  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.
