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We investigate optical properties of bi-isotropic materials under the anomalous Hall effect (AHE) of the axion electrodynamics. Four refractive indices associated with circularly polarized waves are achieved, implying circular birefringence with rotatory power (RP) endowed with double sign reversal, an exotic optical signature for chiral dielectrics. The Kerr rotation and ellipticity are analyzed, with an unusual observation of rotation angle deprived of discontinuity. Anomalous reflection (greater than unity) is also reported, associated with negative refraction stemming from the anomalous transport properties. These effects constitute the singular optical signature of a bi-isotropic media with the AHE., Comment: 6 pages, 7 figures

Unmagnetized cold plasma modes are investigated in the context of the chiral Maxwell-Carroll-Field-Jackiw (MCJF) electrodynamics, where the axion chiral factor acts retrieving some typical properties of magnetized plasmas. The Maxwell equations are rewritten for a cold, uniform, and collisionless fluid plasma model, allowing us to determine the dispersion relation, new refractive indices and propagating modes. We find four distinct refractive indices modified by the purely timelike CFJ background that plays the magnetic conductivity chiral parameter role, associated with right-circularly polarized [RCP] and left-circularly polarized [LCP] waves. For each refractive index, the propagation and absorption zones are determined and illustrated for some specific parameter values. Modified RCP and LCP helicons are found in the low-frequency regime. The optical behavior is investigated, revealing that the chiral factor induces birefringence, measured in terms of the rotatory power (RP). The dichroism coefficient is carried out for the absorbing zones. The negative refraction zones may enhance the involved rotatory power, yielding RP sign reversion, a feature of rotating plasmas and MCFJ chiral plasmas., Comment: 14 pages, 15 figures

In this work, we investigate the reflection properties on the interface between an ordinary dielectric medium and a dielectric supporting a magnetic current (equivalent to a dielectric governed by axion electrodynamics). Considering the usual Maxwell equations and constitutive relations, we derive the general Fresnel coefficients for reflection for an incident wave with $s$ and $p$ polarization, assuming an isotropic magnetic current on a dielectric substrate. We determine all total internal reflection and critical angles (Brewster angles) conditions, which are given by strict relations between all relevant electromagnetic quantities of the system and the frequency. For $s$- and $p$-polarized incident waves, total internal reflection can occur under certain conditions on the constitutive parameters (for each propagating mode) at specific frequency windows and certain incidence angle intervals. All possible conditions to define critical angles for null reflection are determined. This scenario allows polarization changes by reflection. Considering a $p$-polarized incident wave, the frequency and the Brewster angle, allowing null reflection for both propagating modes, are determined. The Goos-H\"anchen shift and the complex Kerr rotation are also evaluated. The Kerr ellipticity angle presents a frequency-dependent behavior, also reported in Weyl semimetals, having maximum values $\eta_{Kerr}=\pm \pi/4$ for specific values of frequency, which may work as a signature of this axion chiral dielectric., Comment: 15 pages, 16 figures, 5 tables

We discuss how classical electromagnetic techniques are useful to describe optical effects in conventional and chiral dielectric systems endowed with optical activity. Starting from the Maxwell equations and constitutive relations of the medium, we obtain the wave equation (for the electric field) that yields the refractive indices and the corresponding propagating modes that define the electromagnetic wave polarization. This procedure is employed for bi-isotropic and bi-anisotropic dielectrics, allowing us to determine birefringence, a manifestation of the space or time inversion breaking, typical of the chiral media. Such a method can also be applied for axion electrodynamics and a dielectric supporting an isotropic chiral magnetic current, similar to the Chiral Magnetic Effect (CME). For a diagonal magnetic conductivity, two distinct refractive indices are found, associated with left circularly polarized (LCP) and right circularly polarized (RCP) waves, and yielding circular birefringence (evaluated in terms of the optical rotatory power). Additionally, the scenario of a bi-isotropic medium endowed with isotropic magnetic current is examined, where a rotatory power marked by sign reversal may work as an optical signature of this particular system., Comment: 15 pages, 4 figures

In this work, we study the propagation and absorption of plasma waves in the context of the Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics with a purely spacelike background playing the role of the anomalous Hall conductivity, concerning the anomalous Hall current. Such a current is also found in an axion field which increases linearly with a space coordinate. 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 analysis begins for propagation along the magnetic axis, examined in the cases of chiral vectors parallel and orthogonal to the magnetic field. Two distinct refractive indices (associated with right-handed circularly polarized [RCP] and left-handed circularly polarized [LCP] waves) are obtained and the associated propagation and absorption zones are determined. The low-frequency regime is discussed and we obtain RCP and LCP helicons. We scrutinize optical effects, such as birefringence and dichroism, and observe rotatory power sign reversion, a property of chiral MCFJ plasmas. We also examine the case of transversal propagation in the direction orthogonal to the magnetic field, providing much more involved results., Comment: 21 pages, 18 figures, 2 tables

The dispersive propagation and absorption in the domain of a Drude-Lorentz dielectric modified by a magnetic current are classically investigated, taking as the starting point the Drude electric permittivity, in connection with the chiral magnetic effect. Using standard electromagnetic methods, the dispersion relations and refractive indices are evaluated and discussed, as well as the group and the energy velocities. We consider three configurations for the magnetic conductivity tensor: isotropic, antisymmetric, and symmetric. In all these cases, we carry out the group velocity and the energy velocity, for investigating the properties of signal propagation. We observe that the isotropic magnetic conductivity enhances the signal propagation at low and intermediary frequencies, while the symmetric and antisymmetric conductivity severely constrains the wave propagation in these frequency windows., Comment: 16 pages, two columns, 13 figures

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., Comment: 23 pages, 2 columns, 10 figures, 3 tables

In this work, we study the propagation and absorption of plasma waves in the chiral Maxwell-Carroll-Field-Jackiw (MCJF) 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., Comment: revtex style, two columns, 19 figures, 19 pages, version published in the PRD

We review the propagation of electromagnetic waves in continuous matter in the presence of Lorentz-violating terms. First, we briefly discuss classical electrodynamics with regard to optical properties of a dielectric medium exhibiting the Chiral Magnetic Effect (CME). Such a medium can be modeled by Maxwell-Carroll-Field-Jackiw (MCFJ) theory. Second, we describe the impact of CPT-odd terms of mass dimensions three and five, respectively, on electromagnetic propagation in continuous matter. Birefringence and absorption are analyzed in the scenarios investigated. Our findings provide new insights into the interplay between classical field theory and optical effects in matter., Comment: Presented at the Ninth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, May 17-26, 2022

Bi-isotropic media constitute a proper scenario for scrutinizing optical effects stemming from magnetoelectric parameters. Chiral magnetic current is a macroscopic effect arising from the chiral magnetic effect that enriches the phenomenology of a classical dielectric medium. This work examines optical aspects of bi-isotropic media in the presence of magnetic conductivity. The full isotropic scenario manifests circular birefringence described by a dispersive rotatory power that changes sign at a given frequency. For a bi-isotropic medium with antisymmetric magnetic conductivity, an intricate dispersive rotatory power is attained, supplied with sign reversal as well. This scenario also indicates a handedness reversion of the medium, an unusual property in dielectrics, which may work as a signature of bi-isotropic media supporting chiral magnetic current., Comment: 9 pages, 3 figures

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., Comment: 20 pages, 2 columns, 7 figures. Accepted for publication in Physical Review A

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 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., Comment: Accepted version for publication in PRD. 24 pages, 2 tables, 9 figures

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 implies 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 insight into typical material properties associated with a magnetic conductivity., Comment: 19 pages, two columns, one table

We investigate dimension five Lorentz-violating nonminimal interactions in the electroweak sector, in connection with the possible generation of electric dipole moment (EDM), weak electric dipole moment (WEDM), magnetic dipole moment (MDM) and weak magnetic dipole moment (WMDM) for leptons. These couplings are composed of the physical fields and LV tensors of ranks ranging from 1 to 4. The CPT-odd couplings do no generate EDM\ behavior and do not provide the correct MDM\ signature, while the CPT-even ones yield EDM and MDM\ behavior, being subject to improved constraining. Tau lepton experimental data is used to constrain the WEDM\ and WMDM couplings to the level of $10^{-4}\left( \text{GeV}\right) ^{-1},$ whereas electron MDM and EDM data is employed to improve constraints to the level of $10^{-17}\left( \text{GeV}\right) ^{-1}$ and $10^{-11}\left( \text{GeV}\right) ^{-1},$ respectively., Comment: It contains 9 pages, 6 tables

In this work we focus on the Carroll-Field-Jackiw (CFJ) modified electrodynamics in combination with a CPT-even Lorentz-violating contribution. We add a photon mass term to the Lagrange density and study the question whether this contribution can render the theory unitary. The analysis is based on the pole structure of the modified photon propagator as well as the validity of the optical theorem. We find, indeed, that the massive CFJ-type modification is unitary at tree-level. This result provides a further example for how a photon mass can mitigate malign behaviors., Comment: 6 pages, 1 figure