relativistic nonlinear optics in laser-plasma interaction institute of atomic and molecular sciences...
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Relativistic nonlinear optics in laser-plasma interaction
Institute of Atomic and Molecular Sciences Academia Sinica, Taiwan
National Central University, Taiwan
Jyhpyng Wang
National Taiwan University, Taiwan
Outline
Relativistic nonlinearity in laser-plasma interaction
Relativistic harmonic generation and optical rectification
Relativistic induced birefringence
Generation of intense few-cycle mid-infrared pulses
peak intensity: 1020 W/cm2 (10-m focal spot)
electric field: 3.21013 V/m (50 Coulomb field in hydrogen )
100-TW laser at Nat’l Central Univ.
Hamiltonian of an electron in a laser field
vector potential
scalar potential
relativistic intensity:
mass increase due to quivering motion:
canonical momentum
Relativistic nonlinearity in laser-plasma interaction
Relativistic effects on plasma refractive index
Wave mixing mediated by plasma waves
Relativistic nonlinearity of the Lorentz force
relativistic self-phase modulation
nonlinear force
Theoretical analysis of the electron motion
Lorentz force
Poisson’s Equation
Continuity Equation
normalized vector and
scalar potentials
: known laser field , ,solution
Phys. Rev. A 76, 063815 (2007)
Modification of the laser field
Maxwell Equation
0- source term optical rectification
1- source term nonlinear refractive index
n- source term harmonic generation
nonlinear source terms (functions of )
Harmonic generation and optical rectification
Phys. Rev. A 80, 023802 (2009)
Phys. Rev. A 76, 063815 (2007)
intensity dependence
Relativistic second harmonic generation
theory experiment
density dependence
2nd harmonic beam profile
fundamental beam profile
E. Takahashi, et al, Phys. Rev. E 65, 016402 (2001)
Relativistic optical rectification
theory
transverse laser profile
THz field particle-in-cell simulation
longitudinal laser profile
THz field
Relativistic induced birefringence
Phys. Rev. A 83, 033801 (2011)
Two-beam interaction via plasma waves
Maxwell Equation
a and a' create plasma waves of k k' , which scatter ax into ax' .
induced birefringence
nonlinear source terms (functions of )
Comparison with particle-in-cell simulation
theory simulation
Generation of few-cycle intense mid-infrared pulses
Phys. Rev. A 82, 063804 (2010)
Nonlinear phase modulation in the bubble regime
density modulation
relativistic self-phase modulation
modulation of refractive index
laser field
electron density
Ge-wafer photo-switch
mid-IR pulse
excitation pulse
pinhole
mid-IR pulse
mid-IR pulse
A. J. Alcock and P. B. Corkum, Can. J. Phys. 57, 1280 (1979)
Ge-wafer photo-switch
mid-IR pulse
excitation pulse
pinhole
mid-IR pulse
mid-IR pulse
A. J. Alcock and P. B. Corkum, Can. J. Phys. 57, 1280 (1979)
Temporal profile of the mid-IR pulse
photo-switch gated transmission
pump pulse: 205 mJ/42 fsexcitation pulse: 500 J/38 fsplasma density: 4.1x1019 cm-3
reconstructed temporal profile
pulse duration
X 4.6 ps 9.8 ps
5-mm Ge window
5-mm Ge window
X ~ 15 fs
mid
-IR
ene
rgy
(arb
. un
its)
inte
nsi
ty (
arb
. u
nits
)
consistent with particle-in-cell simulation
delay of excitation pulse with respect to mid-IR pulse (ps)
Comparing with simulation and theoretical estimation
Simulation: mid-IR peak power in the bubble: > 0.5 TW
Square of the electric field of the numerically filtered mid-IR pulse
The mid-IR pulse is encapsulated in the low-density bubble, hence is not absorbed by the plasma. The wavelength-scale bubble ensures high spatial coherence.
2- 20 m 6- 10 m
2- 6 m 10 - 20 m
Estimation based on Fourier transform of the phase modulated pulse
Measured energy: 3 mJ (conversion efficiency=1.5%)
Summary
By solving the equation of motion for electrons under an intense laser field, one can obtain the nonlinear current density as the source of relativistic nonlinear optics.
Low-order nonlinearity (nonlinear refractive index, harmonic generation, optical rectification, induced birefringence …) can be understood well from such analysis.
The theory has been verified by experiments and 3-D particle-in-cell simulation.
Collaborators
Core members of the 10-TW and 100-TW laser facilities
Prof. Prof. Szu-yuan Chen, Academia Sinica, Taiwan
Prof. Jiunn-Yuan Lin, National Chung-Cheng Univ., Taiwan
Prof. Hsu-Hsin Chu, National Central Univ., Taiwan
Theoretical Analysis
Prof. Gin-yih Tsaur, Tunghai Univ., Taiwan
Computer Simulation
Prof. Shih-Hung Chen, National Central Univ., Taiwan
Thank you for your attention.