Lossy chaotic electromagnetic reverberation chambers: Universal statistical behavior of the vectorial field

TL;DR

This paper extends the effective Hamiltonian formalism to vectorial electromagnetic waves in lossy reverberation chambers, revealing universal statistical behaviors of the electromagnetic field relevant for electromagnetic compatibility testing.

Contribution

It introduces a novel extension of the effective Hamiltonian approach to vectorial waves in lossy chambers, providing a theoretical framework for their intensity and response statistics.

Findings

Good agreement between theoretical predictions and numerical data.

Distribution of phase rigidity matches random matrix theory.

Universal statistical behavior observed in lossy electromagnetic chambers.

Abstract

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a first step, the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory. In this limit the only parameters are the modal overlap and the number of open channels. Using the extended effective Hamiltonian, we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers. Finally, the typical quantity of interest in such chambers, namely, the distribution of the electromagnetic response, is discussed. By determining the distribution of the phase rigidity, describing the coupling to the environment, using random matrix numerical data, we find good agreement between the theoretical prediction and numerical calculations of the response.