Separable metamaterials: analytical ab-initio homogenization and chirality

We investigate the ab-initio homogenization of separable metamaterials with factorized dielectric permittivity profile which can be achieved through suitable grey-scale permittivity design techniques. Separability allows such metamaterials to be physically regarded as the superposition of three fictitious 1D generating media. We prove that, in the long-wavelength limit, separable metamaterials admit simple and analytical description of their electromagnetic bi-anisotropic response which can be reconstructed from the properties of the 1D generating media. Our approach provides a strategy which allows the full ab-initio and flexible design of a complex bianisotropic response by using 1D metamaterials as basic building blocks.