Temporal evolution of superradiance in a small sphere
Richard M. Friedberg, Sven R. Hartmann · Physical Review A · 1974
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 ${(\mathrm{kR})}^{\ensuremath{-}1}|cos\ensuremath{\theta}|\ensuremath{\lesssim}2$ which is at the Bloch equator, where it suddenly disappears. Away from the equator, the spatial variations of dipole density oscillate with amplitude $\ensuremath{\sim}{(\mathrm{kR})}^{2}sin\ensuremath{\theta}$ and frequency $\ensuremath{\sim}{(\mathrm{kR})}^{\ensuremath{-}3}|cos\ensuremath{\theta}|$. All these results agree with the predictions of a theoretical discussion previously published.