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Relativistic nonlinear optics in laser-plasma interaction

Relativistic nonlinear optics in laser-plasma interaction. Jyhpyng Wang. Institute of Atomic and Molecular Sciences Academia Sinica, Taiwan. National Central University, Taiwan. National Taiwan University, Taiwan. Outline. Relativistic nonlinearity in laser-plasma interaction

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Relativistic nonlinear optics in laser-plasma interaction

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  1. Relativistic nonlinear optics in laser-plasma interaction Jyhpyng Wang Institute of Atomic and Molecular Sciences Academia Sinica, Taiwan National Central University, Taiwan National Taiwan University, Taiwan

  2. Outline • Relativistic nonlinearity in laser-plasma interaction • Relativistic harmonic generation • Generation of intense few-cycle mid-infrared pulses • Relativistic induced birefringence

  3. 100-TW laser at Nat’l Central Univ. after focusing: • peak power:3J/30 fs =100 TW • peak intensity:1020 W/cm2 (10-m focal spot) • electric field: 3.21013 V/m(50Coulomb field in hydrogen)

  4. Hamiltonian of an electron in a laser field vector potential canonical momentum scalar potential relativistic intensity: mass increase due to quivering motion:

  5. 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

  6. , , Theoretic analysis of the electron motion normalized vector and scalar potentials Lorentz force Poisson’s Equation Continuity Equation solution : known laser field Phys. Rev. A 76, 063815 (2007)

  7. Modification of the laser field Maxwell Equation nonlinear source terms (functions of ) 0- source term optical rectification 1- source term nonlinear refractive index n- source term harmonic generation

  8. Harmonic generation and optical rectification Phys. Rev. A 76, 063815 (2007) Phys. Rev. A 80, 023802 (2009)

  9. Relativistic second harmonic generation intensity dependence theory experiment density dependence fundamental beam profile 2nd harmonic beam profile E. Takahashi, et al, Phys. Rev. E 65, 016402 (2001)

  10. Relativistic optical rectification fundamental beam profile theory particle-in-cell simulation THz field fundamental beam profile THz field

  11. Generation of few-cycle intense mid-infrared pulses Phys. Rev. A 82, 063804 (2010)

  12. Nonlinear phase modulation in the bubble regime modulation of refractive index density modulation advantages: • no optical damage • large working bandwidth • high spatial coherence relativistic self-phase modulation

  13. mid-IR pulse Ge-wafer photo-switch excitation pulse mid-IR pulse pinhole mid-IR pulse A. J. Alcock and P. B. Corkum, Can. J. Phys. 57, 1280 (1979)

  14. mid-IR pulse Ge-wafer photo-switch excitation pulse mid-IR pulse pinhole mid-IR pulse A. J. Alcock and P. B. Corkum, Can. J. Phys. 57, 1280 (1979)

  15. Temporal profile of the mid-IR pulse reconstructed temporal profile photo-switch gated transmission mid-IR energy (arb. units) intensity (arb. units) delay of excitation pulse with respect to mid-IR pulse (ps) pump pulse: 205 mJ/42 fs excitation pulse: 500 mJ/38 fs plasma density: 4.1x1019 cm-3 5-mm Ge window 5-mm Ge window pulse duration X 4.6 ps 9.8 ps X～15 fs consistent with particle-in-cell simulation

  16. Comparing with simulation and theoretical estimation Estimation based on Fourier transform of the phase modulated pulse Square of the electric field of the numerically filtered mid-IR pulse 2－20 mm 6－10 mm 2－6 mm 10－20 mm Simulation: mid-IR peak power in the bubble: > 0.5 TW 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.

  17. Relativistic induced birefringence Phys. Rev. A 83, 033801 (2011)

  18. Two-beam interaction via plasma waves Maxwell Equation nonlinear source terms (functions of ) a and a' create plasma waves of k  k' , which scatter ax into ax' . induced birefringence

  19. Comparison with particle-in-cell simulation theory simulation

  20. 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.

  21. Core members of the 10-TW and 100-TW laser facilities Collaborators 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

  22. Thank you for your attention.

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