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The effects of the Ohmic and magnetic density currents are investigated inthe linearized Born-Infeld electrodynamics. The linearization is introducedthrough an external magnetic field, in which the vector potential of theBorn-Infeld electrodynamics is expanded around of a magnetic background field,that we consider uniform and constant in this paper. From the Born-Infeldlinearized equations, we obtain the solutions for the refractive indexassociated with the electromagnetic wave superposition, when the currentdensity is ruled by the Ohm law, and in the second case, when the currentdensity is set by a isotropic magnetic conductivity. These solutions arefunctions of the magnetic background $({\bf B})$, of the wave propagationdirection $({\bf k})$, and also it depends on the material conductivity, and onthe wave frequency. As consequence, the dispersion and the absorption of waveschange when ${\bf B}$ is parallel to ${\bf k}$ in relation to the case of ${\bfB}$ perpendicular to ${\bf k}$ in the material medium. These characteristics ofthe refraction index related to directions of ${\bf B}$ and ${\bf k}$ open adiscussion of the birefringence in the material medium.

Dispersion and absorption effects in the linearized Born-Infeld electrodynamics under an external magnetic field