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.