Magnetoelectric birefringence revisited

Electromagnetic wave propagation inside isotropic material media characterized by dielectric coefficients ${\epsilon }_{\mu \nu }(E,B)$ and ${\mu }_{\mu \nu }(E,B)$ is examined. The regime of the eikonal approximation is considered. The Hadamard method of field disturbances is used and the dispersion relations are obtained by solving the Fresnel equation. Some applications of the formalism are presented. Particularly, birefringence phenomena induced by applied external fields are derived and discussed. It is shown that magnetoelectric birefringence effect can occur even without the presence of Kerr and Cotton-Mouton effects, provided the physical system satisfies certain conditions.