Nonperturbative calculation of the probability distribution of plane-wave transmission through a disordered waveguide

Abstract

A nonperturbative random-matrix theory is applied to the transmission of a monochromatic scalar wave through a disordered waveguide. The probability distributions of the transmittances ${T}_{\mathrm{mn}}$ and ${T}_{n}={\ensuremath{\Sigma}}_{m}{T}_{\mathrm{mn}}$ of an incident mode $n$ are calculated in the thick-waveguide limit, for broken time-reversal symmetry. A crossover occurs from Rayleigh or Gaussian statistics in the diffusive regime to lognormal statistics in the localized regime. A qualitatively different crossover occurs if the disordered region is replaced by a chaotic cavity.