}=\frac{1}{2}\epsilon ^{\mu \nu \alpha \beta }
F_{\alpha \beta }$ and $\epsilon ^{\mu \nu \alpha \beta }$ is the Levi-Cività symbol. In general $\theta$ can be a dynamical field, however, we will take it as a constant scalar, making Eq. (\[FF\*\]) a pseudo-scalar. Note that this extension is a total derivative, producing no contribution to the field equations when usual boundary conditions are met. If $\theta$ is not globally constant in the manifold where the theory is defined, then the CS-term fails to be a topological invariant and therefore the corresponding modifications to the field equations must be taken into consideration.

Here we will study Maxwell theory extended by Eq. (\[FF\*\]) defined on a manifold in which there are two domains defined by their different constant values of $\theta$ that are separated by a common interface or boundary $\Sigma$. The $\theta$-term can be thought of as an effective parameter characterizing properties of a novel electromagnetic vacuum possibly arising from a more fundamental theory or, as applied to material media, as an effective macroscopic parameter to describe novel quantum degrees of freedom of matter apart from the usual permittivity $\varepsilon$ and permeability $\mu$. The former approach has been taken in the context 