  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.
