  In this thesis, we re-assess some aspects of axionic electrodynamics by
coupling non-linear electromagnetic effects to axion physics. We present a
number of motivations to justify the coupling of the axion to the photon in
terms of a general non-linear extension of the electromagnetic sector. Our
emphasis in the paper relies on the investigation of the constitutive
permittivity and permeability tensors, for which the axion contribution
introduces a dependence on the frequency and wave vector of the propagating
radiation. Also, we point out how the axion mass and the axion-photon coupling
constant contribute to a dispersive behavior of the electromagnetic waves, in
contrast to what happens in the case of non-linear extensions, when effective
refractive indices appear which depend only on the direction of the propagation
with respect to the external fields. The axion changes this picture by yielding
refractive indices with dependence on the wavelength. We apply our results to
the special case of the Born-Infeld Electrodynamics and we show that it becomes
birefringent whenever the axion is coupled. We also include in our analysis the
Lorentz violation phenomenon through a Carroll-Field-Jackiw term, where we
investigate the influence of this sector on the dispersion relations, and
consequently, on the optical phenomena.
