Abstract
X-waves are shown to be related to Cerenkov-Vavilov (CV) radiation as derived by solving the linearized inhomogeneous scalar wave equation in free space for the case of a source in uniform motion at velocity v that is greater than the speed of waves, c, in the medium, ‖v‖>c. The results apply to wave phenomena in general, both acoustic and electromagnetic. In this context, the supersonic/superluminal properties of X-waves are unambiguously demonstrated to be phase effects. One implication is that even the ideal diffractionless X-wave is not signal-like nor can it exceed the Shannon data rate bandwidth relation, <m;txt>ΔtΔω=2π. Further, it is shown that the continuous power required to propagate an X-wave is analogous to the energy dissipation of a CV particle caused by radiation drag. Thus, generating a diffractionless X-wave requires an infinite total energy input over a spatially infinite source aperture. Finally, the connection between CV radiation and X-waves suggests the possibility of generating X-waves using time-reversal.
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