Self-imaging of molecules from diffraction spectra by laser-induced rescattering electrons

We study high-energy angle-resolved photoelectron spectra of molecules in strong fields. In an oscillating laser electric field, electrons released earlier in the pulse may return to recollide with the target ion, in a process similar to scattering by laboratory prepared electrons. If midinfrared lasers are used, we show that the images generated by the returning electrons are similar to images observed in typical gas-phase electron diffraction (GED). These spectra can be used to retrieve the positions of atoms in a molecule as in GED. Since infrared laser pulses of durations of a few femtoseconds are already available today, the study of these high-energy photoelectrons offers the opportunity of imaging the structure of transient molecules with temporal resolution of a few femtoseconds.

Figure 1

(a) Relation between classical impact parameter $b$ and scattering angle $\theta$ for an electron scattered by the potential of a carbon atom. Different curves for incident energies from 100 eV to 10 keV are shown. The vertical line is used to “define” close collisions. The region in scattering angles where GED and HATI spectra can be used for electron-diffraction studies are indicated. (b) Differential cross sections against momentum transfer $q$ for a carbon atom at different incident energies. For small $q$, the DCS depend on $q$ only. For large $q$, the DCS depend on $q$ and on incident energy. The horizontal line is drawn to indicate the limit where the DCS can be conveniently measured.

Figure 2

Elastic differential cross sections for $e^{-}$-CO${}_2$ collisions at incident energies of 20, 50, 100, and 200 eV. Solid red curves are IAM simulation. Symbols are experimental data from different groups. Asterisks: (a,b) from Register et al. [43], (c,d) from Iga et al. [44]; crosses: from Kanik et al. [45]; empty squares: from Tanaka et al. [46].

Figure 3

(a,b) Experimental (red solid squares) and theoretical (dashed green curves) DCS vs the atomic terms (dotted pink curves). (c,d) Molecular interference terms, comparing experimental data with the IAM. (e,f) Same as (c) and (d) but for molecular contrast factors.

Figure 4

(a) Structure of a hexafluoroethane ${\mathrm{C}}_2$F${}_6$ molecule in a ball-and-stick model. (b, c, d) Molecular interference terms for $e$${}^{-}$-C${}_2$F${}_6$ collisions, experimental data [49] vs IAM, at incident energies of 150, 200, and 300 eV. Elastic DCS plotted against momentum transfer $q$, IAM (e) vs experimental data (f), for the three energies, respectively.

Figure 5

(a,b) Comparison between measured DCS (red solid squares) of ${\mathrm{C}}_2$H${}_4$ at electron incident energies of 100 and 150 eV and the IAM simulations (green solid lines). (c,d) Comparison of the molecular contrast factors. The known bond lengths and the bond angle are shown in (e).

Figure 6

(a) Sensitivity of the molecular contrast factor $\gamma$ vs the change of C–O bond length for $e$${}^{-}$-CO${}_2$ collisions at 100 eV. The bond length has been increased or decreased by $10\%$ and $20\%$ with respect to the equilibrium value, respectively. (b) The same, but for a triangular CO${}_2$, where the bond angle OCO is varied.

Figure 7

(a) Comparison of DCS for parallel-aligned, perpendicularly aligned, and isotropic CO${}_2$ molecules. The atomic term is also shown (barely separable from the ${90}^{°}$ curve at large angles). (b) Same data presented in terms of molecular contrast factor.

Figure 8

(a) Comparison of MCFs of ${\mathrm{C}}_2$F${}_6$ molecules under different alignment conditions for an incident energy of 100 eV. (b) Same as in (a) but for 200 eV.

Figure 9

(a) Simulation of the isomerization of LiCN to NCLi. In the model, the plane of the molecule is fixed and the laser’s polarization is perpendicular to it. The assumed path taken by Li is given by open circles at different steps. From the HATI spectra, the retrieved Li positions from GA are indicated by crosses. (b) A model of a 1-fluoro-4-iodobenzene molecule away from its equilibrium configuration. We assume that the iodine and fluorine atoms are at the positions indicated. Laser polarization is perpendicular to the plane. From the “measured” HATI spectra, this molecular geometry is reconstructed, with results shown in Table .

Figure 10

(a) The difference of the DCS for electrons colliding with 1-fluoro-4-iodobenzene with I and F atoms at and away from their equilibrium positions. (b,c) The diffraction spectra for F and I at the nonequilibrium (b) and the equilibrium (c) configurations. (d) Comparison of the differential cross sections for iodine, fluorine, and carbon atoms. The electron energy is 200 eV.

Figure 11

(a,c) Simulation of HATI spectrum of CO${}_2$ at returning electron energy 100 eV and its corresponding MCF, based on QRS theory with ionization rate included, which is calculated using MO-ADK theory. (b,d) Same as (a) and (b) but at returning energy of 200 eV.