Study of transmission and reflection from a disordered lasing medium

TL;DR

This paper numerically investigates how disorder and amplification affect transmission and reflection in a one-dimensional lasing medium, revealing new length scales and distribution behaviors.

Contribution

It introduces a numerical analysis of transmission and reflection in disordered amplifying media, highlighting non-self-averaging transmittance and new crossover length scales.

Findings

Transmission is non-self-averaging.

Amplification suppresses transmittance above a certain length.

Reflection distribution differs from previous analytical models.

Abstract

A numerical study of the statistics of transmission ($t$) and reflection ($r$) of quasi-particles from a one-dimensional disordered lasing or amplifying medium is presented. The amplification is introduced via a uniform imaginary part in the site energies in the disordered segment of the single-band tight binding model. It is shown that $t$ is a non-self-averaging quantity. The cross-over length scale above which the amplification suppresses the transmittance is studied as a function of amplification strength. A new cross-over length scale is introduced in the regime of strong disorder and weak amplification. The stationary distribution of the backscattered reflection coefficient is shown to differ qualitatively from the earlier analytical results obtained within the random phase approximation.