Generalized reciprocal relations for transmission and reflection of light through a 1D stratified anisotropic metamaterial

Motivated by the recent demonstration of asymmetric transmission of light through stratified systems of various anisotropic metamaterials, we have established generalized reciprocal relations for both transmission and reflection for these systems referring to the two cases of incidence from opposite directions. These relations reduce to those derived previously for simple isotropic systems which guarantee reciprocal symmetry in both transmission and reflection for non-dissipative medium, and provide constraint for reflection from both sides in the presence of absorption. Illustrations of our generalized relations are provided for different material systems.