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.