Phase and ellipticity dependence of the photoelectron angular distribution in non-resonant two-photon ionization of atomic hydrogen. I

We study the ellipticity and the dependence on the phase lag (lead) (between the semimajor and the semiminor axes of the field components) of the photoelectron angular distribution (PAD) in the non-resonant two-photon ionization of atomic hydrogen. We establish exact analytical expressions for azimuthal PAD for 3s, 3p and 3d excited initial states, marked by the occurrence of an asymmetric term. This term gives rise to elliptic dichroism (ED), which can be obtained in two ways: either with the left (versus right) ellipticity, or with the phase lag (versus lead); for 3s and 3p initial states, it is shown that the quantum phase of continua is directly related to the phase lag, one-photon below-threshold ionization, and indirectly one photon above. Another important result is that the magnetic sublevels, m = 0, for 3p and m = ±1, for 3d, do not contribute to the azimuthal PAD. Our numerical results show, for 3s and 3d, and near-threshold ionization, that the PAD has maxima either along the semimajor or the semiminor axis, while for above-threshold ionization, they are always shifted from these axes. However, the maxima of the corresponding ED coincide with the PAD maxima, while for 3p, they are shifted from the PAD minima. A strong dependence of the ED sign is noted, regardless of the state or the process. However, strong ED signals are obtained for the 3s initial state and below-threshold ionization.