Pulse centroid velocity of the Poynting vector

The evolution of the pulse centroid velocity of the Poynting vector for both ultrawideband rectangular and ultrashort Gaussian envelope pulses is presented as a function of the propagation distance in a dispersive, absorptive dielectric material. The index of refraction of the material is described by the Lorentz-Lorenz formula in which a single-resonance Lorentz model is used to describe the mean molecular polarizability. The results show that, as the propagation distance increases above a value that is on the order of an absorption depth at the pulse carrier frequency, the centroid velocity of an ultrawideband/ultrashort pulse tends toward the rate at which the Brillouin precursor travels through the medium. For small propagation distances when the carrier frequency of the optical pulse lies in the absorption band of the material, the centroid velocity can take on superluminal and negative values.