Theory of superradiance in an extended, optically thick medium

Abstract

This paper presents a semiclassical treatment of the evolution of an initially inverted system into a superradiant state in an extended, optically thick medium. In this process spontaneous emission and background thermal radiation initiate the collective radiative decay and produce a superradiant output pulse of intensity proportional to the square of the number of radiators. The treatment is based on the coupled Maxwell-Schrödinger equations, modified to include a fluctuating polarization source properly constructed to account for the effects of spontaneous emission. Computer results show that for a high-gain system only two parameters significantly influence the evolution process: $T_R$, the characteristic radiation damping time of the collective system; and ${\theta }_0$, a function of the conditions which initiate the superradiant process. In this limit one obtains a normalized emission curve and simple analytical expressions for the time delay, pulse width, and peak intensity of the output radiation. These results are in good agreement with experiments. A comparison of our model with previous treatments of superradiance is given.