Mathematical analysis of transmission properties of electromagnetic meta-materials
Provides theoretical and numerical insights into wave propagation in meta-materials, relevant for designing devices with specific transmission properties.
The paper analyzes transmission properties of electromagnetic meta-materials using perfect conductors or high-contrast materials, calculating transmission/reflection coefficients for four geometries. Numerical experiments confirm qualitative predictions and demonstrate the applicability of a Heterogeneous Multiscale Method.
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.