We report experimental and theoretical laser-induced photoelectron spectra of Ne, Ar, Kr and Xe in the direction of the laser polarization at laser intensities in the region 0.5–3.2 × 1014Wcm−2. For Ar and Xe, spectra at different angles are also presented for the laser intensities of 2.4 × 1014Wcm−2 for Ar and 1.3 × 1014Wcm−2 for Xe. Resonance-like structures evolve as a function of the laser intensity in the longitudinal spectra, which become suppressed at large angles. The simulations are in the context of the strong-field approximation, which is augmented to account for rescattering and the atom-specific electron–positive-ion scattering potentials, and they include focal averaging as well as saturation. Agreement between the data and these simulations is generally fair, especially for intensities below the saturation regime.

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.

We investigate high-order above-threshold ionization (HATI) of diatomic molecules having different symmetries by an elliptically polarized laser field using the modified molecular strong-field approximation. The yields of high-energy electrons contributing to the plateau region of the photoelectron spectra strongly depend on the employed ellipticity. This is more pronounced if the major axis of the polarization ellipse is parallel or perpendicular to the molecular axis and at the end of the high-energy plateau. For the ${\text{O}}_{2}$ molecule (characterized by ${\ensuremath{\pi}}_{\text{g}}$ symmetry) the maximum yield is observed for some value of the ellipticity $\ensuremath{\epsilon}$ different from zero. On the other hand, in the same circumstances, the ${\text{N}}_{2}$ molecule $({\ensuremath{\sigma}}_{\text{g}})$ behaves as an atom, i.e., the yield is maximum for $\ensuremath{\epsilon}=0$. These characteristics of the photoelectron spectra remain valid in a wide region of the molecular orientations and laser peak intensities. The symmetry properties of the molecular HATI spectra are considered in detail: by changing the molecular orientation one or other type of the symmetry emerges or disappears. Presenting differential ionization spectra in the ionized electron energy-emission angle plane we have observed similar interference effects as in the HATI spectra governed by a linearly polarized field.

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).

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).

A theory of high-order harmonic generation by diatomic molecules is introduced. Various versions (with or without the dressing of the initial and/or final molecular state) of the molecular strong-field approximation are investigated. Using examples of homonuclear diatomic molecules such as ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, and ${\mathrm{O}}_{2}$, it is shown that clear two-center interference minima in the harmonic spectra as a function of the molecular orientation appear only if the final molecular state is undressed. For ${\mathrm{H}}_{2}$ the positions of these minima are in agreement with the ab initio numerical results. Physically, the returned electron wave packet recombines into a molecular orbital, which is a linear combination of the atomic orbitals having different parities. The interference minima in the harmonic spectrum are caused by the destructive interference of the corresponding partial recombination amplitudes. In accordance with this, we have derived an interference minima condition which is valid for arbitrary homonuclear diatomic molecules.

In the improved strong-field approximation (ISFA), which describes high-order abovethreshold ionization (HATI), rescattering of the ionized electron off its parent ion is usually described within the first-order Born approximation (1BA). Coulomb effects in the rescattering process can be taken into account by replacing the final Volkov wave by the CoulombVolkov wave [1]. One can go beyond the 1BA by replacing in the rescattering amplitude the atomic scattering potential according to V → T (E) = V + V GV (E)V , where GV (E) is the stationary Green’s operator at the energy E(τ) of the recolliding electron at the recollision time τ . This is similar to the low-frequency approximation for laser-assisted scattering ([2] and references therein). We have recently derived the low-frequency approximation (LFA) for HATI [3]. In the present contribution we will show our numerical results for the angle-resolved HATI energy spectra of inert gases; see Fig. 1. We show that the difference between the ISFA and the LFA is significant for scattering away from the laser polarization axis. In the context of quantum-orbit theory and the uniform approximation, we also show that on the backrescattering ridge, the rescattering T -matrix element can be factorized into the product of the incoming flux and the elastic scattering cross section. Hence, the differential cross section of laser-free elastic electron-ion scattering can be extracted from the angle and energy resolved HATI spectra as proposed recently [4]. Fig. 1. 2D momentum distributions for Xe at 1.5× 10 W/cm and 760 nm. The upper (lower) panel: the results obtained using the ISFA (LFA).