A general Monte Carlo method for polarized radiative transfer in multi-dimensional graded-index media

Lights propagate along space curved paths in multi-dimensional graded-index (GRIN) media, which induces a continuous change of their polarization state and makes the simulation of polarized radiative transfer more challenging. Existing methods are generally not suitable for simulating polarized radiative transfer in the media with arbitrary graded index distribution. In this paper, we present a general Monte Carlo (MC) method with the ray trajectories obtained by the Runge-Kutta ray tracing (RKRT) technique and investigate the polarized radiative transfer in multi-dimensional GRIN media with this method. The space curved trajectory of each light is discretized into a series of polylines, and the variation of polarization state along the trajectory is calculated by the transformations at each discrete point. The method is validated by the simulation of the polarized radiative transfer in a one-dimensional (1D) linear GRIN scattering medium. Furthermore, the 1D GRIN model is expanded to 2D and 3D GRIN models, and the polarized radiative transfer in both cases is investigated. Results show that, in the scattering media with multi-dimensional graded index distribution, the polarization state of lights has a notable effect on the radiative transfer, which must be taken into consideration in the fields requiring high-precision.