Timeresolved Chemical Imaging with infrared Lasers Electron diffraction

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)

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

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

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

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

Photoionization crs derived from HHG by comparing Ar vs H

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

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

Ne: 1064 nm, 10. 3 fs (FWHM), 2 x 1014 W/cm 2 Wave-packet from the Lewenstein model is good!

ü Current SFA model not adequate (even for atoms!) ü 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

Improved Lewenstein model or Scattering-wave Strong-Field Approximation (SW-SFA) 800 nm, 10 fs (FWHM), 2 x 1014 W/cm 2 Discrepancy by 2 -3 orders of magnitude here Lewenstein model is good here

Example: HHG from + H 2 Collaborators: D. Telnov, Russia (TDSE for H 2+) P. Fainstein & R. D. Picca, Argentina (photoionization cross section) M. Lein, Germany (TDSE for H 2+, high intensity)

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

SW-SFA results 3 x 1014 W/cm 2, 20 -cycle, 800 nm SFA TDSE for H 2+: D. Telnov SW-SFA is much better than SFA!

Angular dependence of HHG SW-SFA TDSE (parallel)

Retrieving molecular structure from HHG spectra

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

Dependence of HHG vs interatomic distances

Variance vs tested range of R’s

HHG depends on R’s even for nonaligned molecules

R’s can be extracted from nonaligned data

R’s can be extracted from the photoionization cross sections

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