Local-field corrections to the decay rate of excited molecules in absorbing cavities: The Onsager model

The decay rate and the classical radiation power of an excited molecule (atom) in the center of a dispersive and absorbing dielectric sphere, taken as a simple model of a cavity, are calculated adopting the Onsager model for the local field. The local-field correction factor to the external (radiation and absorption) power loss of the molecule is found to be $|3\varepsilon \left(\omega \right)/\left[3\varepsilon \right(\omega )+1\mathrm{}]{|}^2,$ with $\varepsilon \left(\omega \right)$ being the dielectric function of the sphere. However, local-field corrections to the total decay rate (power loss) of the molecule are found to be much more complex including those to the decay rate in the infinite cavity medium, as derived recently by Scheel et al. [Phys. Rev. A $60,$ 4094 (1999)], and similiar corrections to the cavity-induced decay rate. The results obtained can be cast into general forms that do not rely on the specific cavity shape and molecule position considered. This suggests the general results for the local-field corrections to the decay rate and to the external power loss of a molecule in an absorbing cavity that are valid for molecule positions away from the cavity walls.