Reply to Comments on "Generation of focused, nonspherically decaying pulses of electromagnetic radiation"

The criticism made by Hannay [preceding Comment, Phys. Rev. E 62, 3008 (2000)] is unfounded since the steps, familiar from the subluminal regime, that are taken in his argument are not mathematically permissible when the distribution pattern of the source is moving and has volume elements that approach the observer with the speed of light and zero acceleration along the radiation direction. In the superluminal regime, the retarded time is a multivalued function of the observation time and so the retarded potential for the radiation from a localized source cannot be represented, as Hannay assumes, by an integral over all space whose integrand entails a differentiable retarded distribution of the source density. Contrary to what is claimed by Hewish [Comment in this issue, Phys. Rev. E 62, 3007 (2000)], moreover, there is no discrepancy between conventional antenna theory and the analysis that appears in Phys. Rev. E 58, 6659 (1998). The characteristics of the new type of emission predicted by this analysis, and received from pulsars, differ from those of the radiation that is produced by known leaky waveguides because there are at present no antennas in which the emitting electric current is both volume-distributed and has the time dependence of a traveling wave with an accelerated superluminal motion.