Dyadic Green's functions and electromagnetic local density of states

TL;DR

This paper provides a formal proof linking electromagnetic local density of states (LDOS) to dyadic Green's functions, extending the concept to media and analyzing its components in homogeneous and inhomogeneous, including lossy, materials.

Contribution

It offers a rigorous derivation connecting LDOS with Green's functions and extends the concept to complex media, including lossy and dispersive materials.

Findings

LDOS expressed via dyadic Green's functions.

Decomposition of LDOS into homogeneous and scattering contributions.

Unambiguous definition of LDOS in lossy media.

Abstract

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.