Dynamic Pattern of Finite-Pulsed Beams inside One-dimensional Photonic   Band Gap Materials
  The dynamics of two-dimensional electromagnetic (EM) pulses through one-dimensional photonic crystals (1DPC) has been theoretically studied. Employing the time expectation integral over the Poynting vector as the arrival time [Phys. Rev. Lett. 84, 2370, (2000)], we show that the superluminal tunneling process of EM pulses is the propagation of the net forward-going Poynting vector through the 1DPC, and the Hartman effect is due to the saturation effect of the arrival time (smaller and smaller time accumulated) of the net forward energy flow caused by the interference effect of the forward and the backward field (from the interfaces of each layer) happened in the region before the 1DPC and in the front part of the 1DPC. 
Li-Gang Wang and Shi-Yao Zhu