We have extended the tunneling ionization model of Ammosov-Delone-Krainov ͑ADK͒ for atoms to diatomic molecules by considering the symmetry property and the asymptotic behavior of the molecular electronic wave function. The structure parameters of several molecules needed for calculating the ionization rates using this molecular ADK model have been obtained. The theory is applied to calculate the ratios of ionization signals for diatomic molecules with their companion atoms that have nearly identical binding energies. The origin of ionization suppression for some molecules has been identified. The predicted ratios for pairs with suppression (D 2 :Ar, O 2 :Xe) and pairs without suppression (N 2 :Ar, CO:Kr͒ are in good agreement with the measurements. However, the theory predicts suppression for F 2 :Ar, which is in disagreement with the experiment. The ionization signals of NO, S 2 , and of SO have also been derived from the experimental data, and the results are also shown to be in agreement with the prediction of the present molecular ADK theory.

We propose an empirical formula for the static field ionization rates of atoms and molecules by extending the well-known analytical tunnelling ionization rates to the barrier-suppression regime. The validity of this formula is checked against ionization rates calculated from solving the Schrödinger equation for a number of atoms and ions. The empirical formula retains the simplicity of the original tunnelling ionization rate expression but can be used to calculate the ionization rates of atoms and molecules by lasers at high intensities.

Establishing the structure of molecules and solids has always had an essential role in physics, chemistry and biology. The methods of choice are X-ray and electron diffraction, which are routinely used to determine atomic positions with sub-ångström spatial resolution. Although both methods are currently limited to probing dynamics on timescales longer than a picosecond, the recent development of femtosecond sources of X-ray pulses and electron beams suggests that they might soon be capable of taking ultrafast snapshots of biological molecules and condensed-phase systems undergoing structural changes. The past decade has also witnessed the emergence of an alternative imaging approach based on laser-ionized bursts of coherent electron wave packets that self-interrogate the parent molecular structure. Here we show that this phenomenon can indeed be exploited for laser-induced electron diffraction (LIED), to image molecular structures with sub-ångström precision and exposure times of a few femtoseconds. We apply the method to oxygen and nitrogen molecules, which on strong-field ionization at three mid-infrared wavelengths (1.7, 2.0 and 2.3 μm) emit photoelectrons with a momentum distribution from which we extract diffraction patterns. The long wavelength is essential for achieving atomic-scale spatial resolution, and the wavelength variation is equivalent to taking snapshots at different times. We show that the method has the sensitivity to measure a 0.1 Å displacement in the oxygen bond length occurring in a time interval of ∼5 fs, which establishes LIED as a promising approach for the imaging of gas-phase molecules with unprecedented spatio-temporal resolution.

The Quantitative Rescattering Theory (QRS) for high-order harmonic generation (HHG) by intense laser pulses is presented. According to the QRS, HHG spectra can be expressed as a product of a returning electron wave packet and the photo-recombination differential cross section of the laser-free continuum electron back to the initial bound state. We show that the shape of the returning electron wave packet is determined mostly by the laser only. The returning electron wave packets can be obtained from the strong-field approximation or from the solution of the time-

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.

No abstract

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.