Representation of random electromagnetic fields through a correlated plane-wave spectrum

Idealized complex Gaussian fields with Dirac´s delta correlation are able to reproduce the asymptotic statistics of irregular, wave chaotic, electromagnetic cavities. However, in many practical scenarios involving (objects with) losses and (other) perturbations, deviations from those statistics are observed and still await a proper explanation. We develop the concept of correlated plane-wave angular spectrum and infer functionals for the partial wave coherency, which can be used to introduce a finite coherence arc on the total field. Under certain conditions, we find that the long-range spatial decay of the total field correlation function is independent of the inferred functional and follows a universal law. In particular, it is found that correlations of partially-coherent cavity fields decay algebraically, with the square root of the spatial lag. Results could pave the way to understanding the presence of residual correlation in realistic reverberation chambers and other environments exhibiting random fields. Long range correlation could also be important in antenna arrays operating in multiple-input multiple-output wireless channels.