nonlinear polarization evaluated from real field
Second Harmonic component = source of TH
Carrier based approach, no envelope approximations used
Spectral representation natural in optics – Fourier transforms
Collapse Regularization in NLO
NLSE in 2D (critical) and 3D (supercritical) exhibits blow-up
in finite time (distance)
• Fibich et al study Nonlinear Helmholtz equation – propose combination
of nonparaxial and backward wave generation for regularization.
However they ignore linear and nonlinear dispersion!
• All physical collapse regularization mechanisms to date involve either
dispersive regularization, plasma limiting or, possibly, nonlinear saturation.
• Bidirectional UPPE provides a natural platform for rigorously exploring
collapse regularization
• Dispersive regularization – Luther et al. (1994)
Effective Three-Wave Mixing: Qualitative Picture
Incident optical field is scattered
from nonlinear response
Incident field
(0 , k0 )
( , k )
Scattered field
medium wave
(, m)
Dispersion Maps – X’s, O’s and Fish
Qualitative picture from linear dispersion landscape!
k z  k z  , k   k z 0 , k0  
carrier
  0
group velocity
Water Dispersion Maps
  527nm
Normal
  1100nm
Mixed
vg
Silica Dispersion Map
  1750nm
Anomalous
Induced Nonlinear Dynamical Grating
- dynamical 3 wave interaction
- dynamical phase matching:
2   
c2
  k  m
2
  
 2   2



k
vg
Material response perturbation
Angle
Angular Frequency
Local time
c2
Filamentation of Airy beams in water
q spectra (angularly resolved spectra)
Optical frequency – horizontal axis
Transverse K-vector (conical angle) – vertical axis
Analysis of q spectra reveals details of pulse evolution
P. Polynkin, M. Kolesik, J. Moloney, to appear
in September 25 issue of Phys. Rev. Lett. (2009)
Asymptotic Structure in Spectral Space
Experiment
UPPE Simulation
Analytical Structure in Angularly Resolved Spectra
• Angularly-resolved spectrum in water – pump pulse at 1100nm, seed at 527nm
Stokes X-wave = Stokes scattered off peak p:
Pump X-wave = Pump scattered off peak p:
Mixing two stokes photons with one pump X-wave photon:
Mixing two pump photons with one stokes X-wave photon:
Beam shapes commonly used in filamentation studies:
• Gaussian beams
•
Flat-top beams
Beam shaping: Bessel beams
Axicon
Approximate extent of linear focus
1500
Plasma density, experiment
1000
14.5mJ
12.5mJ
10.0mJ
6.5mJ
• Observe single, stable filament
at pulse energies up to 15mJ
a.u.
• Plasma channels cover the entire
extent of linear focus zone of BB
500
0
0
50
100
150
cm
cm
200
250
300
Optics Express, vol. 16, p. 15733 (2008)
Beam shaping: 2D Airy beams
E ( x, y)  Aix / x0  Ai y / x0 
Linear properties of Airy beams:
• Self-healing
• Resist diffraction
• Similar to Bessel beams
• Self-bend or “accelerate”
• Center of mass propagates
along straight line
Y
X
G. Siviloglou, J. Broky, A. Dogairu, D. Christodoulides,
Phys. Rev. Lett., vol. 99, 213901 (2007)
Filamentation of Airy beams in Air
•
•
•
•
Far-Field
35fs pulses
800nm wavelength
5-15mJ energy per pulse
Meter-long propagation
f
Plasma Channel
f
fs pulses
Fourier Plane
Lens
Phase Mask
P. Polynkin, M. Kolesik, J. Moloney,
G. Siviloglou, D. Christodoulides,
Science, vol. 324, p. 229 (2009)
Challenge in simulation of Airy-beam ultrashort pulses
Large spatial extent
Fine-scale structure in the near field
Fine-scale structure in the far-field
Temporal pulsed dynamics
Near field fluence profile
All imply:
Large numerical grids, large-scale simulation
Far-field structure
These simulation capture the intense
filament core.
Capturing weak supercontinuum
spectra is MUCH more challenging...
Curved plasma channels
Challenge in simulation of Airy-beam ultrashort pulses
Simulations:
Large, 3D domain
Fine grid resolution
(1536 – 4096)^2 x (128 – 256)
Simplified model:
●diffraction
●gvd + 3-order dispersion
●instantaneous Kerr
●plasma MPI generation
●plasma induced defocusing
Large spatial extent
Fine-scale structure in the near field
Fine-scale structure in the far-field
Temporal pulsed dynamics
All imply:
Large numerical grids, large-scale simulation
Short Pulse Equation (1D)
Novel self-compression mechanism for ultrashort pulses
• Theoretically studied in glassmembrane fibers with anti-guiding
thickness profile
• Experiments are under way at Max
Planck Institute for Physics of Light
• Simulations predict very large selfcompression at high efficiency. Better
control than normal self-compression in
femto-second filaments.
• Applicable to different media - such as
preformed plasma channel, and gas slab
wave-guides (next slide).
Significant self-compression
Novel self-compression mechanism for ultrashort pulses
Recent interest in slab-geometry gas-filled waveguides (Midorikawa,Mysyrowicz)
glass
argon, air, ...
• Picture: simulated anti-guiding
driven selfcompression from 50fs
to 5fs duration in a planar gasslab wave-guide.
• Simulations are being used to
study different scenarios and
optimize the process.
• Rich system, many potentially
interesting regimes!
Advantages:
potential for energy scaling,
dispersion tuning,
off-axis phase matching,...
Hollow-core photonic crystal fibers
Dispersion management through fabrication
Controlled nonlinear optics in gas-filled hollow core fibers
Multiple filaments in Atmospheric propagation
Propagation up to 30km vertically in atmosphere!
Our TW laser facility
Pavel Polynkin (OSC)
•Assembled in 2007-2008 under support
from AFOSR DURIP
•Supports on-going computational
program at ACMS
•35 femtosecond pulsewidth
•35 mJ pulse energy
•10 Hz PRF
•Integrated pulse shaper (temporal)
•Pulse diagnostics (FROG, correlator)
•Beam shaping via static phase masks
(high pulse energy)
•Beam shaping with programmable 2D
LC matrix (<3mJ)
•High energy OPA: Tunable multi-mJ,
<100fs pulses, wavelength coverage from
470nm to 2.6mm
Filamentation
Laser filaments in air:
Self-focusing are dynamically balanced by plasma de-focusing
Useful properties and applications of filaments in air:
•
•
•
•
Extended propagation (up to hundreds of meters)
Relative immunity to obscurants and turbulence
Forward-emission of broad supercontinuum
Electrical conductivity
Filamentation of Airy beams in Air
• Beam displacement proportional to z2, ~10mm per m2
• Generated plasma channels are curved,
follow parabolic beam trajectory
Beam displacement, mm
7
6
5
4
f=1m data
f=1m fit
f=75cm data
f=75cm fit
3
2
1
0
-1
-80 -60 -40 -20 0 20 40 60 80 100
Distance from Fourier plane, cm
P. Polynkin, M. Kolesik, J. Moloney,
G. Siviloglou, D. Christodoulides,
Science, vol. 324, p. 229 (2009)
Filamentation of Airy beams in Water:
Forward emission from different parts of filament
is angularly resolved
Direct emission patterns, 800nm light blocked
Full pattern
Beginning of filament
End of filament
1O
0O
-1O
-2O
-2O
-1O
0O
1O
2O
-2O
-1O
0O
1O
2O
-2O
-1O
0O
1O
2O
P. Polynkin, M. Kolesik, J. Moloney, to appear
in September 25 issue of Phys. Rev. Lett. (2009)
q spectra, Airy beams in water
Full pattern
Beginning of filament
End of filament
5.0O
2.5O
0.0
O
-2.5O
-5.0O
800nm
633nm 532nm
800nm
633nm 532nm
800nm
633nm 532nm
P. Polynkin, M. Kolesik, J. Moloney, to appear
in September 25 issue of Phys. Rev. Lett. (2009)