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 $T=\mathrm{tr}{t}^{†}t$, where $t$ is the transmission matrix, the density of transmission eigenvalues $\tau$ (the eigenvalues of $t^{†}t)$, and the distribution of the plane-wave transmittances $T_a$ and $T_{\mathrm{ab}}.$ For weak absorption (length $L$ smaller than the exponential absorption length ${\xi }_a)$, we compute moments of the distributions, while for strong absorption $\left(L\gg {\xi }_a\right)$, 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)].