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Pulse self-modulation and energy transfer between two intersecting laser filaments by self-
induced plasma waveguide arrays R. Kupfer, B. Barmashenko and I. Bar
Department of Physics, Ben-Gurion University of the Negev
30 μm 200 μm
250 μm 300 μm𝛍𝐦 𝛍𝐦
𝛍𝐦 𝛍𝐦
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• Light interacts with light via the medium• Intensity dependent refractive index• Light can alter its frequency
Propagation of ultrafast laser pulses in airLow intensity regime ()• Self focusing due to the nonlinear refractive
index • Plasma defocusing due to multiphoton
ionization• Long filaments (up to 2 km)• “Intensity clamping”
A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47(2006).
High intensity regime ()• High ionization• Relativistic self-focusing• Relativistic self-induced transparency
Algorithm description• 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
Initialize Particle PositionSolve Poisson Equation
Solve Maxwell's Curl Equations
Calculate Current Density Caused by Particles Motion
Push Particles According to Lorentz
force
Launch a Pulse on the Simulation Edge
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).
Ei,j
Hi,j
Jx i+1,j
Jy i,j+1
Relativistic self-focusing
A. Pukhov and J. Meyer-ter-Vehn, Phys. Rev. Lett. 76, 3975 (1996).
Simulation parameters: , and
Single bubble regimePulse position
Fast electron beam
• Ponderomotive force “pushes” electrons forming a region nearly void of electrons (ion channel) behind the laser pulse
• The channel exerts an attractive Coulomb force on the blown out electrons causing them to accelerate into the bubble
• A fast electron beam is formed
• Mori and co-workers formulated the condition for this regime:
- speed of light, - pulse duration, - waist, - normalized vector potential and - 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).
Simulation parameters: , and
Objective – spectral and spatiotemporal evolution
Comes in:• Pulse duration: • Spectral linewidth: ~ 20 nm• Gaussian shaped spectrum
Comes out:• Pulse duration: Several pulses o
(splitting) • Spectral linewidth: >> 20 nm
(broadening)• Raman Stokes and anti-Stokes
peaks and supercontinuum generation
• Conical emission
?
Objective – 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
200 μ m
250 μ m 300 μ m
30 μm30 μm 200 μm
250 μm 300 μm𝛍𝐦 𝛍𝐦
𝛍𝐦 𝛍𝐦Simulation parameters: , and
Simulation parameters: , and
Energy transfer between intersecting beams
Conclusions
• 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
• The simulation results were found to be in agreement with previously obtained experimental results
• Efficient frequency conversion and energy transfer can be achieved in a compact and simple setup and over very short distances
• 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
• Characterization of localized surface plasmons in nanoparticle arrays• Second harmonic generation from irradiated solid targets• Raman and Brillouin scattering in liquids