Dyadic Green's Function, Spectral Function, Local Density of States, and Fluctuation Dissipation Theorem

Abstract

In this talk, we will discuss the relation between dyadic, spectral function, local density of states, and fluctuation dissipation theorem in electromagnetics. Using a retarded and advanced Green’s function, one can define a spectral function that is non-causal, but Hermitian. From this spectral function, one can derive the local density of states and density of states quite easily. Since the system is Hermitian, the energy density can be related to quantized electromagnetic field, and hence, the Planck distribution function can be used to derive it. For lossy dispersive media, this connection is less obvious, but a connection to Planck distribution law can still be made. Moreover, this path of deriving the energy density can be related to the fluctuation dissipation theorem for lossy, dispersive media. We will derive useful formulas and show the connection by solving Maxwell’s equations in vacuum, lossless, lossy, and inhomogeneous dispersive media.