Generalized Jones & Mueller calculus for anisotropic media

The interaction of non-paraxial polarized light with anisotropic media is inherently 3-D, and described by the calculus of generalized Jones & Mueller matrix (GJM & GMM). However, existing two calculus treat the interaction as the paraxial transformation with 3-D rotation, neglecting the vector property of the local light path. This makes the calculus fail to produce correct results for 3-D polarization evolution. In this letter, we explore this vector property deeply and introduce a new GJM calculus that enables precise polarization modeling in arbitrary light path within anisotropic media, supplemented by a convinent mathematical approach to map to GMM calculus. Then, we performed an experiment to verify the new theories. The results consistent with simulations, which confirms the reliability of the new GJM & GMM as the basis calculus for 3-D polarization optics.