Analytical expressions for the radiation emergent from a scattering medium exposed to a polarized laser beam

Abstract

Analytical expressions for the spatial variation of the radiation emergent from a multiple-scattering medium exposed to a polarized laser beam are developed. The medium is finite in the vertical direction and infinite in the radial direction. The three-dimensional radiative transfer is described by the vector transport equation. The intensity vector is comprised of the four Stokes parameters, and the scattering is described by a general phase matrix for randomly oriented particles with a plane of symmetry. The radiation incident on the upper surface is cylindrically symmetric, perpendicularly directed, collimated, and polarized, e.g. a Gaussian laser beam. Expressions for the reflection and transmission matrices are presented for this specific loading and the case of normally emergent radiation. Symmetry relationships and matrix rotations are applied to obtain special forms of the normal reflection and transmission matrices. This procedure allows part of the inverse transform to be performed analytically and the angular variation of the reflection and transmission matrices to be found explicitly. The emergent intensity for an unpolarized or circularly polarized beam depends on only the radius; the intensity distribution is two dimensional. For a linearly polarized laser beam, the intensity exhibits three-dimensional effects; the spatial variation of the backscattered and transmitted intensities depends on both the radius and azimuthal angle. Thus, the polarization of the incident radiation can cause the intensity distribution to be either two- or three-dimensional.