Approximate solution to vector radiative transfer in gradient-index medium

Within a gradient-index medium, the radiative rays propagate in curved paths, which makes polarized states change continuously and the solution to the radiative transfer be thus more complex and difficult. In this paper, an arbitrary multilayer model is developed to approximately simulate vector (polarized) radiative transfer in a gradient-index plane-parallel medium. The gradient-index medium is divided into an arbitrary number of sublayers, and each sublayer has a uniform refractive index and two virtual Fresnel's interfaces where only transmission (refraction) is considered. Thus the polarization caused by the curved propagation of lights is approximated by that resulting from refraction on the interfaces. Radiative transfer with consideration of polarization caused by particle scattering and refraction (reflection) on the interfaces (surfaces) in the multilayer model is solved by the MC method. The grid independence of results obtained by the multilayer model for vector radiative transfer in gradient-index medium shows that the convergent solution of Stokes vector will be achieved provided that the sublayer number is large enough. The results for apparent emissivity of gradient-index medium and Stokes vector for two-layer medium are compared well with those in published literatures. Finally, we investigate polarized behaviors of radiative transfer in Rayleigh scattering slabs with linear and sinusoidal gradient indexes and present angular distributions of Stokes vector. Results show that total reflection inside the gradient-index medium resulting from the curved paths traveled by the photons affects greatly the angular distribution characteristics of Stokes vector. (C) 2014 Optical Society of America