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2. High-order harmonic generation in gases Attosecond pulse generation

1. Introduction to nonlinear optics. 2. High-order harmonic generation in gases Attosecond pulse generation. Introduction to nonlinear optics. Polarization induced by a laser field. linear response. nonlinear response. Second harmonic generation. P.A. Franken (1961).

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2. High-order harmonic generation in gases Attosecond pulse generation

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  1. 1. Introduction to nonlinear optics 2. High-order harmonic generation in gases Attosecond pulse generation

  2. Introduction to nonlinear optics Polarization induced by a laser field linear response nonlinear response Second harmonic generation

  3. P.A. Franken (1961) First demonstration of second-harmonic generation The second-harmonic beam was very weak because the process was not phase-matched.

  4. First demonstration of second-harmonic generation The actual published results…

  5. Introduction to nonlinear optics Generate field = solution of a wave equation Fundamental Harmonic generation Different phase velocity 2nd harmonic

  6. Out of phase z Coherence length

  7. Refractive index Frequency Phase-matching second-harmonic generation Refractive index Frequency Using birefringence

  8. Depletion Efficiency (h) L

  9. Dependence of SHG intensity on length Large Dk Small Dk The SHG intensity is sharply maximized if Dk = 0.

  10. Wave vectors

  11. The lengths of the problem Efficiency (h) L

  12. Fgen(z)- Fpol(z) Phase Dipole phase 40 Dispersion z 1 cm -1 cm Dispersion free electrons Focusing -40 Intensity, pressure, focusing, many parameters! Asymmetry before/after the focus

  13. Fgen(z)- Fpol(z) 40 p -1 cm 1 cm Localized in space and in time!

  14. Wave vectors

  15. Generation of short light pulses 2.7 fs 1 eV 30 eV 2 cycles XUV!

  16. Generation of short light pulses Fourier Transform 0.1 eV Time Frequency 10 eV Broad bandwidth!

  17. Strong-Field Atomic Physics I The electron can tunnel through the distorted Coulomb barrier

  18. Interaction with the core III III The electron wave packet interacts with the remaining core The electron is accelerated by the field, and may return to the atomic core II

  19. High-Order Harmonic Generation in Gases Multiphoton Plateau . . Cut-off Ferray et al., J. Phys. B 21, L31 (1988)

  20. High-Order Harmonic Generation in Gases Semi-classical three-step model I The electron tunnels through the distorted Coulomb barrier The free electron is accelerated by the field, and may return to the atomic core II III The electron recombines with the atom, emitting its energy as an XUV photon

  21. High-Order Harmonic Generation in Gases Electron dynamics Field Electrons Atom Several bursts per half laser cycle Long Short Group delay dispersion

  22. High-Order Harmonic Generation in Gases Plateau Cut-off . . The electron recombines with the atom, emitting its energy as an XUV photon III

  23. High-Order Harmonic Generation in Gases Atomic Medium Laser Gas cell with rare gas Titanium-Sapphire, 800 nm 1 kHz,2 mJ,35 fs pulses

  24. Time Tunneling Acceleration in the continuum Recombination Attosecond pulse train Time

  25. Harmonic spectrum Attosecond pulse train Energy Time Is this always true?

  26. Generation of short light pulses

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