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

TL;DR

This paper explores spectral functions and dyadic Green's functions across various media, establishing their relations to local density of states and energy density, and deriving fluctuation-dissipation relations without direct reliance on the theorem.

Contribution

It provides a unified approach to compute Green's functions and spectral functions for diverse media, including lossy and inhomogeneous cases, and relates them to physical observables.

Findings

Spectral functions relate to local density of states in lossless media.

Spectral functions connect to field correlation functions in lossy media.

Derived expressions for local density of states in complex media.

Abstract

The spectral functions are studied in conjunction with the dyadic Green's functions for various media. The dyadic Green's functions are found using the eigenfunction expansion method for homogeneous, inhomogeneous, periodic, lossless, lossy, and anisotropic media, guided by the Bloch- Floquet theorem. For the lossless media cases, the spectral functions can be directly related to the photon local density of states, and hence, to the electromagnetic energy density. For the lossy case, the spectral function can be related to the field correlation function. Because of these properties, one can derive properties for field correlations and the Langevin-source correlations without resorting to the fluctuation dissipation theorem. The results are corroborated by the fluctuation dissipation theorem. An expression for the local density of states for lossy, inhomogeneous, and dispersive media has also been suggested.