Thin \theta-films optics

A Chern-Simons theory in 3D is accomplished by the so-called $\theta$-term in the action, $(\theta/2)\int F\wedge F$, which contributes only to observable effects on the boundaries of such a system. When electromagnetic radiation interacts with the system, the wave is reflected and its polarization is rotated at the interface, even when both the $\theta$-system and the environment are pure vacuum. These topics have been studied extensively. Here, we investigate the optical properties of a thin $\theta$-film, where multiple internal reflections could interfere coherently. The cases of pure vacuum and a material with magneto-electric properties are analyzed. It is found that the film reflectance is enhanced compared to ordinary non-$\theta$ systems and the interplay between magneto-electric properties and $\theta$ parameter yield film opacity and polarization properties which could be interesting in the case of topological insulators, among other topological systems.