Differential forms and bi-anisotropic media

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. However, equations involving bi-anisotropic media have practically never been studied in this formalism, which may be due to missing algebraic tools. Introducing multivector dyadic algebra, a useful toolbox is obtained with which one can formulate medium problems in compact form. Analysis of fields in some classes of media is briefly reviewed in this paper, showing that great simplification in the analysis can be attained through the differential-form formalism. For convenience, an appendix giving the notation and basic algebraic rules for multivectors and dyadics is added at the end of the article.