The dielectric permittivity ε and magnetic permeability μ are usually understood within the 3-vector representation of electrodynamics via the relations D → → = ε ε E → → and B → → = μ μ H → → , where E → → , B → → , D → → , and H → → are, respectively, the electric field, magnetic flux density, electric displacement, and magnetic field intensity, and where ε and μ could be matrices. On the other hand, general relativity is formulated in the language of 4-dimensional tensors. To obtain the tensorial optical metric, medium properties such as permittivity, permeability, and magnetoelectric couplings must first be promoted to 4-dimensional covariant tensors, and the electrodynamics of light propagation through such media residing within a background space-time must also be expressed in a compatible 4-dimensional way. Here, electrodynamic fields will be described in terms of differential forms, exterior algebra, and the exterior derivative. Similar to the way that 3-vectors are denoted with an arrow, as in E → → , 4-dimensional tensors will be denoted by bold symbols, for example E . The musical isomorphisms will be used to indicate raising and lowering of indices with the metric, and a dot notation is used to denote contraction on adjacent indices, e.g. u ⋅ ⋅ F = u α α F α α β β . The speed of light is set to c = 1 , and the vacuum permeability and permittivity are likewise set to 1.