Multiphoton ionization of hydrogen molecular ions in a 480-nm intense laser field is investigated by solving the time-dependent Schrödinger equation numerically in prolate spheroidal coordinates. We discretize space on a generalized pseudospectral grid and propagate the electronic wave function using a second-order split-operator method. By including and excluding the 2pσ u state in the basis expansion, we confirm that the observed 10-eV peak in a recent experiment [Litvinyuk et al., New J. Phys. 10, 083011 (2008)] comes from the enhanced ionization via three-photon resonant excitation of the molecular ions. By folding the calculated ionization rates with the vibrational density distribution, the kinetic energy release spectra are obtained, which are in reasonable agreement with the experimental measurement. Furthermore, using this enhanced ionization, a pump-probe experiment is suggested to trace the vibrational wave packet.

Recent experiments showed that the alignment-dependent ionization probabilities of hydrogen molecules vary as a function of laser intensity, and the anisotropy deviates from the prediction of the molecular tunneling ionization model (MO-ADK). To investigate the physical origins of the deviation, we systematically studied the anisotropy of hydrogen molecules in intense laser fields for three wavelengths, 400 nm (multiphoton ionization), 1850 nm (tunneling ionization), and 800 nm (in between), by solving the time-dependent Schrödinger equation with a model potential. The calculated ratio of the ionization probabilities for laser fields parallel and perpendicular to the molecular axis are in reasonable agreement with experiment. Furthermore, by analyzing the molecular wave function and the model potential, we found that the discrepancies between experiment and the MO-ADK prediction originated from the inaccurate coefficients used in the model and that the assumption of isotropy of the effective potential in the tunneling region is invalid.

We studied the high-harmonic generation of H 2 + ions in an intense laser field by solving the time-dependent Schrödinger equation in prolate spheroidal coordinates. By analyzing the power spectra of the harmonics with the electric field polarized along the molecular axis, we found that the yield of the third-order harmonic drops by several orders of magnitude at a specified aligned angle between the laser polarization direction and the molecular axis. The laser polarization angle of the minimum depends on the internuclear distance and it disappears both in the separated-and united-atom limits. This infers that the minimum is associated with the molecular symmetry. By decomposing individual contributions of the σ and π states, we identified that the minimum is attributed to the cancellation of the induced dipole moments of the σ and π states, like a dynamical Cooper minimum, but the position of the minimum can be tuned by the laser intensity for a given internuclear distance.

We present a time-dependent Schrödinger equation method in the prolate spheroidal coordinates to study the double ionization of hydrogen molecules in an intense laser field. The time propagation of the electronic wave function is performed by a second order split-operator method in the energy representation. With an adiabatic approximation, we obtain the kinetic energy release (KER) spectra by folding the vibrational wave packet of nuclei with the calculated ionization rates. Our results are in reasonable agreement with the experimental measurement. Furthermore, by including or excluding an individual state in the calculation, we identify that the observed KER peak comes from the ionization of the hydrogen molecular ions via the three-photon resonance of the 2pσ u state.