Effective Maxwells equations in general periodic microstructures

We study the time harmonic Maxwell equations in a meta-material consisting of perfect conductors and void space. The meta-material is assumed to be periodic with period $eta > 0$; we study the behaviour of solutions $(E^{eta}, H^{eta})$ in the limit $eta to 0$ and derive an effective system. In geometries with a non-trivial topology, the limit system implies that certain components of the effective fields vanish. We identify the corresponding effective system and can predict, from topological properties of the meta-material, whether or not it permits the propagation of waves.