We investigate high-order above-threshold ionization of diatomic molecules and their companion atoms by linearly polarized strong laser field using improved molecular (atomic) strong-field approximation. The most noticeable feature of the molecular spectra is the existence of minima that are absent in atomic case. We have derived an analytical formula for their position which is independent of the molecular symmetry.

When an electron from a diatomic molecule undergoes tunneling-rescattering ionization, a novel form of destructive interference can be realized that involves all four geometric orbits that are available to the electron when it is freed, because both ionization and rescattering may take place at the same or at different centers. We find experimentally and confirm theoretically that in orientation-averaged angle-resolved high-order above-threshold ionization spectra the corresponding destructive interference is visible for O_{2} but not for N_{2}. This effect is different from the suppression of ionization that is well known to occur for O_{2}.

The multiple-slit type destructive interference in molecular high-order harmonic generation (HHG) leads to the minima in the harmonic yield for particular molecular orientation angle θL and the harmonic order n. For the case of homonuclear diatomic molecules, we have found a condition for this destructive interference in the form of a nonlinear equation over n and θL. This condition strongly depends on the molecular symmetry, on the atomic orbitals of which a particular highest occupied molecular orbital (HOMO) consists and on the internuclear distance R. Therefore, one can learn about the molecular structure and dynamics analysing the HHG spectra of aligned molecules. Using the example of an Ar2 molecule, having 5σu HOMO, for various internuclear distances, we analyse this interference condition and show that, in the (n, θL) plane, it manifests in the form of one or several continuous curves. Furthermore, in the (Rcos θL, λmin) plane, where λmin is an effective de Broglie wavelength of the recombining electron, this condition leads to a set of lines which are positioned between the limiting cases of molecular orbitals consisting of only one type (even or odd) of atomic orbitals (s and p in the Ar2 case).