Constraints on Jones transmission matrices from time-reversal invariance and discrete spatial symmetries

摘要

Optical spectroscopies are most often used to probe dynamical correlations inmaterials, but they are also a probe of symmetry. Polarization anisotropies areof course sensitive to structural anisotropies, but have been much less used asa probe of more exotic symmetry breakings in ordered states. In this paper aJones transfer matrix formalism is discussed to infer the existence of exoticbroken symmetry states of matter from their electrodynamic response for a fullcomplement of possible broken symmetries including reflection, rotation,rotation-reflection, inversion, and time-reversal. A specific condition todistinguish the case of macroscopic time-reversal symmetry breaking isparticularly important as in a dynamical experiment like optics, one mustdistinguish $reciprocity$ from time-reversal symmetry as dissipation violatesstrict time-reversal symmetry of an experiment. Different forms of reciprocitycan be distinguished, but only one is a sufficient (but not necessary)condition for macroscopic time-reversal symmetry breaking. I show theconstraints that a Jones matrix develops under the presence or absence of suchsymmetries. These constraints typically appear in the form of an algebrarelating matrix elements or overall constraints (transposition, unitarity,hermiticity, normality, etc.) on the form of the Jones matrix. I work out anumber of examples including the trivial case of a ferromagnet, and the lesstrivial cases of magnetoelectrics and vector and scalar spin "chiral" states. Ishow that the formalism can be used to demonstrate that Kerr rotation must beabsent in time-reversal symmetric chiral materials. The formalism here isdiscussed with an eye towards its use in time-domain THz spectroscopy intransmission, but with small modifications it is more generally applicable.