Theoretical and numerical analysis of polarization for time-dependent radiative transfer equations

Abstract

We consider the matrix-valued radiative transfer equations for the Stokes parameters for the propagation of light through turbulent atmospheres. A Monte Carlo method is introduced to solve the time dependent matrix-valued radiative transfer equations in 3D geometry. The Monte Carlo method is based on a probabilistic representation of the radiative transfer equations involving an augmented scalar transport equation where the polarization parameters are independent variables. The linear moments of the augmented transport equation with respect to the polarization parameters solve the matrix-valued radiative transfer equations. We show how polarization and depolarization effects develop in time for isotropic and unpolarized point sources, considered for concreteness in spherical and half-space geometries. We analyze in detail the creation of polarization by single- and multiple-scattering effects.