Superluminal X-wave propagation: energy localization and velocity.

The electromagnetic propagation of a Bessel-$X$ wave is analyzed on the basis of a vectorial treatment in order to obtain information about the propagation of energy flux and the velocity of the energy. Knowledge of these quantities is of great interest since they are connected to the production of localized electromagnetic energy and to the topic of superluminality, respectively. The electric and magnetic fields are obtained in the far-field approximation by considering a realistic situation able to generate a Bessel-$X$ wave. The vectorial treatment confirms the capability of this kind of wave to localize energy, while, quite surprisingly, even if the group velocity is superluminal, the energy velocity is equal to the light speed.