Transmission, reflection and localization in a random medium with absorption or gain

TL;DR

This paper analytically investigates how weak and strong absorption or gain affect wave transmission, reflection, and localization in a random medium, revealing regimes where these effects are similar or differ.

Contribution

It provides an exact analysis of absorption and gain effects on wave statistics in a random medium, distinguishing short- and long-length regimes.

Findings

Weak absorption or gain induce similar corrections in localization length.

Strong absorption or gain suppress disorder effects similarly.

Absorption and gain differently affect mean reflection coefficients.

Abstract

We study reflection and transmission of waves in a random tight-binding system with absorption or gain for weak disorder, using a scattering matrix formalism. Our aim is to discuss analytically the effects of absorption or gain on the statistics of wave transport. Treating the effects of absorption or gain exactly in the limit of no disorder, allows us to identify short- and long lengths regimes relative to absorption- or gain lengths, where the effects of absorption/gain on statistical properties are essentially different. In the long-lengths regime we find that a weak absorption or a weak gain induce identical statistical corrections in the inverse localization length, but lead to different corrections in the mean reflection coefficient. In contrast, a strong absorption or a strong gain strongly suppress the effect of disorder in identical ways (to leading order), both in the localization length and in the mean reflection coefficient.