Transient Structure in the Non-linear Superradiance Regime of Widely Doppler Broadened Media

We investigate transient radiation processes in the non-linear superradiance (SR) regime of the Doppler broadened Maxwell-Bloch equations when the velocity distribution is of total bandwidth greatly exceeding that of the transient process itself. We demonstrate the formation of global polarisation phase correlation and the quenching of temporal structure if a smooth distribution is inverted above the critical threshold required to enter the non-linear SR regime. We propose candidate stochastic velocity distributions capable of sustaining finite temporal structure in the non-linear emission process. We develop a novel algorithm for simulating the Doppler broadened Maxwell-Bloch equations which is $O(n)$ complex in the number of velocity channels $n$ whenever the emerging polarisation correlation is of moderate bandwidth, and we apply it to a stochastic velocity distribution in order to demonstrate sustained delay and duration of peak intensity in the widely Doppler broadened limit. We discuss the transverse inversion process and recognise an autoregulation mechanism on the number of molecules cooperatively participating in SR emission. This mechanism has the effect of limiting the temporal duration of the intensity pulse to a lower bound proportional to the length of the sample, which we confirm through simulation.