Temporal evolution of superradiance in a small sphere

We discuss the problem of calculating the superradiant behavior in samples small compared to a radiation wavelength. Difficulties associated with the analysis of Dicke are considered in the framework of quantum electrodynamics and equivalently from a classical point of view. The evolution of superradiance in a small sphere is followed numerically with attention to spatial variation of the Bloch dipole density. Coherence is maintained except in the region ${\mathrm{}\left(\mathrm{kR}\right)\mathrm{}}^{-1\mathrm{}}\left|cos\theta \right|\lesssim 2$ which is at the Bloch equator, where it suddenly disappears. Away from the equator, the spatial variations of dipole density oscillate with amplitude $\sim {\mathrm{}\left(\mathrm{kR}\right)\mathrm{}}^{2}sin\theta$ and frequency $\sim {\mathrm{}\left(\mathrm{kR}\right)\mathrm{}}^{-3\mathrm{}}\left|cos\theta \right|$. All these results agree with the predictions of a theoretical discussion previously published.