Biaxial mediums in the form of naturally occurring orthorhombic, monoclinic and triclinic crystals are of long-standing scientific and technological importance. We consider the conceptualization of artificial biaxial mediums, through the homogenization of simple component mediums. Biaxiality in homogenized composite mediums originates from two noncollinear distinguished axes presented by the component mediums; these distinguished axes can have either an electromagnetic or topological origin. The relationship between the biaxial composite structure and the geometry, orientation and composition of the component mediums is explored for the nondissipative dielectric case. Extending these studies to include the effects of dissipation in dielectric-magnetic materials, a generalized biaxial composite structure is revealed for which the principal axes of real and imaginary parts of the permittivity and permeability constitutive dyadics do not coincide. Furthermore, in the bianisotropic regime, yet more general HCM structures arise; in particular, complex symmetries are presented in the constitutive dyadics which would not be anticipated from a familiarity with the dielectric or dielectric-magnetic case.
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