Aspects of wave propagation in a nonlinear medium: birefringence and the second-order magnetoelectric coefficients

Magnetoelectric materials have the interesting property of exhibiting polarization induced by a magnetic field or magnetization induced by an electric field. As a consequence, a multitude of effects can be produced by means of controllable external fields. A method for deriving phase velocities and its corresponding polarization vectors for light rays in nonlinear optical materials in a nondispersive regime is here revisited and used to study wave propagation in a certain class of second-order magnetoelectric media. In particular, the birefringence effect is theoretically examined and it is shown that it can be used as a tool to obtain most of the second-order magnetoelectric coefficients $\beta_{ijk}$ of a material having an isotropic linear sector. Estimates of the effect are presented. Some optical properties of nonlinear materials presenting a natural optic axis are also discussed.