Superradiance as single scattering embedded in an effective medium

We present an optical picture of linear-optics superradiance, based on a single scattering event embedded in dispersive effective medium composed by the other atoms. This linear-dispersion theory is valid at low density and single-scattering regime, i.e., when exciting field largely detuned. The comparison with coupled-dipole model shows perfect agreement for superradiant decay rate. Then we use two advantages this approach. First make direct experimental data, without any free parameter, show good quantitative agreement. Second, address problem moving atoms, which can be efficiently simulated adding Doppler broadening to theory. In particular, discuss how recover superradiance high temperature.