A study was undertaken into Voigt wave propagation in a homogenized composite material (HCM). The HCM investigated arose from a porous electro-optic host material infiltrated by a fluid of refractive index na, considered in the long-wavelength regime. The extended Bruggeman homogenization formalism was employed to estimate the constitutive parameters of the HCM. In principle, the directions which support Voigt wave propagation in the HCM may be controlled by means of an applied dc electric field; and the degree of control may be sensitive to the porosity of the host material, the shapes, sizes and orientations of the pores, as well as the refractive index na. Here the theoretical methodology is presented; numerical results are presented elsewhere.