Aperture realizations of exact solutions to homogeneous wave equations

Summary form only given. It was shown that it is only the forward propagating (causal) components of any solution of the scalar homogeneous wave equation that are actually recovered from either an infinite- or a finite-sized aperture in an open region. The backward propagating (acausal) components result in an evanescent wave superposition that does not play a significant role in the radiation process. The exact, complete solution can be achieved only from specifying its values and its derivatives on the boundary of any closed region. By using those LW (localized wave) solutions whose forward propagating components have been optimized over the associated backward propagating terms, one can recover the desirable properties of these LW solutions over the extended near-field regions of a finite-sized, independently addressable, pulse-driven array. These results were illustrated with an extreme example, one dealing with the original solution which is superluminal and its finite aperture approximation, a sling-shot pulse.<>