Singularity of the dyadic Green’s function for heterogeneous dielectrics

For heterogeneous media with piecewise constant complex permittivity on regular domains, we show that the dyadic Green’s function has the same singular part as the corresponding free space dyadic Green’s function on every domain of constant permittivity. We give two important applications of this property, namely the distorted-wave Born approximation for composite media and the calculation of the single photon decay rate in spontaneous emission.