Abstract
A mathematical theory of noise-like electromagnetic fields of arbitrary spectral width is formulated. Attention is restricted to 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; hence, it is a tensor theory. Moreover, to make it applicable to fields of arbitrary spectral width, the theory is formulated in terms of a spectral representation, rather than directly in terms of the autocorrelation function of the vector field. The principal field quantity, the dyadic field spectral density (DFS), is interpreted from both a statistical and a physical standpoint. In particular, a statistical analysis of partial polarization is presented with the aim of providing a physical interpretation of the polarization of a quasi-monochromatic field. The differential equations that govern the behavior of the DFS are derived in the presence of a source, in a source free region, and in a generalized dielectric medium. Boundary conditions are derived for the DFS at a dielectric interface, at a perfectly conducting interface, and at infinity. The differential equations are integrated for various cases with the aid of the dyadic Green's function. The resulting integral representation for the DFS is employed to analyze an experiment that involves the measurement of a partially polarized, incoherent, discrete radio star by means of a two-element radio interferometer
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