Reexamination of energy flow velocities of non-diffracting localized waves

Abstract

A universal relation has been established between the local energy transport velocity along the direction of propagation and the group velocity of scalar and vector-valued propagation-invariant spatiotemporally localized superluminal and subluminal electromagnetic waves in free space. Under specific restrictions, this relationship is very closely valid for physically realizable almost propagation-invariant spatiotemporally confined subluminal and superluminal electromagnetic fields. In both cases, although the group velocity may be either superluminal or subluminal, the universal relation is in accord with the well-established result that the upper limit of the energy transport velocity is c, the speed of light in vacuum.