Wave equations for Bi-anisotropic media in differential forms

Differential-form formalism appears to be an ideal tool for electromagnetic analysis because it allows one to express the basic electromagnetic laws in a most compact and elegant form. In fact, the Maxwell equations for the two electromagnetic two-forms are represented by two differential equations of first-order in the simplest possible form. Connection between the two-forms in a homogeneous and time-invariant linear medium is given by a simple algebraic equation. However, constructing the wave equation for a single electromagnetic two-form through elimination appears to be cumbersome and such an equation corresponding to the general bianisotropic medium could not be found in the literature. The present paper gives one possibility for its derivation based on operations in multivector and dyadic algebra. Two special media are considered in more detail leading to wave equations with scalar second-order and factorized fourth-order operators.