We study in some detail the photoelectron angular distributions in two-colour three-photon ionization of the ground state hydrogen atom in its dependence on the polarizations of the two electromagnetic fields. We treat the particular case of photons propagating in the same direction and having elliptic polarizations with the same axes. The azimuthal distributions presented refer to the electrons emitted with momenta orthogonal to the photons direction. The calculations are done in nonrelativistic dipole approximation, in velocity gauge, using third-order perturbation theory. We show that the photoelectron azimuthal angular distributions have a fourfold symmetry only for identical linear or circular polarizations. In all the other cases the distribution has a twofold symmetry.
We study in some detail the photoelectron angular distributions in two-colour three-photon ionization of the ground state hydrogen atom in its dependence on the polarizations of the two electromagnetic fields. We treat the particular case of photons propagating in the same direction and having elliptic polarizations with the same axes. The azimuthal distributions presented refer to the electrons emitted with momenta orthogonal to the photons direction. The calculations are done in nonrelativistic dipole approximation, in velocity gauge, using third-order perturbation theory. We show that the photoelectron azimuthal angular distributions have a fourfold symmetry only for identical linear or circular polarizations. In all the other cases the distribution has a twofold symmetry.
We study dichroic effects in the two-photon ionization of hydrogen from its ground state due to the interaction with a bichromatic field of commensurate frequencies. The two field components have different polarization: one is linearly polarized and the other is circularly polarized. Circular dichroism in the angular distribution of the photoelectrons appears if the helicity of the circularly polarized field is reversed. Numerical results reveal the influence of the photon frequencies chosen on the circular dichroism in the azimuthal angular distribution of the ejected photoelectrons.
Based on analytical equations valid in perturbation theory, we study the process of ionization of the ground state of the hydrogen atom by the absorption of three photons, two of them being of the same frequency. Results are given for the total ionization rate and for the angular distribution of the ejected electrons, in a regime of frequencies in which two-colour two-photon ionization is not possible. The case of orthogonal photon polarizations, investigated in some detail, displays a strong dependence on the electron direction.
We study dichroic effects in the two-photon ionization of hydrogen from its ground state due to the interaction with a bichromatic field of commensurate frequencies. The two field components have different polarization: one is linearly polarized and the other is circularly polarized (CP). Circular dichroism (CD) in the angular distribution of the photoelectrons appears if the helicity of the CP field is reversed. Numerical results reveal the influence of the photon frequencies chosen on the CD in the azimuthal angular distribution of the ejected photoelectrons.
The angular distribution of the emitted electrons, following the two-photon ionization of hydrogen-like ions, is studied within the framework of second order perturbation theory and the Dirac equation. Using a density matrix approach, we have investigated the effects which arise from the polarization of the incoming light as well as from the higher multipoles in the expansion of the electron–photon interaction. For medium- and high- Z ions, in particular, the non-dipole contributions give rise to a significant change in the angular distribution of the emitted electrons, if compared with the electric dipole approximation. This includes a strong forward emission while, in the dipole approximation, the electron emission always occurs symmetrically with respect to the plane which is perpendicular to the photon beam. Detailed computations for the dependence of the photoelectron angular distributions on the polarization of the incident light are carried out for the ionization of H, and Xe 53+ and U 91+ (hydrogen-like) ions.
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.
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.