Investigations into optical phenomena associated with nonlinear magnetoelectric effects are attracting growing attention within the scientific community. Technologies constantly demand new materials capable of exhibiting precise and controllable responses to external electromagnetic fields. In this context, the optics of such materials is of remarkable importance. Here, working in a lossless and nondispersive regime, electromagnetic wave propagation in materials presenting linear and nonlinear optical coefficients is investigated. We expand the discussion of the roles of nonlinear coefficients by examining special cases in which the contribution of the magnetoelectric optical coefficients ${\alpha }_{ij}$, ${\beta }_{ijk}$, and ${\gamma }_{ijk}$ to birefringence and nonreciprocal phenomena is elucidated. Notably, expressions that directly connect the magnetoelectric coefficients to the refractive indices of the medium are fully derived. These expressions enable the direct measurement of all components of each nonlinear magnetoelectric coefficient, providing an advancement over previous works. This development bridges theoretical models with experimental applications, offering possibilities for the optical characterization of magnetoelectric effects.

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• Classical optics
• Non-reciprocal propagation
• Optical materials & elements