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We construct a classification of dispersion relations for the electromagneticwaves non-minimally coupled to the space-time curvature, based on the analysisof the susceptibility tensor, which appears in the non-minimal Einstein-Maxwelltheory. We classify solutions to the Fresnel equation for the model with atrace-free non-minimal susceptibility tensor according to the Petrov scheme.For all Petrov types we discuss specific features of the dispersion relationsand plot the corresponding wave surfaces.

Non-minimal Einstein-Maxwell theory: the Fresnel equation and the Petrov classification of a trace-free susceptibility tensor