The strong-field approximation for ionization of diatomic molecules by an intense laser field is generalized to include rescattering of the ionized electron off the various centers of its molecular parent ion. The resulting spectrum and its interference structure strongly depend on the symmetry of the ground state molecular orbital. For ${\mathrm{N}}_2$, if the laser polarization is perpendicular to the molecular axis, we observe a distinct minimum in the emission spectrum, which survives focal averaging and allows determination of, e.g., the internuclear separation. In contrast, for ${\mathrm{O}}_2$, rescattering is absent in the same situation.

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 ${\mathrm{O}}_2$ but not for ${\mathrm{N}}_2$. This effect is different from the suppression of ionization that is well known to occur for ${\mathrm{O}}_2$.

The very pronounced intensity-dependent enhancements of groups of peaks of high-order above-threshold-ionization spectra of rare-gas atoms are investigated using an improved version of the strong-field approximation, which realistically models the respective atom. Two types of enhancements are found and explained in terms of constructive interference of the contributions of a large number of long quantum orbits. The first type is observed for intensities slightly below channel closings. Its intensity dependence is comparatively smooth and it is generated by comparatively few (of the order of 20) orbits. The second type occurs precisely at channel closings and exhibits an extremely sharp intensity dependence. It requires constructive interference of a very large number of long orbits (several hundreds) and generates cusps in the electron spectrum at integer multiples of the laser-photon energy. An interpretation of these enhancements as a threshold phenomenon is also given. An interplay of different types of the threshold anomalies is observed. The position of both types of enhancements, in the photoelectron-energy—laser-intensity plane, shifts to the next channel closing intensity with the change of the ground-state parity. The enhancements gradually disappear with decreasing laser pulse duration. This confirms the interpretation of enhancements as a consequence of the interference of long strong-laser-field-induced quantum orbits.

The strong-field approximation for ionization of diatomic molecules by a strong laser field [D. B. Milošević, Phys. Rev. A 74, 063404 (2006)] is generalized to include rescattering of the ionized electron wave packet off the molecular centers (the electron’s parent ion or the second atom). There are four rescattering contributions to the ionization rate, which are responsible for the high-energy plateau in the electron spectra and which interfere in a complicated manner. The spectra are even more complicated due to the different symmetry properties of the atomic orbitals of which a particular molecular orbital consists. Nevertheless, a comparatively simple condition emerges for the destructive interference of all these contributions, which yields a curve in the $(E_{{\mathbf{p}}_f},\theta )$ plane. Here $\theta$ is the electron emission angle and $E_{{\mathbf{p}}_f}$ is the electron kinetic energy. The resulting suppression of the rescattering plateau can be strong and affect a large area of the $(E_{{\mathbf{p}}_f},\theta )$ plane, depending on the orientation of the molecule. We illustrate this using the examples of the $3{\sigma }_g$ molecular orbital of ${\mathrm{N}}_2$ and the $1{\pi }_g$ molecular orbital of ${\mathrm{O}}_2$ for various orientations of these molecules with respect to the laser polarization axis. For ${\mathrm{N}}_2$, for perpendicular orientation and the equilibrium internuclear distance $R_0$, we find that the minima of the ionization rate form the curve $E_{{\mathbf{p}}_f}{\cos }^2\theta ={\pi }^2∕\left(2R_0^2\right)$ in the $(E_{{\mathbf{p}}_f},\theta )$ plane. For ${\mathrm{O}}_2$ the rescattering plateau is absent for perpendicular orientation.

Recently performed above-threshold ionization (ATI) experiments with noble gases allow the determination of the complete energy and angular distribution of the emitted photoelectrons. In order to simulate such experiments, we have generalized our numerical code for the calculation of ATI spectra in order to achieve a realistic simulation of ATI of the noble gases He, Ne, Ar, Kr, and Xe. Our method is based on an improved version of the strong-field approximation and includes focal averaging. A semiclassical analysis of the dependence of the cutoff law on the photoelectron emission angle is presented. The effects of channel closings on the high-energy spectra are analyzed.

High-energy above-threshold ionization by a strong linearly polarized laser field is analyzed using the strong-field approximation and the quantum-orbit formalism. An analytical formula for the cutoff is derived. The maximal electron kinetic energy is 10.007U _P + 0.538I _P. The first term with the ponderomotive energy U _P is equivalent to the known classical cutoff law, while the second term is a new result and depends on the ionization potential I _P. The validity of this formula is confirmed by comparison with the numerical results for the high-energy electron spectra.