This work presents results of ab-initio simulations of continuous wave
transport in disordered absorbing waveguides. Wave interference effects cause
deviations from diffusive picture of wave transport and make the diffusion
coefficient position- and absorption-dependent. As a consequence, the true
limit of a zero diffusion coefficient is never reached in an absorbing random
medium of infinite size, instead, the diffusion coefficient saturates at some
finite constant value. Transition to this absorption-limited diffusion exhibits
a universality which can be captured within the framework of the
self-consistent theory (SCT) of localization. The results of this work (i)
justify use of SCT in analyses of experiments in localized regime, provided
that absorption is not weak; (ii) open the possibility of diffusive description
of wave transport in the saturation regime even when localization effects are
strong.Comment: 10 pages, 3 figure