Impossibility of negative group velocities in a periodic layer structure with or without loss

The limiting group velocities available with a one-dimensional periodic medium composed of 1/4 wavelength sections are studied. For all realistic combination of medium parameters, it is found that there are superior and inferior limits to the group velocity. We use numerical analysis to investigate the effect of the refractive index mismatch, the phase velocities and the attenuation coefficient on the limits of group velocity. We show that negative group velocities are not possible in a linear passive periodic medium, and discuss why a recent report of negative tunnelling times in a passive periodic system may be explained in terms of the relatively large experimental uncertainty in determining the tunnelling times.