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 shape. Closed-form expressions for the prolate and oblate spheroids are compared with Chu 's classical result for the sphere, and the effect of invoking metamaterials in the antenna design is discussed. The theory is illustrated by numerical simulations of a monopole antenna with a finite ground plane.