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 g per mean free path. Two distinct regimes are identified. The regime γ N 2 ≫1 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 γ N 2 ≫1, the large- L distribution of the reflectance R becomes very wide and asymmetric, P(R)∝(1−R) −2 for R≪1−γN.