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
• Generation of intense few-cycle mid-infrared pulses
• Relativistic induced birefringence

• peak power: 3J/30 fs =100 TW
• peak intensity: 10²⁰ W/cm² (10-μm focal spot)
• electric field: 3.2×10¹³ V/m (50× Coulomb field in hydrogen )

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after focusing:

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

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• Wave mixing mediated by plasma waves
• Relativistic nonlinearity of the Lorentz force

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relativistic self-phase modulation

nonlinear force

Theoretic 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-ω source term

optical rectification

1-ω source term

nonlinear refractive index

n-ω 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

fundamental beam profile

THz field

particle-in-cell simulation

fundamental beam profile

THz field

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

advantages:

• no optical damage
• large working bandwidth
• high spatial coherence

modulation of refractive index

Ge-wafer photo-switch

mid-IR pulse

excitation

pulse

pinhole

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

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 fs

excitation pulse: 500 μJ/38 fs

plasma 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 energy (arb. units)

intensity (arb. units)

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 μm

6－10 μm

2－6 μm

10－20 μm

Estimation based on Fourier transform of the phase modulated pulse

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 a_x into a_x' .

induced birefringence

nonlinear source terms (functions of )

Comparison with particle-in-cell simulation

theory

simulation

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.