  We study time-harmonic Maxwell's equations in meta-materials that use either
perfect conductors or high-contrast materials. Based on known effective
equations for perfectly conducting inclusions, we calculate the transmission
and reflection coefficients for four different geometries. For high-contrast
materials and essentially two-dimensional geometries, we analyze parallel
electric and parallel magnetic fields and discuss their potential to exhibit
transmission through a sample of meta-material. For a numerical study, one
often needs a method that is adapted to heterogeneous media; we consider here a
Heterogeneous Multiscale Method for high contrast materials. The qualitative
transmission properties, as predicted by the analysis, are confirmed with
numerical experiments. The numerical results also underline the applicability
of the multiscale method.
