Average and instantaneous velocities of energy of evanescent modes

Abstract

Many theoretical and experimental investigations have concluded that evanescent electromagnetic modes can propagate superluminally. However, in this paper we show that the average energy velocity of evanescent modes inside a cutoff waveguide is always less than or equal to the velocity of light in vacuum, while the instantaneous energy velocity can be superluminal, which does not violate causality according to quantum field theory: the fact that a particle can propagate over a spacelike interval does preserve causality provided that a measurement performed at one point cannot affect another measurement at a point separated from the first with a spacelike interval.