Effect of Elliptically Polarized Light on the Angular Distribution of Photoelectrons

The angular distribution of photoelectrons predicted for elliptically polarized light is shown to be the same as that predicted for partially polarized light having incoherent perpendicular electric field components equal to the electric field components along the major and minor axes of the ellipse. Increasing use by atomic experimenters of synchrotron radiation, which is known to be elliptically polarized (Sokolov and Ternov 1957, Joos 1960) and of metallic mirrors, which cause reflected light to be elliptically polarized (Jenkins and White 1957), has focused attention on the expected angular distribution of photoelectrons produced by elliptically polarized light. Schmidt (1973) has obtained an expression for the angular distribution of photoelectrons produced by elliptically polarized light that appears quite different from the expression obtained by Samson (1969, 1970) for photoelectrons produced by partially polarized light. We show here, however, that Schmidt’s formula reduces to that of Samson when one considers the electric vector components along the major and minor axes of the ellipse that characterizes the elliptically polarized beam as the two perpendicular, incoherent electric vector components of a partially polarized beam. We consider light incident along the z axis interacting with an unpolarized atom at the origin via the electric dipole interaction and ejecting a photoelectron along a direction described by the angles θx, θy, and θz (cf Figure 1). If the incident light is linearly polarized, then the angular distribution of photoelectrons produced in many such collisions is described by the differential cross section (Yang 1948, Cooper and Zare 1969): (1) In equation (1), σ is the total cross section, β is the asymmetry parameter, P2(cos θ) ≡ 3/2 cos2 θ – 1⁄2, and θ is measured from the electric vector of the incident light. Now by “partially polarized light,” we mean partially linearly polarized light because partially circularly polarized light is equivalent to unpolarized light plus circularly polarized light, and circularly polarized light gives the same photoelectron angular distribution as unpolarized light (Peshkin 1970, Jacobs 1972). Thus we may for our present purpose consider partially polarized light as equivalent to two incoherent linearly polarized beams vibrating along orthogonal axes (Born and Wolf 1959, § 10.8.2). 1806 e l l i p t i c a l l y p o l a r i z e d l i g h t & a n g u l a r d i s t r i b u t i o n o f p h o t o e l e c t r o n s 1807 The resulting angular distribution is thus obtained as the sum of two differential cross sections having the form of equation (1) :