We have extended the tunneling ionization model of Ammosov-Delone-Krainov (ADK) 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 $({\mathrm{D}}_2:\mathrm{Ar},$ ${\mathrm{O}}_2:\mathrm{Xe})$ and pairs without suppression $({\mathrm{N}}_2:\mathrm{Ar},$ CO:Kr) are in good agreement with the measurements. However, the theory predicts suppression for ${\mathrm{F}}_2:\mathrm{Ar},$ which is in disagreement with the experiment. The ionization signals of NO, ${\mathrm{S}}_2,$ 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.

It was recently shown that the highest molecular orbital of ${\mathrm{N}}_2$ could be reconstructed from a series of high harmonic measurements. Existing theories of high harmonic generation and orbital tomographic imaging are based on the single active electron approximation that ignores essential quantum mechanical properties such as the indistinguishability of identical particles and the Pauli exclusion principle. We show that, when fully antisymmetrized multielectron wave functions and electronic relaxation in the cation are considered, molecular orbital tomography records the image of the Dyson orbital plus exchange contributions from inner shells. The mixing of contributions from more than one molecular orbital gives access to additional wave function information. By utilizing the exchange term, harmonic emission from a closed-shell 4-electron system can be interpreted as a complete Hartree-Fock wave function.

The orientation-dependent strong-field ionization of CO molecules is investigated using the fully propagated three-dimensional time-dependent Hartree-Fock theory. The full ionization results are in good agreement with recent experiments. The comparisons between the full method and the single active orbital method show that although the core electrons are generally more tightly bound and contribute little to the total ionization yields, their dynamics cannot be ignored, which effectively modifies the behavior of electrons in the highest occupied molecular orbital. By incorporating it into the single active orbital method, we identify that the dynamic core polarization plays an important role in the strong-field tunneling ionization of CO molecules, which is helpful for the future development of the tunneling ionization theory of molecules beyond the single active electron approximation.

The strong field approximation is used to investigate the harmonic generation of aligned ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ molecules. It is shown that the angular dependence of the yields of high-order harmonic generation from ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ molecules are different, which can be attributed to the orbital symmetry of the outmost electrons. The theory is applied to study the angular dependence of harmonic generation from recent pump-probe experiments where the pump pulse was used to produce the time-dependent partial alignment of molecules and the probe pulse was used to generate high-order harmonics. Good agreement with the experiments was found.

It is shown that the alignment dependence of the yields of high-order harmonic generation (HHG) from molecules by intense lasers is governed by the orbital symmetry of the outermost electron(s). For ${\mathrm{N}}_2$, with its outermost ${\sigma }_g$ electron, the HHG yield is maximal when the molecules are aligned with the laser polarization direction, in agreement with the recent experiment of Itatani et al. [Nature 432, 867 (2004)]. For ${\mathrm{O}}_2$, with its outermost ${\pi }_g$ electron, the HHG yield peaks when the molecules are aligned at about 45° from the polarization axis. We emphasize that the alignment dependence is determined mostly by the orbital symmetry and weakly on the laser parameters or the species.

We perform a joint measurement of terahertz waves and high-harmonics generated from argon atoms driven by a fundamental laser pulse and its second harmonic. By correlating their dependence on the phase delay between the two pulses, we determine the generation of THz waves in tens of attoseconds precision. Compared with simulations and models, we find that the laser-assisted soft collision of the electron wave packet with the atomic core plays a key role. It is demonstrated that the rescattering process, being indispensable in high-harmonic generation processes, dominates THz wave generation as well in a more elaborate way. The new finding might be helpful for the full characterization of the rescattering dynamics.