ultra-intense laser pulse propagation in gaseous and condensed media
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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 - PowerPoint PPT PresentationTRANSCRIPT
Ultra-intense Laser Pulse Propagationin Gaseous and Condensed Media
Jerome V Moloney and Miroslav KolesikArizona 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!
• Waves with the same frequency propagate with different phase and group velocities
• Decomposition into two envelope contribution not unique
Which envelope at this frequency?
Breakdown of SVEA – Third Harmonic Generation in AirBreakdown of SVEA – Third Harmonic Generation in Air
Spectrally narrow slowly-varying Spectrally narrow slowly-varying envelopes at envelopes at and 3 and 3
Classic two envelope model fails!Classic two envelope model fails!
Full Scalar Bidirectional UPPE Model
Exact linear dispersion
Unidirectional Pulse Propagating Equation (z-UPPE)
Plasma-related current
Nonlinear polarization evaluated from real field
Accurate chromatic dispersion
Second Harmonic component = source of TH
Carrier based approach, no envelope approximations used
Unidirectional Maxwell - Scalar UPPE
Spectral representation natural in optics – Fourier transforms
Collapse Regularization in NLO
NLSE in 2D (critical) and 3D (supercritical) exhibits blow-upin 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)
Scattered field
Incident field
medium wave
Incident optical field is scattered from nonlinear response
( , )m
0 0( , )k
( , )k
Effective Three-Wave Mixing: Qualitative Picture
Dispersion Maps – X’s, O’s and Fish
Qualitative picture from linear dispersion landscape!
00 0, ,z z z
g
k k k k kv
Water Dispersion MapsWater Dispersion Maps
527nm 1100nm Silica Dispersion MapSilica Dispersion Map
1750nm
Normal Mixed AnomalousNormal Mixed Anomalous
carrier group velocity carrier group velocity
Induced Nonlinear Dynamical Grating - dynamical 3 wave interaction- dynamical phase matching:
2 22 2
2 2g
k m kc v c
Local timeAngular Frequency
Ang
le
Material response
perturbation
Filamentation of Airy beams in water
spectra (angularly resolved spectra)
Optical frequency – horizontal axisTransverse K-vector (conical angle) – vertical axisAnalysis of 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
Pump X-wave = Pump scattered off peak p:
Stokes X-wave = Stokes scattered off peak p: Mixing two stokes photons with one pump X-wave photon:
Mixing two pump photons with one stokes X-wave photon:
• Angularly-resolved spectrum in water – pump pulse at 1100nm, seed at 527nm
Beam shapes commonly used in filamentation studies:• Gaussian beams• Flat-top beams
Beam shaping: Bessel beamsAxicon
Approximate extent of linear focus
cm
0 50 100 150 200 250 300
a.u.
0
500
1000
150014.5mJ12.5mJ10.0mJ6.5mJ
cm
Plasma density, experiment• Observe single, stable filament at pulse energies up to 15mJ
• Plasma channels cover the entire extent of linear focus zone of BB
Optics Express, vol. 16, p. 15733 (2008)
X
Y
00 /Ai/Ai),( xyxxyxE
Linear properties of Airy beams:• Self-healing• Resist diffraction• Similar to Bessel beams• Self-bend or “accelerate”• Center of mass propagates
along straight line
G. Siviloglou, J. Broky, A. Dogairu, D. Christodoulides, Phys. Rev. Lett., vol. 99, 213901 (2007)
Beam shaping: 2D Airy beams
Filamentation of Airy beams in Air
• 35fs pulses• 800nm wavelength• 5-15mJ energy per pulse• Meter-long propagation
fs pulses
Far-Field
ff
Phase Mask
LensFourier Plane
Plasma Channel
P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, D. Christodoulides, Science, vol. 324, p. 229 (2009)
Challenge in simulation of Airy-beam ultrashort pulsesLarge spatial extent Fine-scale structure in the near fieldFine-scale structure in the far-fieldTemporal pulsed dynamics
All imply:Large numerical grids, large-scale simulation
Near field fluence profile
Curved plasma channels
Far-field structure
These simulation capture the intense filament core.Capturing weak supercontinuum spectra is MUCH more challenging...
Challenge in simulation of Airy-beam ultrashort pulsesLarge spatial extent Fine-scale structure in the near fieldFine-scale structure in the far-fieldTemporal pulsed dynamics
All imply:Large numerical grids, large-scale simulation
Simulations:
Large, 3D domainFine grid resolution (1536 – 4096)^2 x (128 – 256)
Simplified model:●diffraction●gvd + 3-order dispersion●instantaneous Kerr●plasma MPI generation●plasma induced defocusing
Short Pulse Equation (1D)
Novel self-compression mechanism for ultrashort pulses
• Theoretically studied in glass-membrane fibers with anti-guiding thickness profile
• Experiments are under way at Max Planck Institute for Physics of Light
• Simulations predict very large self-compression 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
• Picture: simulated anti-guiding driven selfcompression from 50fs to 5fs duration in a planar gas-slab wave-guide.
• Simulations are being used to study different scenarios and optimize the process.
• Rich system, many potentially interesting regimes!
glass
argon, air, ...
Recent interest in slab-geometry gas-filled waveguides (Midorikawa,Mysyrowicz)
Advantages: potential for energy scaling, dispersion tuning,off-axis phase matching,...
Hollow-core photonic crystal fibers
Controlled nonlinear optics in gas-filled hollow core fibers
Dispersion management through fabrication
Multiple filaments in Atmospheric propagation
Propagation up to 30km vertically in atmosphere!
•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 2.6m
Our TW laser facilityPavel Polynkin (OSC)
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
Distance from Fourier plane, cm-80 -60 -40 -20 0 20 40 60 80 100
Be
am
dis
pla
ce
me
nt,
mm
-1
0
1
2
3
4
5
6
7f=1m dataf=1m fitf=75cm dataf=75cm fit
P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, D. Christodoulides, Science, vol. 324, p. 229 (2009)
1O
0O
-1O
-2O
0O 1O 2O-1O-2O 0O 1O 2O-1O-2O 0O 1O 2O-1O-2O
Direct emission patterns, 800nm light blocked
Full pattern Beginning of filament End of filament
Filamentation of Airy beams in Water:Forward emission from different parts of filamentis angularly resolved
P. Polynkin, M. Kolesik, J. Moloney, to appear in September 25 issue of Phys. Rev. Lett. (2009)
spectra, Airy beams in water
Full pattern Beginning of filament End of filament5.0O
2.5O
0.0O
-2.5O
-5.0O
800nm 633nm 532nm800nm 633nm 532nm 800nm 633nm 532nm
P. Polynkin, M. Kolesik, J. Moloney, to appear in September 25 issue of Phys. Rev. Lett. (2009)