We show that there exists a sum rule for the local mode density that is associated with radiative spontaneous decay of an atom in an absorbing dielectric material. The existence of such a sum rule in particular means that dielectric surroundings merely redistribute the local density of states along the real frequency axis. This result supercedes a previously obtained sum rule [S. M. Barnett and R. Loudon, Phys. Rev. Lett. 77, 2444 (1996)] that is valid only for strictly nonabsorbing dielectric materials. The new sum rule also provides a way of computing the integrated density of states associated with nonradiative decay channels.

• Received 30 November 2007

DOI:https://doi.org/10.1103/PhysRevA.78.013841