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Journal of Experimental and Theoretical Physics

The polarization-angular structure and elliptical dichroism of the cross sections for three-photon bound-bound transitions in atoms

Nikolai L. Manakov, Alexey V. Meremyanin

Published Jun 1, 1997• 11 citations
Publisher

Abstract

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.

DOI
10.1134/1.558244

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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.
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.
A compact expression is derived for the cross section of scattering of arbitrarily polarized light by oriented atomic systems, in which the dependence on the geometric parameters and on the Stokes parameters preassigning the state of partial polarization of incident radiation is explicitly separated. It is found that the cross section of any photoprocess accompanied by photon absorption (stimulated emission) contains the sum of the products of the circular and linear dichroisms of the process by the respective Stokes parameters. The effect of the atomic orientation and of the dissipation of light energy on the polarization singularities and angular distribution of scattered light is investigated. In particular, it is demonstrated that, in the case of an open dissipation channel, the angular distribution remains dependent on the atomic orientation even in the case of zero degree of circular polarization of scattered radiation.
Within the framework of perturbation theory and of dipole approximation, the angular distribution for third order processes can be expressed for any state of quantum numbers (n, l) of the hydrogen atom as θθθ 642 coscoscos dcba +++; whatever the polarisation state (linear or circular). The explicit expressions of the corresponding angular coefficients are given for ns and np initial states. It is shown for the particular case of linear polarization that, the isotropic term a occurs only for initial states with orbital quantum number l greater than zero, and contains exactly twenty one contributing terms for np states; in the case of circularly polarized light, the distribution follows a sin6θ behaviour for ns states, while for np states, it is expressed as a combination of sin4θ and sin6θ. Using the implicit summation technique, nine radial transitions matrix elements are determined and a quantitative analysis of these coefficients is made for 1s, 2s, 3s, 2p and 3p initial states at various wavelengths, including the three photons ionization threshold; for linear polarization, the shapes are strongly dependent on both quantum numbers (n, l); while for circular polarization the shapes remain the same. Furthermore, the corresponding total cross sections obtained indirectly from these coefficients, are globally in agreement with that obtained directly from other methods.
The polarization dependence of the photoionization probability was analyzed in the case when a randomly oriented atom is irradiated by two crossing polarized monochromatic photon beams with the same frequency. It was found that the angular distributions of photoelectrons exhibit the effect of circular dichroism (CD), which consists of the dependence of the photoionization probability on the sign of the circular polarization degree of each beam. We demonstrate that the CD effect exists only for coherent crossing photon beams. It was shown that CD effects are strongly dependent on the phase difference between the electric field vectors of the photon beams and have a quite large magnitude. The possibilities of the experimental observation of CD effects are discussed.
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 expression for the cross section of scattering of an arbitrarily polarized light by aligned atomic systems is obtained, in which the dependence on the geometric parameters and the Stokes parameters specifying the state of partial polarization of the incident radiation is represented in explicit form. The effect of atomic alignment and the processes of dissipation of the light energy on the polarization specific features and the angular distribution of the scattered light is investigated. In particular, it is shown that, if a dissipative channel is accessible, the angular distribution and the degree of linear polarization of scattered light depend on the degree of circular polarization of the incident radiation η 2 . Dissipative processes also induce the circular polarization of the light scattered by aligned atoms when η 2 =0.