Homogenization of Dielectric Photonic Quasi Crystals

Abstract

We adapt two-scale convergence to the homogenization of photonic quasi-periodic structures such as Penrose tilings. This convergence relies upon the irrational nature of a parameter characterizing a quasi-crystalline phase through its associated cut-and-projection matrix of permittivity: We generate quasi crystals by considering a periodic structure in an upper-dimensional space. We apply this tool to the homogenization of the vector Maxwell system.