Classical Approaches to Chiral Polaritonics

We provide a theoretical framework based on classical electromagnetism, to describe optical properties of Fabry-P\'erot cavities, filled with multilayered and linear chiral materials. We find a formal link between transfer-matrix, scattering-matrix and Green-function approaches to compute the polarization-dependent optical transmission, and cavity-modified circular dichroism signals. We show how general symmetries like Lorentz reciprocity and time-reversal symmetry constrain the modelling of such cavities. We apply this approach to investigate numerically and analytically the properties of various Fabry-P\'erot cavities, made of either metallic or helicity-preserving dielectric photonic crystal mirrors. In the latter case, we analyze the onset of chiral cavity-polaritons in terms of partial helicity-preservation of electromagnetic waves reflected at the mirrors interfaces. Our approach is relevant for designing innovative Fabry-P\'erot cavities for chiral-sensing, and for probing cavity-modified stereochemistry.