Pulse self-modulation and energy transfer induced plasma waveguide arrays

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 μm
200 μm
𝛍𝐦
250 μm
𝛍𝐦
300 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 air
𝐖
Low intensity regime (𝐈 ~ 𝟏𝟎𝟏𝟑 𝐜𝐦𝟐)
• Self focusing due to the nonlinear
refractive index 𝑛2
• Plasma defocusing due to multiphoton
ionization
• Long filaments (up to 2 km)
• “Intensity clamping”
𝐖
High intensity regime (𝐈 > 𝟏𝟎𝟏𝟖 𝐜𝐦𝟐)
•
•
•
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
𝜌
𝛻2𝜑 = −
𝜀0
𝑬 = −𝛁𝜑
•
•
Launch a Pulse on the
Simulation Edge
•
•
Solve Maxwell's Curl
Equations
1
𝛁
𝜇0
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
𝝏𝐄
× 𝑩 = 𝜀0 𝜕𝑡 + 𝑱
𝜕𝑩
𝛁 × 𝑬 = − 𝜕𝑡
Calculate Current
Density Caused by
Particles Motion
𝑱 = 𝑛𝑞𝒗
Jx i+1,j
Hi,j
Push Particles
According to Lorentz
force
𝑑𝛾𝑚𝒗
= 𝑞(𝑬 + 𝒗 × 𝑩)
𝑑𝑡
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 μm
W
cm2
e
, τ = 200 fs, n = 4 × 1025 m3 and
Single bubble regime
• Ponderomotive
force
“pushes”
electrons forming a region nearly void
of electrons (ion channel) behind the
laser pulse
Pulse position
Fast electron beam
• 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 μm
W
cm2
e
,τ = 20 fs, n = 1.73 × 1024 m3
• A fast electron beam is formed
• Mori and co-workers formulated the
condition for this regime:
cτ ≤ w0 ≈ 2 a0 ωcp
c - speed of light, τ - pulse duration, w0 - waist, a0 normalized vector potential and ωp - 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 – spectral and
spatiotemporal evolution
Comes in:
• Pulse duration: 𝜏 = 45 fs
• Spectral linewidth: ∆𝜆 ~ 20 nm
• Gaussian shaped spectrum
?
Comes out:
• Pulse duration: Several pulses
of ~ 15 fs (splitting)
• Spectral linewidth: ∆𝜆 >> 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
30 μm
30 μm
200 μm
200 μm
𝛍𝐦
250 μm
250 μm
300 μm
𝛍𝐦
300 μm
𝛍𝐦
Simulation parameters: I = 6 × 1016
Simulation parameters: I = 6 × 1016
W
cm2
e
,τ = 45 fs, n = 2.1 × 1025 m3 and w0 = 5.3 μm
W
cm2
e
,τ = 34 fs, n = 2.1 × 1025 m3 and w0 = 5.3 μm
𝛍𝐦
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