  We explore a model akin to axion electrodynamics in which the axion field
$\theta (t,\mathbf{x})$ 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.
