The class of decomposable media in four-dimensional representation

The well-known TE/TM decomposition of time-harmonic electromagnetic fields in uniaxial anisotropic media is generalized in terms of four-dimensional differential-form formalism by requiring that the field two-form satisfies an orthogonality condition with respect to two given bivectors. Conditions for the electromagnetic medium in which such a decomposition is possible are derived and found to define three subclasses of media. Two of the subclasses are defined by medium dyadics which satisfy certain equation of the second order while while the medium dyadic defining the third subclass satisfies an equation of the first order. One of the subclasses is previously known through an analysis applying three-dimensional Gibbsian dyadics. Dispersion equations for plane waves are derived and the corresponding eigenpolarizations are found for all three subclasses.