  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.
