Abstract
In this work we derive the average and the variance of the cross-correlation of a noise wavefield. The noise cross-correlation function (NCF) is widely used to passively estimate the Green's function between two probes and is proportional to the cross density of states (CDOS) in photonic and plasmonic systems. We first explain from the ladder approximation how the diffusion halo plays the role of secondary sources to reconstruct the mean Green's function. We then show that fluctuations of NCF are governed by several non-Gaussian correlations. An infinite-range correlation term dominates fluctuations of NCF-CDOS and proves that NCF is not a self-averaging quantity with respect to the plurality of noise sources. The link between these correlations and the intensity ones is highlighted. These results are supported by numerical simulations and are of importance for passive imaging applications and material science.
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