Phase and Ellipticity Dependence of the Photoelectron Angular Distribution in Non Resonant Three Photon Ionization of Atomic Hydrogen

We studied the ellipticity and the dependence on the phase lag (lead) (between the semi major and the semi minor axes of the field components) of the photoelectron angular distribution (PAD) in the non resonant three photon ionization of atomic hydrogen. The exact analytical expressions for azimuthal PAD for 1s, 2s, 3s, 2p, 3p and 3d, initial states, are given.
In comparison with dipole-dipole transitions, the number of quantum paths increases from: two to three for s-states; three to six for p-states; four to seven for d-states; while the number of angular coefficients goes from four to six, with two asymmetric terms. It is important that these asymmetric terms giving rise to the elliptic dichroism (ED), are only constituted with the imaginary part of the interference associated to the authorized channels leading to final states. Using the ED expression, we have established the phase shift isolation’s equation for l=0 instead of l=0,1, initial states, previously. Similarly, it is notable that, the submagnetic levels, m=0 for l=1; m=±1, for l=2, initial states, do not contribute to the PAD.
Numerical evaluation of the angular coefficients is given for each state. The PAD shapes and the ED signals have been analyzed. It is found that, the maxima or the minima and the directions, of the PAD (1s, 2s, 3s, 3p), depend on the competing angular coefficients, which in return are affected by the interference terms. It is interesting to note that ,the asymmetric terms contribute only when the PAD maxima are shifted from the semi major or semi minor axes(2p,3d);and the isotropic shape(1s,2s,2p,3p,3d) is strongly dependent on the isotropic term. It is also observed that, when the photoelectron has a preference for the left handed or the right handed, the azimuthal detection difference between these two limit angles is reduced of one half than that obtained for dipole-dipole transitions. The highest ED signal (2p, 3p), occurs from the combination of the strong contributing asymmetric terms with the competing four first PAD terms. Besides, for 1s initial state, a nonzero ED signal is observed, at a particular value of the phase lag matching the phase shifts difference, for nearly circularly and nearly linearly polarized light.