Description of a wave packet propagating in anomalous dispersion media-a new expression of propagation velocity

The propagation velocity of a wave packet applicable to anomalous dispersion media is newly derived using the saddle point method. This velocity includes the effects of both packet deformation and spreading, and coincides with the group velocity at the normal dispersion limit. A method to determine the saddle point frequency from a given initial condition is presented and the trajectory of a wave packet incident on a semi-infinite medium is obtained by integrating the new propagation velocity. It reveals that the propagation of a wave packet in anomalous dispersion media is characterized by three regions, i.e. backward, fast and slow propagation regions. The difficulty of group velocity in anomalous dispersion media is overcome.