Dispersive properties of self–induced transparency in two–level media

We focus on self-induced transparency (SIT) in the propagation of a pulse in a dispersive medium. The latter can be an ordinary optical medium or, more interestingly, a quantum metamaterial. In both cases we consider a sequence of two level atoms each with a characteristic resonant frequency ω0. The propagation features are controlled by the ratio of the pulse frequency ω over the dipole resonant frequency, i.e. on the quantity X=ω/ω0. We consider analytically two pulse limits, viz. the sharp line limit as well as the inhomogeneouly broadened case. In the first case we find that for pulse frequencies larger than ω0, i.e. for X>1 the SIT pulse may be fully stopped through absorption by the medium provided its time width exceeds a certain critical value. In the latter case of inhomogeneously broadened medium we find no such frequency restrictions provided the pulse is wide enough. As a result an SIT pulse can be arbitrarily arrested by the absorbing medium. This dispersion-induced pulse stopping is a manifestation of the quantum nature of the medium and of possible use in metamaterial applications.