For simple electric (magnetic) anisotropy a single
function – one that maps a given direction of space to a specific value of
permittivity (permeability) – is able to describe the electromagnetic
behavior of the medium. Accordingly, the well-known classification of
non-magnetic anisotropic crystals, as either uniaxial or biaxial, depends
only on the characteristics of the permittivity function. However, when
studying metamaterials, we frequently deal with general anisotropy
characterized by two linear constitutive operators: the permittivity and
permeability functions. Using the mathematical language of Clifford
(geometric) algebra, we show – for general (reciprocal) anisotropy – that
the direct interpretation of those two constitutive operators cannot provide
an accurate description of the medium anymore. Namely, a new operator – one
that depends on both those two constitutive operators – is needed, thereby
leading to a new classification scheme. Therefore, although the
uniaxial/biaxial characterization is still possible, the corresponding
physical meaning is completely restated. Furthermore, a new concept – the
pseudo-isotropic medium – emerges as a natural consequence of the new
classification scheme.