In general, the Stocks vector cannot be calculated in reverse in the vector radiative transfer. This paper presents a novel backward and forward Monte Carlo simulation strategy to study the vector radiative transfer in the participated medium. A backward Monte Carlo process is used to calculate the ray trajectory and the endpoint of the ray. The Stocks vector is carried out by a forward Monte Carlo process. A one-dimensional graded index semi-transparent medium was presented as the physical model and the thermal emission consideration of polarization was studied in the medium. The solution process to non-scattering, isotropic scattering, and the anisotropic scattering medium, respectively, is discussed. The influence of the optical thickness and albedo on the Stocks vector are studied. The results show that the U, V-components of the apparent Stocks vector are very small, but the Q-component of the apparent Stocks vector is relatively larger, which cannot be ignored.
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