The magnetoelectric coupling in electrodynamics

We explore a model akin to axion electrodynamics in which the axion field theta(t, x) rather than being dynamical is a piecewise constant effective parameter theta encoding the microscopic properties of the medium inasmuch as its permittivity or permeability, defining what we call a theta-medium. This model describes a large class of phenomena, among which we highlight the electromagnetic response of materials with topological order, like topological insulators for example. We pursue a Green's function formulation of what amounts to typical boundary-value problems of theta-media, when external sources or boundary conditions are given. As an illustration of our methods, which we have also extended to ponderable media, we interpret the constant theta as a novel topological property of vacuum, a so called theta-vacuum, and restrict our discussion to the cases where the permittivity and the permeability of the media is one. In this way we concentrate upon the effects of the additional theta coupling which induce remarkable magnetoelectric effects. The issue of boundary conditions for electromagnetic radiation is crucial for the occurrence of the Casimir effect, therefore we apply the methods described above as an alternative way to approach the modifications to the Casimir effect by the inclusion of topological insulators.