Wave chaotic analysis of weakly coupled reverberation chambers

Abstract

In this paper, we analyze the field fluctuations in weakly coupled complex cavities by using a random matrix theory to model the chaotic scattering within each cavity. Universal (chaotic) and non-universal are separated. In particular, nonuniversal are found to be conveniently described by the radiation impedance concept. Inherently, the development of the random field regime is accounted for by taking each mode of the cavity as a random plane wave expansion. Sources and sinks inside the cavities are assumed to be electrically small. A model for the cascaded cavities scenario is derived through the electric network theory and random matrix theory for both lossy and lossless cases. The adopted physical framework is a linear chain of twoport cavities terminated by a one-port cavity. The field flowing into this last cavity is related to the current excitation on the first cavity through the coupling radiation impedance. Closedform expressions are derived for two interconnected cavities, mimicking the nested reverberation chamber scenario. Finally, the practical issue of measurements in a nested reverberation chamber is presented and discussed. Accordingly, based on physical arguments, the small fluctuations theory applies. Results are of interest in interference propagation through complex electromagnetic environment or planar circuits, EMC immunity tests, and reverberation chambers.

Nonlinear wave chaos: statistics of second harmonic fields

“…2). This choice was motivated by earlier work on the statistics of impedance and power fluctuations in chains of wave chaotic cavities connected by weak but linear coupling [24,25,43]. As shown in Fig.…”

“…Based on the success of the RCM, it is of interest to explore directions extending its generality. Along this line, theories have been developed for "mixed" systems which include both regular and chaotic ray dynamics [23], and for networks of coupled cavities in which waves propagate from one sub-system to another [24,25]. While such previous extensions have focused on linear systems, it is of great interest to see how nonlinearity would modify the RCM.…”

Universal behaviour of a wave chaos based electromagnetic reverberation chamber

“…Predictions of Random Matrix Theory (RMT) have been extensively verified, both numerically and experimentally in two-dimensional (2D) or pseudo-2D electromagnetic cavities [16,17,15,18,19] as well as in the 3D case [20,21,22,23,24]. Previous works have already called for the similitude between the expected statistical properties a well-stirred RC and the intrinsic behaviour of individual ergodic modes of a chaotic cavity, to propose strategies for improved operation of an EM RC [7,25,26]. We believe that, along with these studies, the results presented here have practical implications for an effective reduction of the lowest usable frequency (LUF) in chaotic RCs.…”