Modeling of stochastic absorption in a random medium

Abstract

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 a 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=ξ_wξ_α /(ξ_w+ξ_α), where ξ_w and ξ_α 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 a 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 in a larger parameter space. We also emphasize the major differences between the results of stochastic and coherent absorption.