Transcript Slide 1
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 Second harmonic generation P 0 ( (1) E (2) E 2 (3) E3 ) linear response P NL 2 0dE2 nonlinear response First demonstration of second-harmonic generation P.A. Franken (1961) The second-harmonic beam was very weak because the process was not phase-matched. First demonstration of second-harmonic generation The actual published results… Introduction to nonlinear optics Generate field = solution of a wave equation Fundamental Harmonic generation 2nd harmonic 2 2 NL 1 E 1 P 2 E 2 2 2 c t c t 2 E ( z, t ) 12 E1 ( z, t )eit ik z cc k n c 2it 2ik z 1 P2NL ( z , t ) P ( z , t ) e cc 2 2 Different phase velocity E2 ( z, t ) 12 E2 ( z, t )e2it ik2 z cc e e z Lcohk Lcoh 2it 2ik z 4n 2it ik2 z Coherence length Out of phase n(2 ) n( ) Refractive index Phase-matching second-harmonic generation Frequency 2 no (2 ) ne ( ) Refractive index Using birefringence ne no Frequency 2 Efficiency (h) h L2 Depletion h sin 2 (L / Lcoh ) Lcoh L Dependence of SHG intensity on length Large k Small k The SHG intensity is sharply maximized if k = 0. Wave vectors 3 1 2 3 k1 k2 k3 2 1 k3 k2 k1 The lengths of the problem Efficiency (h) h L2 hLe 2 L / Labs Labs h sin 2 (L / Lcoh ) Lcoh Lamp L L2 Fq ( L) Phase Fgen(z)- Fpol(z) Dipole phase 40 i I (z) Dispersion kz z -1 cm Dispersion free electrons Focusing q tan1 (2 z / b) 1 cm -40 Intensity, pressure, focusing, many parameters! Asymmetry before/after the focus Fgen(z)- Fpol(z) 40 -1 cm 1 cm Lcoh ( z ) / [F gen ( z ) F pol ( z )] z Lcoh ( z) Lcoh ( z, t ) Localized in space and in time! Wave vectors 3 1 2 3 k1 k2 k3 2 1 k3 k2 k1 Generation of short light pulses 2.7 fs 1 eV 30 eV 2 cycles 2 T c XUV! Generation of short light pulses Fourier Transform 0.1 eV Frequency 10 eV Time 0.4 Broad bandwidth! Strong-Field Atomic Physics I The electron can tunnel through the distorted Coulomb barrier Interaction with the core III III The electron wave packet interacts with the remaining core II The electron is accelerated by the field, and may return to the atomic core High-Order Harmonic Generation in Gases 3 5 7 . . (2q 1) Multiphoton Plateau Cut-off Ferray et al., J. Phys. B 21, L31 (1988) High-Order Harmonic Generation in Gases Semi-classical three-step model I The electron tunnels through the distorted Coulomb barrier II The free electron is accelerated by the field, and may return to the atomic core III The electron recombines with the atom, emitting its energy as an XUV photon High-Order Harmonic Generation in Gases Electron dynamics Electrons Atom Several bursts per half laser cycle Group delay dispersion Field High-Order Harmonic Generation in Gases 3 5 Plateau 7 (2q 1) Photons . . H37 Cut-off H43 H31 H49 H53 50 III 60 70 Energy (eV) 80 The electron recombines with the atom, emitting its energy as an XUV photon High-Order Harmonic Generation in Gases Laser Atomic Medium Gas cell with rare gas Titanium-Sapphire, 800 nm 1 kHz, 2 mJ, 35 fs pulses Tunneling Acceleration in the continuum Recombination Time Time Attosecond pulse train Harmonic spectrum Attosecond pulse train 0 20 Frequency domain Time domain L 2L Energy Harmonic spectrum =20eV 2 Time Attosecond pulse train 2 200 as Energy Broad spectrum Time Single attosecond pulse Energy Is this always true? Time Generation of short light pulses