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=tr t dagger t, where t is the transmission matrix, the density of transmission eigenvalues tau (the eigenvalues of t dagger t), and the distribution of the plane-wave transmittances T-a and T-ab. For weak absorption (length L smaller than the exponential absorption length xi(a)), we compute moments of the distributions, while for strong absorption (L much greater than xi(a)), 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)]. [S0163-1829(98)029 17-8].