When atoms and molecules are ionized by laser pulses of finite duration and increasingly high intensities, the validity of the much-used dipole approximation, in which the spatial dependence and magnetic component of the external field are neglected, eventually breaks down. We report that, when going beyond the dipole approximation for the description of atoms exposed to ultraviolet light, the spatial dependence of the pulse shape, the envelope, provides the dominant correction, while the spatial dependence of the carrier is negligible. We present a first-order beyond-dipole correction to the Hamiltonian which accounts exclusively for nondipole effects stemming from the carrier envelope of the pulse. We demonstrate by ab initio calculations for hydrogen that this approximation, which we refer to as the envelope approximation, reproduces the full interaction beyond the dipole approximation for absolute and differential observables and proves to be valid for a broad range of high-frequency fields. This is done both for the Schrodinger and the Dirac equation. Moreover, it is demonstrated that the envelope approximation provides an interaction-term which gives rise to faster numerical convergence in terms of partial waves compared to its exact counterpart.

We present a theoretical study of the ionization dynamics of a hydrogen atom exposed to attosecond laser pulses in the extreme ultraviolet region at very high intensities. The pulses are such that the electron is expected to reach relativistic velocities, thus necessitating a fully relativistic treatment. We solve the time-dependent Dirac equation and compare its predictions with those of the corresponding nonrelativistic Schrodinger equation. We find that as the electron is expected to reach about 20% of the speed of light, relativistic corrections introduce a finite yet small decrease in the probability of ionizing the atom.

We present a generalized velocity gauge form of the relativistic laser-matter interaction. In comparison with the (equivalent) regular minimal coupling description, this form of light-matter interaction results in superior convergence properties for the numerical solution of the time-dependent Dirac equation. This applies both to the numerical treatment and, more importantly, to the multipole expansion of the laser field. The advantages of the alternative gauge is demonstrated in hydrogen by studies of the dynamics following the impact of superintense laser pulses of extreme ultraviolet wavelengths and subfemtosecond duration.