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

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 $T_n={\Sigma }_m{T}_{\mathrm{mn}}$ 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.