  Magnetoelectric phenomena are intimately linked to relativistic effects and
also require the material to break spatial inversion symmetry and time reversal
invariance. Magnetoelectric coupling can substantially affect light-matter
interaction and lead to non-reciprocal light propagation. Here, we confirm on a
fully experimental basis, without invoking either symmetry-based or
material-specific assumptions, that the optical magnetoelectric effect in
materials with non-parallel magnetization ($\boldsymbol{M}$) and electric
polarization ($\boldsymbol{P}$) generates a trilinear term in the refractive
index, $\delta
n\propto\boldsymbol{k}\cdot(\boldsymbol{P}\times\boldsymbol{M})$, where
$\boldsymbol{k}$ is the propagation vector of light. Its sharp magnetoelectric
resonances, that are simultaneously electric and magnetic dipole active
excitations, make Co$_{2}$Mo$_3$O$_8$ an ideal compound to demonstrate this
fundamental relation via independent variation of $\boldsymbol{M}$,
$\boldsymbol{P}$ and $\boldsymbol{k}$. Remarkably, the material shows almost
perfect one-way transparency in moderate magnetic fields at some of the
magnetoelectric resonances.
