Dispersion and absorption effects in the linearized Euler–Heisenberg electrodynamics under an external magnetic field

Abstract

In this paper, the effects of the Ohmic and magnetic density currents are investigated in the linearized Euler–Heisenberg (EH) electrodynamics (ED). The linearization is introduced through an external magnetic field, in which the vector potential of the EH ED is expanded around a magnetic background field that we consider uniform and constant in this paper. From the EH linearized equations, we obtain the solutions for the refractive index associated with the electromagnetic wave superposition, when the current density is ruled by the Ohm law, and in the second case, when the current density is set by an isotropic magnetic conductivity. These solutions are functions of the magnetic background [Formula: see text] of the wave propagation direction [Formula: see text]. It also depends on the conductivity and on the wave frequency. As a consequence, the dispersion and the absorption of plane waves change when [Formula: see text] is parallel to [Formula: see text] in relation to the case of [Formula: see text] perpendicular to [Formula: see text] in the medium. The characteristics of the refraction index are related to direction of [Formula: see text] and of the wave polarization, where there is an open discussion for the birefringence in this medium.