Diffuse field cross-correlations: scattering theory and electromagnetic experiments

Abstract: The passive estimation of impulse responses from ambient noise correlations arouses increasing interest in seismology, acoustics, optics and electromagnetism. Assuming the equipartition of the noise field, the cross-correlation function measured with non-invasive receiving probes converges towards the difference of the causal and anti-causal Green's functions. Here, we consider the case when the receiving field probes are antennas which are well coupled to a complex medium -- a scenario of practical relevance in electromagnetism. We propose a general approach based on the scattering matrix formalism to explore the convergence of the cross-correlation function. The analytically derived theoretical results for chaotic systems are confirmed in microwave measurements within a mode-stirred reverberation chamber. This study provides new fundamental insights into the Green's function retrieval technique and paves the way for a new technique to characterize electromagnetic antennas.