The problem we discuss is that of directing an electromagnetic signal into a given three dimensional sector by prescribing electric current on the surface of an antenna in such a way that the power radiated through the sector is maximized. We will formulate this problem in terms of the partial differential equations governing the propagation of time harmonic electromagnetic waves in a region exterior to a closed bounded simply connected subset of ${\cal R}\sp3$. Although existence of an optimal solution is guaranteed for a variety of control domains, i.e., classes of surface functions subject to particular restrictions, we restrict our attention to surface currents in the ${\cal L}\sp2$ unit ball. A numerical scheme will be outlined and implemented for two control domains. Several sectors and antenna designs are used in the calculations. For each of these sectors and shapes, the results of the two control domains will be exhibited for comparison.