Transmission and reflection from a disordered lasing medium

A numerical study of the statistics of the transmission $\mathrm{}\left(t\right)\mathrm{}$ and reflection $\mathrm{}\left(r\right)\mathrm{}$ of quasiparticles 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 crossover length scale above which the amplification suppresses the transmittance is studied as a function of amplification strength. A new crossover 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.