We report a detailed and systematic study of wave propagation through a
stochastic absorbing random medium. Stochastic absorption is modeled by
introducing an attenuation constant per unit length α in the free
propagation region of the one-dimensional disordered chain of delta function
scatterers. The average value of the logarithm of transmission coefficient
decreases linearly with the length of the sample. The localization length is
given by ξ = ξw​ξα​/(ξw​+ξα​), where ξw​ and
ξα​ are the localization lengths in the presence of only disorder and
of only absorption respectively. Absorption does not introduce any additional
reflection in the limit of large α, i.e., reflection shows a monotonic
decrease with α and tends to zero in the limit of α→∞, in
contrast to the behavior observed in case of coherent absorption. The
stationary distribution of reflection coefficient agrees well with the
analytical results obtained within random phase approximation (RPA) in a larger
parameter space. We also emphasize the major differences between the results of
stochastic and coherent absorption.Comment: RevTex, 6 pages,2 column format, 9 .eps figures include