Average and instantaneous velocities of energy of evanescent modes

Many theoretical and experimental investigations have presented a conclusion that evanescent electromagnetic modes can superluminally propagate. However, in this paper, we show that the average energy velocity of evanescent modes inside a cut-off 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 space-like interval does preserve causality provided that here a measurement performed at one point cannot affect another measurement at a point separated from the first with a space-like interval.