Diffuse field cross-correlations: scattering theory and electromagnetic experiments

TL;DR

This paper develops a scattering matrix approach to analyze how ambient noise correlations can retrieve Green's functions in electromagnetic media, validated by microwave experiments, offering new insights for antenna characterization.

Contribution

It introduces a general scattering matrix framework for understanding noise correlation convergence in complex electromagnetic media, supported by experimental validation.

Findings

Theoretical results match microwave measurements in chaotic systems.

The approach enhances understanding of Green's function retrieval in electromagnetism.

Provides a new method for electromagnetic antenna characterization.

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.