Classical electrodynamics as a tool to examine optical effects of chiral dielectrics and media with magnetic conductivity

We discuss how classical electromagnetic techniques are useful to describe optical effects in conventional and chiral dielectric systems endowed with optical activity. Starting from the Maxwell equations and constitutive relations of the medium, we obtain the wave equation (for the electric field) that yields the refractive indices and the corresponding propagating modes that define the electromagnetic wave polarization. This procedure is employed for bi-isotropic and bi-anisotropic dielectrics, allowing us to determine birefringence, a manifestation of the space or time inversion breaking, typical of the chiral media. Such a method can also be applied for axion electrodynamics and a dielectric supporting an isotropic chiral magnetic current, similar to the Chiral Magnetic Effect (CME). For a diagonal magnetic conductivity, two distinct refractive indices are found, associated with left circularly polarized (LCP) and right circularly polarized (RCP) waves, and yielding circular birefringence (evaluated in terms of the optical rotatory power). Additionally, the scenario of a bi-isotropic medium endowed with isotropic magnetic current is examined, where a rotatory power marked by sign reversal may work as an optical signature of this particular system.