Observation of Magnetoelectric Directional Anisotropy

We report the first observation of a new optical phenomenon, magnetoelectric directional anisotropy (MEA). MEA is a polarization-independent anisotropy which occurs in crossed electric field $\mathbf{E}$ and magnetic field $\mathbf{B}$ perpendicular to the wave vector $\mathbf{k}$ of the light. It is described by a contribution to the refractive index of the form $\delta n=\gamma \mathbf{k}·\mathbf{E}\times \mathbf{B}$. Our experiment was performed on a $\mathrm{E}{\mathrm{r}}_{\mathrm{1.5}}{\mathrm{Y}}_{\mathrm{1.5}}\mathrm{A}{\mathrm{l}}_{\mathrm{5}}{\mathrm{O}}_{\mathrm{12}}$ crystal, but MEA should exist in all media. The relation of this new effect with recently discovered magnetoelectric birefringence is discussed.