Differential-Form Electromagnetics and Bi-Anisotropic Q-Media

Abstract

It is known that differential-form formalism in four dimensions gives the simplest possible representation to the Maxwell equations. The constitutive equation for the general linear (bi-anisotropic) medium is a relation between the two electromagnetic two-forms through a medium dyadic of the Hodge type. It was previously shown that when the medium dyadic satisfies a certain simple condition, the wave equation for the electromagnetic two-form reduces to one with a second-order scalar operator. The corresponding class of bi-anisotropic media ('Q-media') allows one to solve the basic electromagnetic problem analytically. In this paper we find the corresponding conditions for the four three-dimensional medium dyadics familiar in the Gibbsian vector analysis. Repeated use of multivector and dyadic identities is made in deriving the conditions which can be identified with those recently defined for time-harmonic problems in the literature. As an example, the solution for the potential of an impulsive point source in a Q-medium is given.