Minimum reflection channel in amplifying random media

We present a numerical study on the minimum reflection channel in a disordered waveguide and its modification by coherent amplification of light. The minimum reflection channel is formed by destructive interference of quasi-normal modes at the front surface of the random medium. While the lowest reflection eigenvalue increases with gain in most random realizations, the minimum reflection channel can adjust its modal composition to enhance the destructive interference and slow down the growth of reflectance with gain. Some of the random realizations display a further reduction of the minimum reflectance by adding optical gain. The differential amplification of the modes can make their destructive interference so effective that it dominates over the amplitude growth of the modes, causing the reflectance to drop with gain. Therefore, the interplay between interference and amplification makes it possible to further minimize light reflection from a strong scattering medium by introducing optical gain.