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Transcript
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 , k0 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) Aix / 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, mm • Beam displacement proportional to z2, ~10mm per m2 • Generated plasma channels are curved, follow parabolic beam trajectory 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)
