Reflectance Fluctuations in an Absorbing Random Waveguide

We study the statistics of the reflectance (the ratio of reflected and incident intensities) of an $N$-mode disordered waveguide with weak absorption $\gamma$ per mean free path. Two distinct regimes are identified. The regime $\gamma N^2\gg1$ shows universal fluctuations. With increasing length $L$ of the waveguide, the variance of the reflectance changes from the value $2/15 N^2$, characteristic for universal conductance fluctuations in disordered wires, to another value $1/8 N^2$, characteristic for chaotic cavities. The weak-localization correction to the average reflectance performs a similar crossover from the value $1/3 N$ to $1/4 N$. In the regime $\gamma N^2\ll1$, the large-$L$ distribution of the reflectance $R$ becomes very wide and asymmetric, $P(R)\propto (1-R)^{-2}$ for $R\ll 1-\gamma N$.