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Optics and Spectroscopy

Manifestation of the second-order alignment in light scattering by polarized atoms

M. Ya. Agre

Published Feb 1, 2003• 1 citation
Publisher

Abstract

An expression for the cross section of light scattering by axisymmetrically aligned atomic systems is derived in a compact form. The cross section under consideration is proportional to the state multipole of the fourth rank. The effect of the second-order alignment determined by the fourth-rank state multipole on the polarization and the angular distribution of scattered light is investigated. The polarization of incident light can be arbitrary and, in the general case, is specified by the Stokes parameters. In particular, it is demonstrated that the second-order alignment cannot induce circular polarization of scattered light and does not influence the dissipation-induced effects of circular dichroism associated with the first-order alignment but leads to a change in the angular distribution and the degree of linear polarization of the scattered light.

DOI
10.1134/1.1555173

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An expression for the cross section of light scattering by axisymmetrically aligned atomic systems is derived in a compact form. The cross section under consideration is proportional to the state multipole of the fourth rank. The effect of the second-order alignment determined by the fourth-rank state multipole on the polarization and the angular distribution of scattered light is investigated. The polarization of incident light can be arbitrary and, in the general case, is specified by the Stokes parameters. In particular, it is demonstrated that the second-order alignment cannot induce circular polarization of scattered light and does not influence the dissipation-induced effects of circular dichroism associated with the first-order alignment but leads to a change in the angular distribution and the degree of linear polarization of the scattered light.
A compact expression is derived for the part of the cross section for light scattering by axisymmetrically polarized atomic systems proportional to the third-rank state multipole. The effect of the second-order orientation determined by this state multipole on the polarization and angular distribution of the scattered light is studied. The polarization of the incident light can be arbitrary and is specified by the Stokes parameters. A number of orientation effects in the scattering process are shown to be induced precisely by the second-order orientation. In particular, when nonpolarized light is scattered by an oriented atom, the scattering intensity in the perpendicular direction depends on the second-order orientation alone. The second-order orientation also preserves circular dichroism in the linear polarization of the forward-and back-scattered light.
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.
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.
The angular distribution and polarization of the resonance radiation are deduced for elliptically polar- ized light incident on an atomic system of arbitrary initial and intermediate total angular momenta. The incident and re-radiated light are characterized by Stokes's representation, which allows an immediate generalization to partially polarized incident radiation. The results follow closely in form those deduced for free electron (Rayleigh) scattering but give, in general, a rather smaller degree of anisotropy for the resonance radiation. The results also determine the complete correlation, in polarization and direction of propagation, of two successive quanta emitted by a radiating system
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.
Direct observability of polarization moments of a higher order—octupole orientation of atomic angular momenta (κ=3) and their hexadecapole alignment (κ=4)—from polarization of quadrupole radiation is discussed. The case when atoms are excited through dipole absorption of light producing orientation or alignment of angular momenta with κ=1 or 2 and higher polarization moments are induced by collisions with a beam of particles is considered. It is shown that differences in the laws of transformation of polarization moments of various ranks κ in rotations of coordinate axes allow us to select the pure contribution of the higher polarization moment under study from the signal of polarization of quadrupole emission by excluding the contribution of orientation or alignment with κ=1 or 2. Optimum systems of coordinate axes for the observation of octupole orientation from circular polarization of light and for the observation of hexadecapole alignment from linear polarization of light, in which the pure contribution of the higher polarization moment under study to polarization of quadrupole emission reaches its maximum, are calculated.