Ultra-intense Laser Pulse Propagation in Gaseous and Condensed Media

1. Ultra-intense Laser Pulse Propagationin Gaseous and Condensed Media Jerome V Moloney and Miroslav Kolesik Arizona Center for Mathematical Sciences

2. 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

3. Maxwell’s Equations Phenomenology • Long distance propagation • Ultrafast waveforms • Electromagnetic shocks • Spectral broadening Direct solution of Maxwell’s equation not feasible!

4. Breakdown of SVEA – Third Harmonic Generation in Air Spectrally narrow slowly-varying envelopes at  and 3 Classic two envelope model fails! Which envelope at this frequency? • Waves with the same frequency propagate with different phase and group velocities • Decomposition into two envelope contribution not unique

5. Full Scalar Bidirectional UPPE Model Exact linear dispersion

6. Plasma-related current Accurate chromatic dispersion Nonlinear polarization evaluated from real field Second Harmonic component = source of TH Unidirectional Maxwell - Scalar UPPE Unidirectional Pulse Propagating Equation (z-UPPE) Carrier based approach, no envelope approximations used Spectral representation natural in optics – Fourier transforms

8. 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)

9. Incident field medium wave Scattered field Effective Three-Wave Mixing: Qualitative Picture Incident optical field is scattered from nonlinear response

10. Dispersion Maps – X’s, O’s and Fish Qualitative picture from linear dispersion landscape! carrier group velocity Water Dispersion Maps Silica Dispersion Map Normal Mixed Anomalous

11. Induced Nonlinear Dynamical Grating • dynamical 3 wave interaction • dynamical phase matching: Material response perturbation Angle Local time Angular Frequency

12. Filamentation of Airy beams in water q-w spectra (angularly resolved spectra) Optical frequency – horizontal axis Transverse K-vector (conical angle) – vertical axis Analysis of q-w spectra reveals details of pulse evolution P. Polynkin, M. Kolesik, J. Moloney, to appear in September 25 issue of Phys. Rev. Lett. (2009)

13. Asymptotic Structure in Spectral Space Experiment UPPE Simulation

14. 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: Mixing two stokes photons with one pump X-wave photon: Pump X-wave = Pump scattered off peak p: Mixing two pump photons with one stokes X-wave photon:

15. Plasma density, experiment cm • Beam shapes commonly used in filamentation studies: • Gaussian beams • Flat-top beams • Beam shaping: Bessel beams Axicon Approximate extent of linear focus • 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)

16. Y X Beam shaping: 2D Airy beams • 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)

17. Filamentation of Airy beams in Air • 35fs pulses • 800nm wavelength • 5-15mJ energy per pulse • Meter-long propagation Far-Field f f Plasma Channel Fourier Plane fs pulses Lens Phase Mask P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, D. Christodoulides, Science, vol. 324, p. 229 (2009)

18. 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 All imply: Large numerical grids, large-scale simulation Near field fluence profile Far-field structure These simulation capture the intense filament core. Capturing weak supercontinuum spectra is MUCH more challenging... Curved plasma channels

19. 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 All imply: Large numerical grids, large-scale simulation 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

20. Short Pulse Equation (1D)

21. 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

22. glass argon, air, ... Novel self-compression mechanism for ultrashort pulses Recent interest in slab-geometry gas-filled waveguides (Midorikawa,Mysyrowicz)‏ Advantages: potential for energy scaling, dispersion tuning, off-axis phase matching,... • 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!

23. Hollow-core photonic crystal fibers‏ Dispersion management through fabrication Controlled nonlinear optics in gas-filled hollow core fibers

24. Multiple filaments in Atmospheric propagation Propagation up to 30km vertically in atmosphere!

25. 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

26. Filamentation Laser filaments in air: Self-focusing are dynamically balanced by plasma de-focusing

27. 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

28. Filamentation of Airy beams in Air • Beam displacement proportional to z2, ~10mm per m2 • Generated plasma channels are curved, • follow parabolic beam trajectory P. Polynkin, M. Kolesik, J. Moloney, G. Siviloglou, D. Christodoulides, Science, vol. 324, p. 229 (2009)

29. 1O 0O -1O -2O -2O -1O 1O 2O 0O 0O 0O -2O -1O 1O 2O -2O -1O 1O 2O 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 offilament P. Polynkin, M. Kolesik, J. Moloney, to appear in September 25 issue of Phys. Rev. Lett. (2009)

30. 5.0O 2.5O 800nm 800nm 800nm 532nm 532nm 532nm 633nm 633nm 633nm 0.0O Full pattern Beginning of filament End offilament -2.5O -5.0O q-w spectra, Airy beams in water P. Polynkin, M. Kolesik, J. Moloney, to appear in September 25 issue of Phys. Rev. Lett. (2009)