The Purcell-Dicke effect in the emission from a coated small sphere of resonant atoms placed inside a matrix cavity

I investigate a system where both the Purcell effect and Dicke’s superradiance are present. I compute the frequency eigenmode for an ensemble of identical two-level atoms enclosed in a coated nanosphere that is embedded in a matrix. I show that, in a number of configurations, the rate of superradiant emission from the atomic system can be increased many folds from that of a similar cloud of atoms in free space.