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Pulse self-modulation and energy transfer between two intersecting laser filaments by selfinduced plasma waveguide arrays R. Kupfer, B. Barmashenko and I. Bar Department of Physics, Ben-Gurion University of the Negev 30 ΞΌm 200 ΞΌm ππ¦ 250 ΞΌm ππ¦ 300 ΞΌm ππ¦ ππ¦ Computational physics in the eyes of experimentalists and theorists Ultrafast lasers 1fs = 10-15 sec = 0.000000000000001 sec Peak intensity > 1016 W/cm2 = 10000000000000000 W/cm2 Nonlinear optics β’ Light interacts with light via the medium β’ Intensity dependent refractive index β’ Light can alter its frequency Propagation of ultrafast laser pulses in air π Low intensity regime (π ~ ππππ ππ¦π) β’ Self focusing due to the nonlinear refractive index π2 β’ Plasma defocusing due to multiphoton ionization β’ Long filaments (up to 2 km) β’ βIntensity clampingβ π High intensity regime (π > ππππ ππ¦π) β’ β’ β’ High ionization Relativistic self-focusing Relativistic self-induced transparency A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47(2006). Algorithm description Initialize Particle Position Solve Poisson Equation π π»2π = β π0 π¬ = βππ β’ β’ Launch a Pulse on the Simulation Edge β’ β’ Solve Maxwell's Curl Equations 1 π π0 The pulse parameters can be controlled: Duration, intensity, spatial and temporal profile, linewidth, angle, waist and wavelength The simulation area is surrounded by a perfectly matched layer. Spectrum analysis using Goertzel algorithm Only numerical assumptions Ei,j ππ × π© = π0 ππ‘ + π± ππ© π × π¬ = β ππ‘ Calculate Current Density Caused by Particles Motion π± = πππ Jx i+1,j Hi,j Push Particles According to Lorentz force ππΎππ = π(π¬ + π × π©) ππ‘ Jy i,j+1 Analyze Spectrum of Outgoing Pulse on the Edge A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed., Norwood, MA (2005). Relativistic self-focusing A. Pukhov and J. Meyer-ter-Vehn, Phys. Rev. Lett. 76, 3975 (1996). Simulation parameters: I = 1.5 × 1019 w0 = 3.5 ΞΌm W cm2 e , Ο = 200 fs, n = 4 × 1025 m3 and Single bubble regime β’ Ponderomotive force βpushesβ electrons forming a region nearly void of electrons (ion channel) behind the laser pulse Pulse position Fast electron beam β’ The channel exerts an attractive Coulomb force on the blown out electrons causing them to accelerate into the bubble Simulation parameters: I = 1 × 1018 and w0 = 6.7 ΞΌm W cm2 e ,Ο = 20 fs, n = 1.73 × 1024 m3 β’ A fast electron beam is formed β’ Mori and co-workers formulated the condition for this regime: cΟ β€ w0 β 2 a0 Οcp c - speed of light, Ο - pulse duration, w0 - waist, a0 normalized vector potential and Οp - plasma density H. Burau et al. IEEE Trans. Plasma. Sci. 38, 2831 (2010). W. Lu, M. Tzoufras, C. Joshi, F. S. Tsung and W. B. Mori, Phys. Rev. ST Accel. Beams 10, 061301 (2007). Objective β spectral and spatiotemporal evolution Comes in: β’ Pulse duration: π = 45 fs β’ Spectral linewidth: βπ ~ 20 nm β’ Gaussian shaped spectrum ? Comes out: β’ Pulse duration: Several pulses of ~ 15 fs (splitting) β’ Spectral linewidth: βπ >> 20 nm (broadening) β’ Raman Stokes and anti-Stokes peaks and supercontinuum generation β’ Conical emission Objective β energy transfer between intersecting beams Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestiers, and A. Mysyrowic, Phys. Rev. Lett. 105, 055003 (2010). Spectral and temporal evolution 30 ΞΌm 30 ΞΌm 200 ΞΌm 200 ΞΌm ππ¦ 250 ΞΌm 250 ΞΌm 300 ΞΌm ππ¦ 300 ΞΌm ππ¦ Simulation parameters: I = 6 × 1016 Simulation parameters: I = 6 × 1016 W cm2 e ,Ο = 45 fs, n = 2.1 × 1025 m3 and w0 = 5.3 ΞΌm W cm2 e ,Ο = 34 fs, n = 2.1 × 1025 m3 and w0 = 5.3 ΞΌm ππ¦ Energy transfer between intersecting beams Conclusions β’ PIC simulation of the spectral and spatio-temporal evolution of a single pulse in a high density plasma channel, as well as energy transfer between two intersecting pulses β’ The simulation results were found to be in agreement with previously obtained experimental results β’ Efficient frequency conversion and energy transfer can be achieved in a compact and simple setup and over very short distances β’ It is anticipated that this model will be able to simulate laser-plasma interactions even in more complicated geometries and to predict the behavior under different conditions Future work β’ Characterization of localized surface plasmons in nanoparticle arrays β’ Second harmonic generation from irradiated solid targets β’ Raman and Brillouin scattering in liquids