Transmission through a many-channel random waveguide with absorption

We compute the statistical distribution of the transmittance of a random waveguide with absorption in the limit of many propagating channels. We consider the average and fluctuations of the conductance T=trt^t, where t is the transmission matrix, the density of transmission eigenvalues τ (the eigenvalues of t^t), and the distribution of the plane-wave transmittances Tₐ and Tab. For weak absorption (length L smaller than the exponential absorption length ξₐ), we compute moments of the distributions, while for strong absorption (Lξₐ), we can find the complete distributions. Our findings explain recent experiments on the transmittance of random waveguides by Stoytchev and Genack [Phys. Rev. Lett. 79, 309 (1997)].