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 μ m 200 μ m

250 μ m 300 μ m𝛍𝐦 𝛍𝐦

𝛍𝐦 𝛍𝐦

Computational physics in the eyes of experimentalists and theorists

Ultrafast lasers1fs = 10-15 sec = 0.000000000000001 secPeak 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 μ m30 μ m 200 μ m

250 μm 300 μ m𝛍𝐦 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