Universal Statistics of the Scattering Coefficient of Chaotic Microwave Cavities

Abstract

We consider the statistics of the scattering coefficient S of a chaotic microwave cavity coupled to a single port. We remove the non-universal effects of the coupling from the experimental S data using the radiation impedance obtained directly from the experiments. We thus obtain the normalized, complex scattering coefficient whose Probability Density Function (PDF) is predicted to be universal in that it depends only on the loss (quality factor) of the cavity. We compare experimental PDFs of the normalized scattering coefficients with those obtained from Random Matrix Theory (RMT), and find excellent agreement. The results apply to scattering measurements on any wave chaotic system.