An analysis of the second moment of fluctuating electromagnetic fields part I: Theory

This paper presents a mathematical treatment of the second-order coherence properties of fluctuating vector electromagnetic fields of arbitrary spectral width. We consider only fields whose random fluctuations result exclusively from the chaotic nature of the source. The theory is expressed in terms of the second-order moment of the field vector and hence is a tensor theory. In order to apply it to fields of arbitrary spectral width, the theory is formulated in terms of a spectral representation. The principal field quantity, the dyadic field spectral density (DFS), is interpreted from both a statistical and a physical standpoint. The differential equations and boundary conditions governing the behavior of the DFS within and external to the source are presented. The differential equations are integrated with the aid of the dyadic Green's function and the resulting formulas are discussed.