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Magnetoelectric materials have the interesting property of exhibitingpolarization induced by a magnetic field or magnetization induced by anelectric field. As a consequence, a multitude of effects can be produced bymeans of controllable external fields. A method for deriving phase velocitiesand its corresponding polarization vectors for light rays in nonlinear opticalmaterials in a nondispersive regime is here revisited and used to study wavepropagation in a certain class of second-order magnetoelectric media. Inparticular, the birefringence effect is theoretically examined and it is shownthat it can be used as a tool to obtain most of the second-ordermagnetoelectric coefficients $\beta_{ijk}$ of a material having an isotropiclinear sector. Estimates of the effect are presented. Some optical propertiesof nonlinear materials presenting a natural optic axis are also discussed.

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