Superluminal Behaviors of Modified Bessel Waves
  Much experimental evidence of superluminal phenomena has been available by electromagnetic wave propagation experiments, with the results showing that the phase time do describe the barrier traversal time. Based on the extrapolated phase time approach and numerical methods, we show that, in contrary to the ordinary Bessel waves of real argument, the group velocities of modified Bessel waves are superluminal, and obtain the following results: 1) the group velocities increase with the increase of propagation distance, which is similar to the evanescent plane-wave cases; 2) for large wave numbers, the group velocities fall off as the wave numbers increase, which is similar to the evanescent plane-wave cases; 3) for small wave numbers, the group velocities increase with the increase of wave numbers, this is different from the evanescent plane-wave cases. 
Zhi-Yong Wang, Cai-Dong Xiong