Time-resolved Chemical Imaging with infrared Lasers

1. Time-resolved Chemical Imaging with infrared Lasers • Electron diffraction and X-ray diffraction cannot be used for time-resolved imaging at the femtoseconds level • Can use IR lasers to probe molecular structure? • First needs to identify the role of molecular structure in laser-induced phenomena: electron momentum spectra and HHG • Retrieve the molecular structure (inverse scattering)

2. Tomography of Molecular Orbitals • HHG from molecules via rescattering/recombination • HHG depends on the target HOMO orbital • Retrieve HOMO orbital from HHG via Tomography

3. Validity of the plane wave approximation: not adequate for typical returning electrons PWA – Tomographic imaging of Itatani et al Nature 2004 (HHG)TDSE=(WP) (crs)exact (HHG)SFA=(WP) (crs)PWA

4. Extract Photo-recombination cross sections from HHG— based on results from TDSE Model: HHG= (wave packet) x (photo-recombination cross section) -- Electron wave packet is determined by the driving laser only --- Compare two atomic systems with identical ionization potential Neon vs Scaled atomic hydrogen -- or from strong field approximation

5. Electron wave Packets “derived” from HHG 4-cycle pulse

6. Photoionization crs derived from HHG by comparing Ar vs H

7. Model for molecules W: Returning electron wave-packet σ: Photorecombination cross section θ: Alignment angle (for molecule) k: Electron momentum, k2/2=ω-Ip W is largely independent of target for targets with similar Ip

8. Phase Cross section Cooper minimum Cooper minimum Photo-recombination can be extracted with high accuracy! Different lasers are used

9. Ne: 1064 nm, 10.3 fs (FWHM), 2x1014 W/cm2 Wave-packet from the Lewenstein model is good!

10. Current SFA model not adequate (even for atoms!) • For molecules, the interference minimum positions not correctly predicted by SFA Our strategy: use the wave-packet from SFA or TDSE for system with similar ionization potential

11. Improved Lewenstein model orScattering-wave Strong-Field Approximation(SW-SFA) 800 nm, 10 fs (FWHM), 2x1014 W/cm2 Discrepancy by 2-3 orders of magnitude here Lewenstein model is good here

12. Example: HHG from H2+ Collaborators: D. Telnov, Russia (TDSE for H2+) P. Fainstein & R. D. Picca, Argentina (photoionization cross section) M. Lein, Germany (TDSE for H2+, high intensity)

13. Photoionization cross section Exact (with scattering waves) Fainstein et al PWA: Plane-wave approx. 0o PWA 30o 45o Electron energy (eV) Electron energy (eV)

14. SW-SFA results 3x1014W/cm2, 20-cycle, 800 nm SFA SW-SFA is much better than SFA! TDSE for H2+: D. Telnov

16. Angular dependence of HHG TDSE (parallel) SW-SFA

17. Retrieving molecular structure from HHG spectra

18. Retrieving Interatomic distances from HHG for linear molecules • We test the method using HHG generated from SFA • The fitting method is very efficient and requires less data – alignment and intensity • effect of isotropic molecules and phase matching • extract structure from dipole moment deduced from HHG

19. Dependence of HHG vs interatomic distances

20. Variance vs tested range of R’s

21. HHG depends on R’s even for nonaligned molecules

22. R’s can be extracted from nonaligned data

23. R’s can be extracted from the photoionization cross sections

24. other issues • effect of propagation in the medium (in progress) • extension to polyatomic molecules first test within the SFA model– efficient codes for calculating dipole matrix elements from molecules