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 $\ensuremath{\alpha}$ 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 $\ensuremath{\xi}={\ensuremath{\xi}}_{w}{\ensuremath{\xi}}_{\ensuremath{\alpha}}/({\ensuremath{\xi}}_{w}+{\ensuremath{\xi}}_{\ensuremath{\alpha}}),$ where ${\ensuremath{\xi}}_{w}$ and ${\ensuremath{\xi}}_{\ensuremath{\alpha}}$ 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 $\ensuremath{\alpha},$ i.e., reflection shows a monotonic decrease with $\ensuremath{\alpha}$ and tends to zero in the limit of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\alpha}}\ensuremath{\infty},$ 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.