Optimal current, superdirectivity problem, and gain limitation of a 'real' dipole

A solution is presented to the problem of finding a dipole current distribution which corresponds to the maximum modulus of a specified field component at a fixed point in space. Either the radiation power or the total antenna input power are assumed to be constant. Integral equations are obtained for the optimal current, and it is shown that there exists a limit to the gain of a 'real' dipole. The proposed approach can be extended to other antenna types and synthesis problems.