Modeling of stochastic absorption in a random medium

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 $\alpha$ 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 $\xi ={\xi }_w{\xi }_{\alpha }/({\xi }_w+{\xi }_{\alpha }),$ where ${\xi }_w$ and ${\xi }_{\alpha }$ 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 $\alpha ,$ i.e., reflection shows a monotonic decrease with $\alpha$ and tends to zero in the limit of $\overrightarrow{\alpha }\infty ,$ 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 in a larger parameter space. We also emphasize the major differences between the results of stochastic and coherent absorption.