Spontaneous decay in the presence of dispersing and absorbing bodies: General theory and application to a spherical cavity - art. no. 053804

A formalism for studying spontaneous decay of an excited two-level,atom in the presence of dispersing and absorbing dielectric bodies is developed. An integral equation, which is suitable for numerical solution, is derived fo r the atomic upper-state-probability amplitude. The emission pattern and th e power spectrum of the emitted light are expressed in terms of the Green t ensor of the dielectric-matter formation, including absorption and dispersi on. The theory is applied to the spontaneous decay of an excited atom at th e center of a three-layered spherical cavity, with the cavity wall being mo deled by a band-gap dielectric of Lorentz type. Both weak and strong coupli ng are studied, the latter with a special emphasis on cases where the atomi c transition is (i) in the normal-dispersion zone near the medium resonance , and (ii) in the anomalous-dispersion zone associated with the band gap. I n a single-resonance approximation, conditions of the appearance of Rabi os cillations and closed solutions to the evolution of the atomic state popula tion are derived, which are in good agreement with the exact numerical resu lts.