Strong excitation of emitters in an impedance matched cavity: the area theorem, π-pulse and self-induced transparency

I theoretically study the behavior of strong pulses exciting emitters inside a cavity. The ensemble is supposed to be inhomogeneously broadened and the cavity matched finding application in quantum storage of optical or RF photons. My analysis is based on energy and pulse area conservation rules predicting important distortions for specific areas. It is well supported by numerical simulations. I propose a qualitative interpretation in terms of slow-light. The analogy with the free space situation is remarkable.