An analysis is made of a one-dimensional problem involving superradiance of four-level active media. The rate equations for the populations and the transport equations for the superradiance fluxes are used to derive differential equations for the description of the behavior of the integrated population and the observed superradiance flux in the active medium excited by the pump flux. A detailed analysis is made of the superradiance decay. Analytic dependences are obtained to describe the decay of the normalized superradiance flux. The gain of the active medium at the onset of decay occurs as the parameter in these dependences and they are used as the basis of a technique for obtaining upper and lower estimates of this parameter.
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.