Previous numerical work on the spatiotemporal distributions of the atomic polarization and of the difference in levels population of a one-dimensional system of two-level atoms initially inverted strongly suggested that the dynamics of the slab atomic ensemble in the linear regime of superradiance may best be treated by an eigenmode analysis. This method proved effective in obtaining both the time dependence of the atomic polarization and the spectral distribution of the emitted radiation from the slab in a number of physically interesting problems in the linear regime. In the present paper, I use the eigenfunction expansion technique to reduce the Maxwell-Bloch system of partial differential equations into a system of coupled first-order ordinary differential equations whose solutions clearly detail the contributions of the different modes to the system dynamics in the nonlinear regime of superradiant emission. I compute also the delay in time of the peak of the superradiant burst and its magnitude as functions of the ratio of the longitudinal decay rate to the transverse decay rate of the system.
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.
This Brief Report gives the spectral distribution of the supercontinuum generated from a system of initially partially excited two-level atoms. The expansion in the eigenfunctions of the one-dimensional Li\'enard-Wiechert kernel which was successful in obtaining previously the results in the linear regime is generalized to the nonlinear regime. The detailed spectral distribution of the emitted radiation is computed without invoking either the phenomenological simplified physical model for the active medium or the mathematical approximations commonly used in treating propagation in absorbing media. The numerical solutions presented are those of the complete set of the coupled Maxwell-Bloch equations.