Amplification and Disorder Effects on the Coherent Backscattering in a Kronig-Penney Chain of Active Potentials

TL;DR

This paper investigates how amplification and disorder influence coherent backscattering in a one-dimensional Kronig-Penney lattice, revealing complex behaviors in transmission and reflection due to these effects.

Contribution

It provides analytical and numerical insights into amplification effects on wave transport in active periodic lattices, highlighting the interplay with disorder and localization.

Findings

Transmission and reflection increase for small lengths

Maximum transmission diverges as amplification vanishes

Disorder limits amplification growth and causes nonmonotonic transmission behavior

Abstract

We report in this paper the analytical and numerical results on the effect of amplification on the transmission and reflection coefficient of a periodic one-dimensional Kronig-Penney lattice. A qualitative agreement is found with the tight-binding model where the transmission and reflection increase for small lengths before strongly oscillating with a maximum at a certain length. For larger lengths the transmission decays exponentially with the same rate as in the growing region while the reflection saturates at a high value. However, the maximum transmission (and reflection) moves to larger lengths and diverges in the limit of vanishing amplification instead of going to unity. In very large samples, it is anticipated that the presence of disorder and the associated length scale will limit this uninhibited growth in amplification. Also, there are other interesting competitive effects between disorder and localization giving rise to some nonmonotonic behavior in the peak of transmission.