Optical properties of Chern-Simons (3 +1 )D θ -systems

Chern-Simons (CS) $\ensuremath{\theta}$-systems are described by a $\ensuremath{\theta}\ensuremath{\int}F\ensuremath{\wedge}F$ term in the action ($\ensuremath{\theta}$ is an adimensional parameter), which does not change field equations in the bulk, but affects the system behavior when it is bounded. When two of those $\ensuremath{\theta}$-systems, each one characterized by a different value of $\ensuremath{\theta}$ (even zero), share a common boundary, surface effects are then induced by a CS $\ensuremath{\theta}$ term. Here, we study the consequences of the above in the propagation of electromagnetic radiation in $\ensuremath{\theta}$-systems. In a previous paper, electromagnetic radiation properties traversing a $\ensuremath{\theta}$-vacuum were analyzed, where a number of interesting features arise related to polarization and energy distribution. Now, we investigate how electric and magnetic properties of the $\ensuremath{\theta}$-system affect the optical response. Apart from the well-known Kerr polarization rotation found for the particular case of topological insulators, we examine in detail the issue, and the results could be applied in other contexts where the $\ensuremath{\theta}$ term accounts for the system dynamics. In particular, we find two different Brewster angles, for $s$ and $p$ polarization of reflected radiation, respectively, with peculiar features derived from the $\ensuremath{\theta}$ term influence. Possible applications of these results are discussed.