Edge reflection-driven transition in transmission eigenvalue statistics in random media

We show both analytically and numerically that in quasi-one-dimensional (1D) diffusive samples the distribution of transmission eigenvalue (DTE) displays a phase transition as the asymmetry in the reflections of the sample edges increases. We also show numerically in 1D localized samples a similar transition, but in the distribution of resonant transmittance (DRT). These results reveal that rich physics arises from the interplay between edge reflection and the coherence of waves. This opens up new possibilities for controlling the transparency and the transmission eigenchannel structure of opaque media.