Reciprocity in reflection and transmission of light

The manifestation of the time-reversal symmetry in the optical response is considered. Using the formulation of the reciprocity law for unpolarized light, the symmetry in the coherent reflection and/or transmission matrix R and the Stokes matrix Q is deduced by analyzing a gedanken measurement for the R or Q matrix. Implications of the combined time-reversal and spatial symmetry are studied for oblique specular reflection, forward transmission and, more extensively, for the normal-incidence reflection. The case of chiral gyrotropic media is discussed, and it is shown that a circular dichroism is symmetry allowed if the normal-incidence reflection leads to a partial depolarization of the beam. Nonreciprocity in the optical response is discussed. Phenomenological symmetry analysis of the experiments searching for the time-reversal-symmetry violation in high-${\mathit{T}}_{\mathit{c}}$ superconductors is presented.