Efficient homogenization of multicomponent metamaterials: chiral effects

We extend an efficient homogenization procedure based on a Haydock representation of the microscopic wave operator for the calculation of the macroscopic dielectric response of a periodic composite to the case of an arbitrary number of components of arbitrary composition. As a test, we apply our numerical procedure to the calculation of the optical properties of a Bouligand structure, made of a large number of anisotropic layers stacked on top of each other and progresively rotated. This system consitutes a photonic crystal with circularly polarized electromagnetic normal modes, naturally ocurring in the cuticle of several arthropods, and which has a gap for one polarization, which corresponds to the observation of circularly polarized strong metallic like reflections. Our numerical procedure is validated through its good agreement with the analytical solution for this simple chiral system.