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)