In this work we study how $CPT$-odd Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics as well as a dimension-5 extension of it affect the optical activity of continuous media. The starting point is dimension-3 MCFJ electrodynamics in matter whose modified Maxwell equations, permittivity tensor, and dispersion relations are recapitulated. Corresponding refractive indices are achieved in terms of the frequency and the vector-valued background field. For a purely timelike background, the refractive indices are real. Their associated propagation modes are circularly polarized and exhibit birefringence. For a purely spacelike background, one refractive index is always real and the other can be complex. The circularly polarized propagating modes may exhibit birefringence and dichroism (associated with absorption). Subsequently, we examine a dimension-five MCFJ-type electrodynamics, previously scrutinized in the literature, in a continuous medium. Following the same procedure, we find the refractive indices from a sixth-order dispersion equation. For a purely timelike background, three distinct refractive indices are obtained, one of them being real and two being complex. They are associated with two circularly polarized propagating modes that exhibit birefringence or dichroism, depending on the frequency range. Scenarios of propagation and absorption analogous to those found in dispersive dielectrics are also observed for purely spacelike background configurations. We conclude by comparing the dimension-three and five results and by emphasizing the richer phenomenology of the propagating modes in the higher-derivative model. Our results are applicable in the realm of Weyl semimetals.

The chiral magnetic effect (CME) has been investigated as a new transport phenomenon in condensed matter. Such an effect appears in systems with chiral fermions and involves an electric current generated by a magnetic field by means of an “exotic” magnetic conductivity. This effect can also be connected with extensions of the usual Ohm’s law either in magnetohydrodynamics or in Lorentz-violating scenarios. In this work, we study the classical propagation of electromagnetic waves in isotropic dispersive matter subject to a generalized Ohm’s law. The latter involves currents linear in the magnetic field and implies scenarios inducing parity violation. We pay special attention to the case of a vanishing electric conductivity. For a diagonal magnetic conductivity, which includes the CME, the refractive index is modified such that it leads to birefringence. For a nondiagonal magnetic conductivity, modified refractive indices exhibiting imaginary parts occur ascribing a conducting behavior to a usual dielectric medium. Our findings provide new insights into typical material properties associated with a magnetic conductivity.

In this work, we study the propagation and absorption of plasma waves in the chiral Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics. The Maxwell equations are rewritten for a cold, uniform, and collisionless fluid plasma model, allowing us to determine the new refractive indices and propagating modes. The cases of propagation parallel and orthogonal to the magnetic field are examined considering a purely timelike CFJ background that plays the role of the magnetic conductivity chiral parameter. The collective electromagnetic modes are associated with four distinct refractive indices associated with right-circularly polarized and left-circularly polarized waves. For each index, the propagation and absorption zones are illustrated for some specific parameter values. In low-frequency regime, we have obtained modified helicons with right- and left-circularly polarizations. The optical behavior is investigated by means of the rotatory power (RP) and dichroism coefficient. The existence of a negative refraction zone enhances the rotatory power. It is also observed RP sign reversal, a feature of rotating plasmas.

The Maxwell equations and the constitutive relations describe the classical propagation of electromagnetic waves in continuous matter. Here, we investigate the effects stemming from extended constitutive relations on the propagation of waves in bi-isotropic and bi-anisotropic media using a classical general approach based on the evaluation of dispersion relations and refractive indices. For the bi-anisotropic media, we specify two classes of magnetoelectric parameters represented by symmetric and antisymmetric tensors. The three cases examined have provided real and distinct refractive indices for two propagating modes, which implies birefringence. The propagating modes were also carried out in all cases. The anisotropy or birefringence effect, given by the rotatory power or phase difference, was evaluated in terms of the magnetoelectric parameters of the theory in each case. The propagation orthogonal to the vectors used to parametrize the symmetric and antisymmetric magnetoelectric tensors is described by distinct modes, representing a route to identify the kind of bi-anisotropic medium examined. The group velocity and Poynting vector were also evaluated for all the cases examined to discuss the energy propagation in these anisotropic media.

We examine a dielectric medium supporting a magnetic current in connection with optical properties and energy propagation. The dispersion relations, propagating modes, and some optical effects are examined for isotropic and anisotropic magnetic conductivity tensors, with the latter ones implying nonreciprocal permittivities. The eigenvalues of the effective permittivity are carried out and associated with the optical symmetries (uniaxial, biaxial) and the subjacent crystal systems. Aspects of electromagnetic energy transport for such systems are also discussed, with the group and energy velocities being presented and carried out for all the particular cases addressed. Our results suggest that a dielectric supporting magnetic current breaks the usual equivalence between group velocity and energy velocity that holds in a nonabsorbing medium, while establishing the equivalence between them in an effective absorbing scenario, two unexpected behaviors.