Impedance and Power Fluctuations in Linear Chains of Coupled Wave Chaotic Cavities

The flow of electromagnetic wave energy through a chain of coupled cavities is considered. The cavities are assumed to be of sufficiently irregular shape that their eigenmodes are described by random matrix theory. The cavities are coupled by electrically short single mode transmission lines. Approximate expressions for the power coupled into successive cavities are derived, and the predictions are compared with Monte Carlo simulations. The analytic formulas separate into a product of factors. Consequently, the distribution of power in the last cavity of a very long chain approaches lognormal. For lossless cavities, signatures of Anderson localization, similar to those of the conductances of quantum wires, are observed.