Class of electromagnetic SD media

Applying the four-dimensional differential-form formalism the electromagnetic medium conditions can be represented in compact form through the medium dyadic mapping two-forms to two-forms. In the present paper one of the most basic classes of media is studied, the one defined by medium dyadics satisfying an algebraic equation of the second order (labeled as that of SD media). The general form of the medium dyadic in this class is derived and shown to involve 20 scalar medium parameters out of the 36 corresponding to the most general bi-anisotropic medium. Because each such medium dyadic defines two involutory linear transformations (called left- and right-hand duality transformations), in terms of which the medium dyadic is invariant (self-dual), the class can also be labeled as that of self-dual media. Further, the two eigen-two-forms of the medium dyadic are shown to be self-dual and anti-self-dual with respect to the two transformations. The eigenfields of the SD medium are shown to obey second-order differential equations. As a special case, the 10-parameter class of principal SD media is considered, which is shown to have no birefringence.