By analyzing accurate theoretical results from solving the time-dependent Schrödinger equation of atoms in few-cycle laser pulses, we established the general conclusion that laser-generated high-energy electron momentum spectra and high-order harmonic spectra can be used to extract accurate differential elastic scattering and photo-recombination cross sections of the target ion with free electrons, respectively. Since both electron scattering and photoionization (the inverse of photo-recombination) are the conventional means for interrogating the structure of atoms and molecules, this result implies that existing few-cycle infrared lasers can be implemented for ultrafast imaging of transient molecules with temporal resolution of a few femtoseconds.

When an atom or molecule is exposed to a short intense laser pulse, electrons that were removed at an earlier time may be driven back by the oscillating electric field of the laser to recollide with the parent ion, to incur processes like high-order harmonic generation (HHG), high-energy above-threshold ionization (HATI) and nonsequential double ionization (NSDI). Over the years, a rescattering model (the three-step model) has been used to understand these strong field phenomena qualitatively, but not quantitatively. Recently we have established such a quantitative rescattering (QRS) theory. According to QRS, the yields for HHG, HATI and NSDI can be expressed as the product of a returning electron wave packet with various field-free electron-ion scattering cross sections, namely photo-recombination, elastic electron scattering and electron-impact ionization, respectively. The validity of QRS is first demonstrated by comparing with accurate numerical results from solving the time-dependent Schrödinger equation (TDSE) for atoms. It is then applied to atoms and molecules to explain recent experimental data. According to QRS, accurate field-free electron scattering and photoionization cross sections can be obtained from the HATI and HHG spectra, respectively. These cross sections are the conventional tools for studying the structure of a molecule; thus, QRS serves to provide the required theoretical foundation for the self-imaging of a molecule in strong fields by its own electrons. Since infrared lasers of duration of a few femtoseconds are readily available today, these results imply that they are suitable for probing the dynamics of molecules with temporal resolutions of a few femtoseconds.

A comprehensive quantitative rescattering (QRS) theory for describing the production of highenergy photoelectrons generated by intense laser pulses is presented. According to the QRS, the momentum distributions of these electrons can be expressed as the product of a returning electron wave packet with the elastic differential cross sections (DCS) between free electrons with the target ion. We show that the returning electron wave packets are determined mostly by the lasers only, and can be obtained from the strong field approximation. The validity of the QRS model is carefully examined by checking against accurate results from the solution of the time-dependent Schrödinger equation for atomic targets within the single active electron approximation. We further show that experimental photoelectron spectra for a wide range of laser intensity and wavelength can be explained by the QRS theory, and that the DCS between electrons and target ions can be extracted from experimental photoelectron spectra. By generalizing the QRS theory to molecular targets, we discuss how few-cycle infrared lasers offer a promising tool for dynamic chemical imaging with temporal resolution of a few femtoseconds.

Two-dimensional ͑2D͒ electron momentum distributions and energy spectra for multiphoton ionization of atoms by intense laser pulses, calculated by solving the time-dependent Schrödinger equation ͑TDSE͒ for different wavelengths and intensities, are compared to those predicted by the strong-field approximation ͑SFA͒. It is shown that the momentum spectra at low energies between the TDSE and SFA are quite different and the differences arise largely from the absence of a long-range Coulomb interaction in the SFA. We further found that the low-energy 2D momentum spectra from the TDSE exhibit ubiquitous fanlike features where the number of stripes is due to a single dominant angular momentum of the low-energy electron. The specific dominant angular momentum in turn has been found to be decided by the minimum number of photons needed to ionize the atom only. The electron momentum spectra predicted by models modified from the SFA are also examined and found to lack the fanlike features as in the SFA.

We studied the two-dimensional electron momentum spectra of Ar by femtosecond intense laser pulses with mean wavelength from 400 nm to 800 nm, to compare with experimental results of Maharjan et al. ͓J. Phys. B 39, 1955 ͑2006͔͒. At the higher intensities we found that the effects of ground-state depletion and laser-focus volume are very important such that the peak laser field strength is not reached in experiment. The ubiquitous fanlike stripes in the low-energy electron momentum spectra and the evidence of Freeman resonances in the experimental data are well reproduced in the theoretical calculations. We emphasize that depletion of the initial state should be carefully evaluated for ionization of atoms in the tunneling region.

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.

We illustrate a new method of analyzing three-dimensional momentum images of high-energy photoelectrons generated by intense phase-stabilized few-cycle laser pulses. Using photoelectron momentum spectra that were obtained by velocity-map imaging of above-threshold ionization of xenon and argon targets, we show that the absolute carrier-envelope phase, the laser peak intensity, and pulse duration can be accurately determined simultaneously (with an error of a few percent). We also show that the target structure, in the form of electron-target ion elastic differential cross sections, can be retrieved over a range of energies. The latter offers the promise of using laser-generated electron spectra for probing dynamic changes in molecular targets with subfemtosecond resolution.

Single ionization of helium by 102 eV electron impact has been studied by measuring the momentum vectors of all final-state particles, i.e., two electrons and the He + ion, with an advanced reaction microscope. Fully differential cross sections for asymmetric scattering geometry, which have been normalized to an absolute scale, have been obtained covering a large range of emission angles for the emitted low-energy (E 15 eV) electron and different scattering angles for the fast electron. Strong electron emission out of the projectile scattering plane is confirmed for electron impact, as was observed before for heavy-ion impact ionization. The data are compared with theoretical predictions from a three-Coulomb wavefunction model, first-order and second-order distortedwave approaches, as well as a convergent close-coupling calculation.