Eletrodinâmicas estendidas em meios contínuos e efeitos ópticos

Abstract

In this work, we discuss the electromagnetic propagation and optical properties in dielectric media governed by an extended electrodynamics by means of modified constitutive relations or higher derivatives. We study polarization, modes of propagation, birefringence, optical rotation and dichroism through Maxwell’s Classical Electrodynamics, within the framework of Classical Field Theory. First we present in chapter 2 the basic mathematical tools which are used throughout this work. In chapter 3, we comment about the chiral magnetic effect (CME), the generation of a macroscopic electric current in the presence of a magnetic field due to an asymmetry between the number density of left- and right-handed fermions in the system. Such an effect is, on the one hand, and the optical properties of continuous media, on the other hand, is a strong motivation for our investigation. Here we propose a generalization of Ohm’s law in order to describe isotropic and dispersive media endowed with a magnetic conductivity. For the case of an isotropic magnetic conductivity, which includes the CME, the refractive indices are modified, implying birefringence. For the scenarios of a non-diagonal magnetic conductivity, the modified refractive indices exhibit imaginary pieces, ascribing conducting behavior to a usual dielectric medium. In chapter 4, we investigate the effects originating from extended constitutive relations on electromagnetic-wave propagation in bi-isotropic and bi-anisotropic media, by calculating dispersion relations and refractive indices. For the bi-anisotropic media, we specify two classes of magnetoelectric parameters represented by symmetric and antisymmetric tensors. The anisotropy of the birefringence effect is determined through the rotatory power or the phase shift, which are evaluated in terms of the magnetoelectric parameters. We also discuss the group velocities and Poynting vector in each case. In chapter 5, we investigate the rotatory-power reversal effect on bi-isotropic media in the presence of a magnetic conductivity. For the case of an isotropic conductivity, birefringence occurs, described by the dispersive rotatory power that changes its sign at a given frequency. For the case of an antisymmetric conductivity, one obtains the corresponding rotatory power and dichroism coefficients for the both scenarios of null and non-null Ohmic conductivity. All these cases indicate a chirality reversal of the medium when the magnetic conductivity is isotropic, and that anisotropies in the magnetic current can prevent chirality reversal. In chapter 6, we study how the CPT-odd Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics and its dimension-5 extension modify the optical behavior of continuous media. We start by reviewing the MCFJ model in a dielectric medium, determining the modified Maxwell equations and dispersion relations. For the purely timelike case, the refractive indices are real, exhibiting birefringence, and the propagation modes are described by circularly polarized vectors. In the purely spacelike case, one refractive index is always real and the other one may be complex. The circularly polarized propagation modes may exhibit birefringence and dichroism. Fo the MCFJ model modified by the CPT-odd terms of dimension 5, also discussed in chapter 6, we determine the refractive indices from a sixth order dispersion equation. For the purely timelike case, we obtain three refractive indices, one being real and the other complex conjugates of each other. These refractive indices are associated with two circularly polarized propagation modes. Furthermore, depending on the frequency regime, one obtains birefringence and dichroism. In the purely spacelike case, we find scenarios of electromagnetic propagation analogous to those that occur in dispersive dielectrics.