Model of stochastization of the oscillatory regime of superradiance

Based on the analysis of the experimental data on the observation of the fluorescence and superradiance of praseodymium ions in a matrix of lanthanum trifluoride, a model of superradiance of three-level radiators with two close upper levels is developed in the mean-field approximation and studied. The uppermost level is coherently pumped by an ultrashort pulse of electromagnetic field, after which the excitation is transferred to the close energy level, from which the superradiance transition occurs to the lower level. In limiting cases, the considered model is reduced to the known models of superradiance and describes the ordinary regimes of monopulse and multipulse (oscillatory) superradiance. However, in a certain region of parameters, the model under discussion describes such a multipulse superradiance signal in which electromagnetic field spikes composing it follow in time with random intervals and amplitudes, so that the regime of regular chaotic dynamics is demonstrated in a single superradiance signal. In a certain time interval, the proposed model can be described by the Lorenz equations with the parameters corresponding to the chaotic dynamics of spikes composing the superradiance signal. The presented results of the numerical simulation of the model equations qualitatively correspond to the picture of stochastic pulsations observed experimentally.