Symmetry classification of temporal reciprocity in time-varying electromagnetic media

Abstract: Time-varying electromagnetic media exhibit rich nonstationary wave phenomena, but the symmetry governing reversal of arbitrary temporal modulation sequences has remained unclear. We show that, in lossless, spatially homogeneous media with identical initial and final states, the scattering matrices of ordered and reversed sequences are related by inverse--conjugation, independent of the number of stages. This yields a classification of temporal reciprocity in bi-isotropic media: isotropic and chiral media are channel-preserving, whereas Tellegen media are channel-exchanging despite Lorentz nonreciprocity. Deterministic time rewinding follows directly. Our results provide a framework for predicting and designing temporal scattering responses in photonic media.