Material slow and fast light in a zero-dispersion configuration

We study the propagation of light pulses in an absorbing medium when the frequency of their carrier coincides with a zero of the refractive index dispersion. Although slow light and, a fortiori , fast light are not expected in such conditions, we show that both can be obtained by selecting particular phase components of the transmitted field. Analytical expressions of the resulting signals are obtained by a procedure of periodic continuation of the incident pulse, and a proof of principle of the predicted phenomena is performed by means of a very simple electrical network; the transfer function of which mimics that of the medium.