Toward a cylindrical cloak via inverse homogenization

An effective cylindrical cloak may be conceptualized as an assembly of adjacent local neighborhoods, each of which is made from a homogenized composite material (HCM). The HCM is required to be a certain uniaxial dielectric-magnetic material, characterized by positive-definite constitutive dyadics. It can arise from the homogenization of component materials that are remarkably simple in terms of their structure and constitutive relations. For example, the components can be two isotropic dielectric-magnetic materials, randomly distributed as oriented spheroidal particles. By carefully controlling the spheroidal shape of the component particles, a high degree of HCM anisotropy may be achieved which is necessary for the cloaking effect to be realized. The inverse Bruggeman formalism can provide estimates of the shape and constitutive parameters for the component materials, as well as their volume fractions.