  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. It is shown that the previously
known classes of generalized Q-media and generalized P-media are particular
cases of the proposed decomposable media (DCM) associated to a quadratic
equation for the medium dyadic. As a novel solution, another class of special
decomposable media (SDCM) is defined by a linear dyadic equation. The paper
further discusses the properties of medium dyadics and plane-wave propagation
in all the identified cases of DCM and SDCM.
