Relative local density of states for homogeneous lossy materials

We derive the appropriate form of the relative local density of states (RLDOS) for the two-dimensional Helmholtz equation in a homogeneous lossy medium, and give the corresponding result for the three-dimensional equation. The RLDOS enables the calculation of the enhancement or suppression of the energy radiated in the form of transverse electromagnetic waves by a localized source in the medium, and so would be useful in studies of either electromagnetic communication from inside a cloaking system or detection of the cloaking system by radiation from thermally excited atoms within it.