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Physical Review A

Nondipole effects in the angular distribution of photoelectrons in two-photon two-color above-threshold atomic ionization

Alexei N. Grum-Grzhimailo, Грызлова Елена Владимировна

Published Apr 23, 2014• 22 citations
Publisher

Abstract

Expressions for the angular distribution of photoelectrons produced in two-photon two-color atomic ionization are obtained within the statistical tensor formalism, taking into account a full multipole expansion of the radiation in electric and magnetic moments. The general expressions are reduced to a simpler form for a particular geometry used in experiments with XUV + optical radiation beams and analyzed within the first-order nondipole corrections for different polarization states of the photons. As a numerical example, the Ne $1s$ above-threshold ionization by two-color radiation is considered within the second-order perturbation theory. A large forward-backward asymmetry in the photoelectron angular distribution is predicted.

DOI
10.1103/physreva.89.043424

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Expressions for the angular distribution of photoelectrons produced in two-photon two-color atomic ionization are obtained within the statistical tensor formalism, taking into account a full multipole expansion of the radiation in electric and magnetic moments. The general expressions are reduced to a simpler form for a particular geometry used in experiments with XUV + optical radiation beams and analyzed within the first-order nondipole corrections for different polarization states of the photons. As a numerical example, the Ne 1s1s1s above-threshold ionization by two-color radiation is considered within the second-order perturbation theory. A large forward-backward asymmetry in the photoelectron angular distribution is predicted.
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.
The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.
The angular correlation between the photoelectron and subsequent polarized fluorescent radiation measured in coincidence is analysed theoretically for atomic photoionization. Using the density matrix and statistical tensor formalism the general expression for the correlation function is obtained for an arbitrary polarized incident photon beam. The particular geometry of a recent experiment (Beyer et al., 1995) is considered and the parameters which determine the angular correlation are expressed in terms of photoionization amplitudes. It is demonstrated that the photoelectron- (polarized) fluorescence coincidence measurements reveal strong circular and linear dichroism. As an example the photoionization of Ca atoms near the 4p 2P3/2 threshold is calculated within the framework of multichannel quantum defect theory.
We study nondipole effects in multiphoton ionization of a two-dimensional hydrogen-like atom by a flat-top laser pulse of varied intensity. For this purpose, we solve numerically a two-dimensional Schrödinger equation treating a propagating laser pulse exactly. The resulting distributions are then compared to those calculated in the dipole approximation. A directional dependence of the energy-angular photoelectron distributions is demonstrated numerically in the case of a propagating laser pulse of a moderate and a high intensity. It is analytically interpreted based on the leading order relativistic expansion of the electron Volkov state, showing a significant contribution of the electron recoil to that behavior. In contrast, the retardation correction originating from the space- and time-dependence of the laser field leads to a tiny redshift of the photoelectron energy spectra. Other features of ionization distributions are also analyzed, including the sidelobes and the double-hump structures of multiphoton peaks, or their disappearance for intense propagating laser pulses.
Within the framework of second order time dependent perturbation theory and non relativistic dipole approximation, the exact expressions of the radial transition amplitude from 3d, 3p and 3s excited states, were obtained from the integral representation of the Green Coulomb function. Below threshold and above one photon ionization threshold, it can be expressed as an analytic combination of three Appell hypergeometric functions of first order, one of which is degenerated; while at threshold, it can be obtained in terms of an expansion of Gauss confluent hypergeometric functions. The angular coefficients are numerically evaluated and analysed for some available laser wavelengths.
An experimental and theoretically study is performed of the angular photoelectron distribution for three-photon ionization of Ba atoms through the 2(omega) -excited intermediate state 6p2 (1So) and the auto- ionized state 6p8s(3P1). Rotation of the polarization plane of dye-laser radiation allowed us to investigate the photoelectron angular distribution. Electrons were counted with the help of a time-of-flight electron spectrometer. Employing the density-matrix formalism, expressions have been obtained for angular dependence of the differential ionizations probability. Possible experiments are discussed.