Maximum directivity of arbitrary dipole arrays

A fully analytical form, more general than any reported previously, for the optimum current distribution and maximum directivity of an arbitrary array consisting of dipoles parallel with each other, is derived. For an array configuration consisting of several hundred elements, a calculation takes a fraction of a second making many-element superdirective arrays candidates for adaptive antenna applications. Examples for two-dimensional (2D) and 3D arrays are given and some earlier superconductive arrays are revisited. It is also shown in further examples that superconductivity is not incompatible with moderate values of the quality factor.