Dyadic Green's functions and electromagnetic local density of states

A formal proof to relate the concept of electromagnetic local density of states (LDOS) to the electric and magnetic dyadic Green's functions is provided. The expression for LDOS is obtained by relating the electromagnetic energy density at any location in a medium at uniform temperature $T$ to the electric and magnetic dyadic Green's functions. With this the concept of LDOS is also extended to material media. The LDOS is split into two terms -- one that originates from the energy density in an infinite, homogeneous medium and the other that takes into account scattering from inhomogenieties. The second part can always be defined unambiguously, even in lossy materials. For lossy materials, the first part is finite only if spatial dispersion is taken into account.