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.