Plane-parallel polarized radiative transfer in graded-index media via a lattice Boltzmann method

The polarized state of light scattered by media provides much more characteristic information than the intensity alone. Thus, numerous polarimetric measurements are carried out to understand the media characteristics. Polarized radiative transfer is used to interpret these polarimetric measurements and obtain the media parameters, where the plane-parallel approximation model is usually adopted. Meanwhile, the graded-index phenomenon is widespread in nature, and the curved ray trajectory in graded-index media makes the computation of polarized radiative transfer more challenging. A suitable and effective numerical tool is of great value. In this work, we propose a lattice Boltzmann method (LBM) for plane-parallel polarized radiative transfer in graded-index media. The rigorous mathematical relation between the vector radiative-transfer equation and the LB model is proved. The Stokes vector can be obtained by the LB model through simple collision and streaming processes. Numerical tests show that the present LBM is effective and accurate for plane-parallel polarized radiative transfer in graded-index media, and also applicable to polarized radiative transfer in uniform refractive-index media under the plane-parallel approximation. Furthermore, we adopt the LBM to investigate the remote sensing problem of the atmosphere-ocean system with graded-index seawater, and find that the observed Stokes vector in the graded-index atmosphere-ocean system is markedly different from that in homogeneous system.