Physical limitations on antennas: isoperimetric inequalities and the effect of metamaterials
In this paper, physical limitations on antennas are presented based on the holomorphic properties of the forward scattering dyadic. As a direct consequence of causality and energy conservation, a forward dispersion relation for the extinction cross section is established, and isoperimetric inequalities for the partial realized gain and partial directivity are derived for antennas of arbitrary shap