# Olivier Legrand - UCA, CNRS, INPHYNI, UMR 7010, 06100 Nice, France - Keywords: Wave Chaos

Electromagnetic reverberation chambers (RC) are commonly used for Electro-Magnetic Compatibility (EMC) tests. Due to mechanical or electronic stirring and to the presence of loss mechanisms leading to modal overlap, the resulting field is generally assumed to be statistically isotropic, uniform and depolarized. Such properties are well understood and correspond to the well-known Hill’s hypotheses when the excitation frequency is well above the so-called Lowest Useable Frequency (LUF). However, a need for the use of RCs at lower frequencies requires that the above statistical properties still hold at moderate modal overlap when Hill's assumptions are no longer valid in a conventional RC. We show that these statistical requirements can be naturally fulfilled in chaotic reverberation chambers for all frequencies as a consequence of the universal statistical features of chaotic cavities.

We present experimental and theoretical studies of the statistics of the electromagnetic response in new types of chaotic RCs. Through several experimental investigations, intensity and phase statistics of the response in a conventional mode-stirred RC are compared with those in a chaotic RC near or below the LUF. These works illustrate how the universal statistical properties of the field in an actual chaotic RC can ensure the validity of the standard criterion proposed by the EMC community to evaluate the uniformity of the field distribution. In particular, through a theoretical approach based on the random matrix theory and the extended effective hamiltonian applied to open chaotic systems, we find that the modal overlap seems to be the only relevant parameter of the corresponding field statistical distribution. We propose an Ansatz to predict the latter analytically, which proves to be in excellent agreement with experimental results.