It is a familiar fact that, in an isolated sphere or ellipsoid of uniform polarization density, the electrostatic field also is uniform. Because of this, the state of uniform polarization in a spherical sample of uniformly distributed two-level atoms is an eigenmode of the coherent decay process in the limit of a small radius compared to the resonant wavelength of a single atom. Consequently, in this special geometry, the Dicke picture of uniform exponential decay should hold. In nonspheroidal geometries or in spherical geometries with nonuniform atomic density, the decay should be more complicated. Here, we find the characteristic equations that determine the eigenmodes of the Lienard-Wiechert interaction for a partly hollowed sphere of identical two-level atoms in two different radial configurations. We show that the Dicke picture for emission from a coherently prepared sample does not correctly describe the system's dynamics even when we take the radius of the sphere to be much smaller than the radiation wavelength.

• Received 28 September 2011

DOI:https://doi.org/10.1103/PhysRevA.85.013834