Bounds on Metamaterials in Scattering and Antenna Problems

This paper reports on physical limitations on metamaterials in scattering and antenna problems. A dispersion relation for the extinction cross section is derived from the holomorphic properties of the forward scattering dyadic. The result states that for a given volume, there is only a limited amount of scattering and absorption available in the entire frequency range. The dispersion relation is verified numerically for the perfectly conducting circular disk, and theoretical bounds are illustrated for a plasmonic stratified sphere.