Description of spontaneous photon emission and local density of states in presence of a lossy polaritonic inhomogenous medium

We provide a description of spontaneous emission in a dispersive and dissipative linear inhomogeneous medium based on the generalized Huttner-Barnett model [Phys. Rev. A 46, 4306 (1992)]. Our discussion considers on an equal footing both the photonic and material fluctuations which are necessary to preserve unitarity of the quantum evolution. Within this approach we justify the results obtained in the past using the Langevin noise method that neglects the removal of photonic fluctuations. We finally discuss the concept of local density of states (LDOS) in a lossy and dispersive inhomogeneous environment that provides a basis for theoretical studies of fluorescent emitters near plasmonic and polaritonic antennas.