HIGHLY DIRECTIVE CURRENT DISTRIBUTIONS - GENERAL-THEORY

A theoretical scheme for studying the properties of localized, monochr omatic, and highly directive classical current distributions in two an d three dimensions is formulated and analyzed. For continuous current distributions, it is shown that maximizing the directivity D in the: f ar field while constraining C=N/T,where N is the integral of the squar e of the magnitude of the current density and T is proportional to the total radiated power, leads to a Fredholm integral equation of the se cond kind for the optimum current. This equation is a useful analytica l tool for studying currents that produce optimum directivities above the directivity of a uniform distribution. Various consequences of the present formulation are examined analytically for essentially arbitra ry geometries of the current-carrying region. In particular, certain p roperties of the optimum directivity are derived and differences betwe en the continuous and discrete cases are pointed out. When C-->infinit y, the directivity tends to infinity monotonically, in accord with Ose en's ''Einstein needle radiation.''