  The solution of polarized radiative transfer equation with angle-dependent
(AD) partial frequency redistribution (PRD) is a challenging problem. Modeling
the observed, linearly polarized strong resonance lines in the solar spectrum
often requires the solution of the AD line transfer problems in one-dimensional
(1D) or multi-dimensional (multi-D) geometries. The purpose of this paper is to
develop an understanding of the relative importance of the AD PRD effects and
the multi-D transfer effects and particularly their combined influence on the
line polarization. This would help in a quantitative analysis of the second
solar spectrum (the linearly polarized spectrum of the Sun). We consider both
non-magnetic and magnetic media. In this paper we reduce the Stokes vector
transfer equation to a simpler form using a Fourier decomposition technique for
multi-D media. A fast numerical method is also devised to solve the concerned
multi-D transfer problem. The numerical results are presented for a
two-dimensional medium with a moderate optical thickness (effectively thin),
and are computed for a collisionless frequency redistribution. We show that the
AD PRD effects are significant, and can not be ignored in a quantitative fine
analysis of the line polarization. These effects are accentuated by the finite
dimensionality of the medium (multi-D transfer). The presence of magnetic
fields (Hanle effect) modifies the impact of these two effects to a
considerable extent.
