Propagation methods for stochastic field emissions and source reconstruction

Modelling of complex wave sources is an important topic in several scientific and engineering communities. In the context of electromagnetic compatibility, the complexity of field emissions from extended and broadband planar sources allows for the use of statistical methods to characterise the development of far field interferences from near field scanning at planes parallel to the source. We review and describe recent progresses of an analogue near-to-far field operator for statistical sources, whose exact version is directly related to Green's function formalism. This operator exploits directional and positional informations encoded in the two-point correlation function through a phase-space representation (Wigner function), at which the propagation can be approximated by ray tracing a density of waves and includes diffusion of evanescent waves - important at planes close to the source. This formalism is used to propagate the correlation function from two-probe near-field scanning measurements in free-space, and can be extended to propagation within arbitrary cavities. After pointing out the equivalence between propagating voltage-voltage and field-field correlations, we compare exact and approximated correlation matrices propagated from a partially coherent source, which results in good agreement. Finally, we present an impedance based source reconstruction algorithm that uses the significant eigenvalues of the voltage-voltage correlations obtained from near-field scanning to estimate the current-current correlation across the surface of the source. Results are relevant for the emission source microscopy of statistical sources.