Statistics of Chaotic Impedance and Scattering Matrices: The Random Coupling Model

We propose a model to study the statistical properties of the impedance (Z) and scattering (S) matrices of open electromagnetic cavities with several transmission lines or waveguides connected to the cavity. The model is based on assumed properties of chaotic eigenfunctions for the closed system. Analysis of the model successfully reproduces features of the random matrix model believed to be universal, while at the same time incorporating features which are specific to individual systems. Statistical properties of the cavity impedance Z are obtained in terms of the radiation impedance (i.e., the impedance seen at a port with the cavity walls moved to infinity). Effects of wall absorption and nonreciprocal media (e.g., magnetized ferrite) are discussed. Theoretical predictions are tested by direct comparison with numerical solutions for a specific system.