Solving the time-dependent Schrödinger equation from first principles, the laser-induced breakup dynamics of hydrogen is studied beyond the electric dipole approximation, at very high laser intensities. It is assumed that the atom is being irradiated by an extreme ultraviolet laser light pulse at a wavelength of 13 nm, corresponding to a photon energy of 95 eV. It has already been experimentally demonstrated that the free-electron laser (FEL) FLASH in Hamburg can deliver irradiance levels up to about ${10}^{16}\text{W}/{\mathrm{cm}}^2$ in this wavelength range. Although we will go to even higher intensities in the present work, in order to spot nondipole effects, this merely demonstrates that ultrahigh light intensities can be achieved with present FEL technologies. Furthermore, with new seeding techniques the laser power is expected to go even higher in the future. In our study the atom is exposed to a short attosecond laser pulse, and the role of higher-order corrections to the electric dipole approximation is studied systematically. The main findings are that higher-order corrections beyond the leading first-order term, to a good approximation, can be neglected for all intensities within the nonrelativistic regime, provided the pulse duration is not too long. This means that the effect of second- and higher-order corrections only needs to be accounted for when entering the relativistic regime, within the scope of the Dirac equation. It is further found that the leading first-order correction to the dipole approximation has a great impact on the angular emission pattern of the low-energy photoelectrons.

• Received 25 September 2014

DOI:https://doi.org/10.1103/PhysRevA.90.053411