  Similar to the case of solar system planets, reflected starlight from
exoplanets is expected to be polarized due to atmospheric scattering and the
net disk integrated polarization should be non-zero owing to the asymmetrical
illumination of the planetary disk. The computation of the disk-integrated
reflected flux and its state of polarization involves techniques for the
calculation of the local reflection matrices as well as the numerical recipes
for integration over the planetary disks. In this paper, we present a novel
approach to calculate the azimuth-dependent reflected intensity vectors at each
location on the planetary disk divided into grids. We achieve this by solving
the vector radiative transfer equations that describe linear polarization. Our
calculations incorporate self-consistent atmospheric models of exoplanets over
a wide range of equilibrium temperature, surface gravity, atmospheric
composition, and cloud structure. A comparison of the flux and the amount of
polarization calculated by considering both single and multiple scattering
exhibits the effect of depolarization due to multiple scattering of light
depending on the scattering albedo of the atmosphere. We have benchmarked our
basic calculations against some of the existing models. We have also presented
our models for the hot Jupiter HD 189733 b, indicating the level of precision
required by future observations to detect the polarization of this planet in
the optical and near-infrared wavelength region. The generic nature and the
accuracy offered by our models make them an effective tool for modeling the
future observations of the polarized light reflected from exoplanets.
