Antisymmetric six-dyadics and BI-anisotropic media

Novel analytical methods are introduced for antisymmetric six-dyadics which form a linear space of 15 dimensions. By defining new multiplication operations analogous to those of the classical Gibbsian dyadics, algebraic handling of equations is greatly simplified. As an application, time-harmonic electromagnetic fields expressed in concise six-vector form are considered. A certain class of bi-anisotropic media, labeled as A media, is defined for which the six-dyadic Maxwell operator can be expressed in terms of an antisymmetric operator. It is shown that, applying six-dyadic identities, the corresponding antisymmetric six-dyadic Green function can be straightforwardly expressed in explicit form.