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

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

Extract Photo-recombination cross sections from HHG— based on results from TDSE

4-cycle pulse

Electron wave Packets “derived” from HHG

Photoionization crs derived from HHG by comparing Ar vs H

Model for molecules

),()( ),(),()(~),( kii ekeWNdw

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

Cooper minimum

Different lasers are usedPhoto-recombination can be extracted with high accuracy!

PhaseCross section

Cooper minimum

Ne: 1064 nm, 10.3 fs (FWHM), 2x1014 W/cm2

Wave-packet from the Lewenstein model is good!

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

)()()()(

SFA

PWA

exactSFASW SS

800 nm, 10 fs (FWHM), 2x1014 W/cm2

Discrepancy by 2-3 orders of magnitude here

Lewenstein model is good here

Improved Lewenstein modelor Scattering-wave Strong-Field Approximation (SW-SFA)

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)

Photoionization cross section

PWA: Plane-wave approx.Exact (with scattering waves)

Fainstein et al

Electron energy (eV)

PWA

Electron energy (eV)

0o

30o

45o

SW-SFA results

SW-SFA is much better than SFA!

SFA

TDSE for H2+: D. Telnov

3x1014W/cm2, 20-cycle, 800 nm

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