Reconciling the eigenmode analysis with the Maxwell–Bloch equations approach to superradiance in the linear regime

The superradiance from a slab of inverted two-level atoms is theoretically analyzed in the linear regime from both the perspective of the expansion in eigenfunctions of the integral equation with the Lienard–Wiechert potential as kernel, and that of linearizing the Maxwell–Bloch equations. We show the equivalence of both approaches. We show that the so-called Reduced Maxwell–Bloch equations do not yield even approximately the correct solution when applied in the obvious way, but that they can be made to give the correct solution by adding a fictitious input field.