  Using the transfer matrix formalism, we study the transmission properties of
a Bragg grating constructed from a layered axionic material. Such a material
can be realized by a topological insulator subject to a time-symmetry breaking
perturbation, such as an external magnetic field or surface magnetic
impurities. Whilst the reflective properties of the structure are only
negligibly changed by the presence of the axionic material, the grating induces
a Faraday rotation and ellipticity in the transmitted light. We find that for
TM polarized light incident on a 16 layer structure at 76 degrees to the normal
the Faraday rotation can approach ~232 mrad (~13 degrees), whilst interference
from the multi-layered structure ensures high transmission. This is
significantly higher than Faraday rotations for the TM polarization at normal
incidences or the TE polarization at any incident angle. Thus, Bragg gratings
in this geometry show a strong optical signal of the magneto-electric and,
hence, provide an ideal system in which to observe this effect by optical
means.
