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Journal of Physics B Atomic Molecular and Optical Physics

Elliptic dichroism and angular distribution of electrons in two-photon ionization of atoms

Nikolai L. Manakov, A. Maquet, S. I. Marmo, Valérie Vëniard, G. Ferrante

Published Aug 3, 1999• 41 citations
Publisher

Abstract

The three-dimensional angular distribution of electrons in two-photon ionization of atoms by an elliptically polarized laser beam, from an initial state with arbitrary angular momentum J i , is expressed in terms of six frequency-dependent invariant atomic parameters. The specific effect of the field polarization on the angular distribution (the elliptic dichroism, ED) is discussed for the general case of elliptic polarization. The necessary conditions for a non-zero ED are established and its physical origin is explained. The general theory is illustrated by a simple analytical calculation for the -potential model. Numerical calculations of the angular distribution parameters for H and Cs atoms are also performed and the dependence of ED magnitude on the atomic quantum numbers and the photon frequency is discussed for different frequencies.

DOI
10.1088/0953-4075/32/15/308

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The three-dimensional angular distribution of electrons in two-photon ionization of atoms by an elliptically polarized laser beam, from an initial state with arbitrary angular momentum J i , is expressed in terms of six frequency-dependent invariant atomic parameters. The specific effect of the field polarization on the angular distribution (the elliptic dichroism, ED) is discussed for the general case of elliptic polarization. The necessary conditions for a non-zero ED are established and its physical origin is explained. The general theory is illustrated by a simple analytical calculation for the -potential model. Numerical calculations of the angular distribution parameters for H and Cs atoms are also performed and the dependence of ED magnitude on the atomic quantum numbers and the photon frequency is discussed for different frequencies.
Using the electric dipole approximation, we present, in invariant form, the cross section of an arbitrary three-photon transition between the discrete states of an atom with total angular momenta J i and J f . The cross section contains scalar and mixed products of the photon polarization vectors, and invariant atomic parameters dependent only on the photon frequencies. We determine the number of independent atomic parameters at fixed values of J i and J f and obtain their explicit expressions in terms of the reduced composite dipole matrix elements. The polarization dependence of the cross sections is expressed in terms of the degrees l and ξ of linear and circular photon polarizations. We analyze the phenomenon of dissipation-induced circular dichroism in three-photon processes, i.e., the difference Δ of the cross sections for opposite signs of the degree of circular polarization of all the photons. We study in detail the case of two identical photons and the phenomenon of elliptical dichroism, when Δ∼ lξ holds and dichroism occurs only when the photons are elliptically polarized, with 0<| ξ |<1. Finally, we discuss the dissipation-induced effects of atom polarization in three-photon processes involving linearly polarized or unpolarized photons.
Elliptical dichroism is known in atomic photoionization as the difference in the photoelectron angular distributions produced in nonlinear ionization of atoms by left- and right-handed elliptically polarized light. We theoretically demonstrate that the maximum dichroism |Δ_{ED}|=1 always appears in two-photon ionization of any atom if the photon energy is tuned in so that the electron emission is dominantly determined by two intermediate resonances. We propose the two-photon ionization of atomic helium in order to demonstrate this remarkable phenomenon. The maximum elliptical dichroism could be used as a sensitive tool for analyzing the polarization state of photon beams produced by free-electron lasers.
In multiphoton ionization of atoms, elliptical dichroism may arise in the photoelectron angular distributions due to the interference of the possible ionization pathways. We here consider the interaction of atoms with an elliptically polarized biharmonic ($\ensuremath{\omega} + 2\ensuremath{\omega}$) field which simultaneously allows one- and two-photon ionization of the atoms. The interference between these two ionization pathways introduces contributions to the elliptical dichroism in addition to the dichroism that arises from the two-photon ionization alone. We show that these additional dichroism contributions can lead to a stronger dichroism in comparison to the one arising from two-photon ionization only. We present a relativistic analysis of the corresponding photoelectron angular distributions and discuss individual contributions to the dichroic phenomena. Detailed computations have been performed for biharmonic ionization of neutral helium atoms.
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.
A compact invariant expression for the angular distribution of photoelectrons escaping from unpolarized atoms and molecules in the process of two-photon ionization is derived on the basis of the general symmetry considerations. The dependence on all geometric parameters is completely separated in the angular distribution. It is shown that the circular dichroism effect can be observed in the angular distribution of photoelectrons escaping from the optically active molecules, while the specific elliptical dichroism effect only remains for the optically inactive molecules and atoms. The invariant expression for the total probability of two-photon ionization of axisymmetrically polarized (oriented and aligned) atomic systems is also derived, and caused by the orientation and alignment effects of circular and elliptical dichroism are analysed.
The theory of two-photon ionization of a hydrogenic state in the nonrelativistic dipole approximation is generalized for elliptically polarized light. An application to the metastable 2S state of atomic hydrogen is made. Significant differences in the angular distribution of the outgoing electrons are found depending upon the polarization of the photons. It is claimed that two-photon ionization employing elliptically polarized photons from lasers may provide an additional test for the theories of multiphoton ionization.