Modelling 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 $\alpha$ 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 $\alpha \to \infty$, 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 (RPA) in a larger parameter space. We also emphasize the major differences between the results of stochastic and coherent absorption.

7 pages RevTex, 9 eps figures included, modified version of cond-mat/9909327, to appear in PRB, mpeg simulations at http://www.iopb.res.in/~joshi/mpg.html

References in corpus (1)

• Transmission and reflection studies of periodic and random systems with gain

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