The non-birefringent limit of all linear, skewonless media and its unique light-cone structure

Based on a recent work by Schuller et al., a geometric representation of all skewonless, non-birefringent, linear media is obtained. The derived constitutive law is based on a "core", encoding the optical metric up to a constant. All further corrections are provided by two (anti-)selfdual bivectors, and an "axion". The bivectors are found to vanish if the optical metric has signature (3,1) - that is, if the Fresnel equation is hyperbolic. We propose applications of this result in the context of transformation optics and premetric electrodynamics.