Relativistic plasma nonlinear optics

Institute of Atomic and Molecular Sciences Academia Sinica, Taiwan

National Central University, Taiwan

Jyhpyng Wang (汪治平)

National Taiwan University, Taiwan

Collaborators

Core members of the 10-TW and 100-TW laser facilities

Prof. Prof. Szu-yuan Chen (陳賜原), Academia Sinica, Taiwan

Prof. Jiunn-Yuan Lin (林俊元), National Chung-Cheng Univ., Taiwan

Prof. Hsu-Hsin Chu (朱旭新),, National Central Univ., Taiwan

Theoretical Analysis

Prof. Gin-yih Tsaur (曹景懿), Tunghai Univ., Taiwan

Computer Simulation

Prof. Shih-Hung Chen (陳仕宏), National Central Univ., Taiwan

Outline

• Relativistic nonlinearity in laser plasma interaction
• Quasi-phase matching of relativistic harmonic generation
• Generation of intense few-cycle mid-infrared pulses
• Relativistic induced birefringence

• peak power: 3J/30 fs =10¹⁴ W (10,000 nuclear power plants)
• peak intensity: 10²⁰ W/cm² (sunshine at noon = 0.1 W/cm² )
• electric field: 3.2×10¹³ V/m (50× Coulomb field in hydrogen )
• acceleration on electron: 5×10²³ g (near a black hole )

after focusing:

100-TW laser at Nat’l Central Univ.

• Laser-wakefield electron accelerator
• Soft x-ray laser
• X-ray free electron laser
• Laser-plasma ion accelerator
• Laboratory astrophysics

Potential applications

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 )

intensity dependence

Relativistic second harmonic generation

theory

experiment

2nd harmonic beam profile

Phys. Rev. A 76, 063815 (2007)

Quasi-phase matching of relativistic harmonic generation

Phys. Rev. Lett. 98, 033901 (2007)

coherence length

phase mismatch

region of high gain

region of low reverse-gain

Masking off the region of reverse conversion

3rd harmonic energy

L₁=67 μm, L₂=100 μm

Anticipated net growth by quasi-phase matching

3rd harmonic energy

with periodic waveguide for quasi-phase matching

2

4

6

8

0

Tomography of harmonic growth

Phys. Rev. Lett. 98, 033901 (2007)

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

Ge-wafer photo-switch

mid-IR pulse

excitation

pulse

pinhole

mid-IR pulse

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

Energy: 7 mJ, duration 12 fs, 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 )

Verified by 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.
• Nonlinear refractive index, harmonic generation, optical rectification, induced birefringence, etc. can be understood well from such analysis.
• The theory has been verified by experiments and 3-D particle-in-cell simulation.

Thank you for your attention.