Efficient Homogenization of Multicomponent Metamaterials: Chiral Effects

Herein, an efficient homogenization procedure is extended based on a Haydock representation of the microscopic wave operator for the calculation of the retarded macroscopic dielectric response of a binary periodic composite to the case of an arbitrary number of components of arbitrary composition. As a test, this numerical procedure is applied to the calculation of the optical properties of a Bouligand structure, made up of a large number of anisotropic layers stacked on top of each other and progressively rotated. This system constitutes a photonic crystal with circularly polarized electromagnetic normal modes, naturally occurring in the cuticle of several arthropods. It presents a gap for one helicity, which corresponds to the observation of circularly polarized strong metallic like reflections. This numerical procedure is validated through its good agreement with the results of alternative formulations, including an analytical solution for this simple chiral system.