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

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.

Important revisions and expansion caused by a crucial property of $\hat{Q}$

References in corpus (5)

• Transmission and reflection studies of periodic and random systems with gain
• Theory of the propagation of coupled waves in arbitrarily-inhomogeneous stratified media
• Localization fom conductance in few-channel disordered wires
• Relation between Anderson- and Invariant Imbedding Models for Transport in Finite Chains and Study of Phase- and Delay Time Distributions for Strong Disorder
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Cited by in corpus (1)

• Gain/loss induced localization in one-dimensional PT-symmetric tight-binding models