Controlling transmission eigenchannels in random media by edge reflection

TL;DR

This paper demonstrates that edge reflection asymmetry in quasi-1D diffusive media controls transmission eigenchannels, revealing a transition in their statistical distribution and linking high transmission channels to Anderson localization phenomena.

Contribution

It uncovers how edge reflection asymmetry governs transmission eigenchannels and identifies a transition point affecting their distribution, connecting wave transport to Anderson localization.

Findings

Existence of a threshold asymmetry parameter for high transmission channels.

Critical statistics of transmission eigenvalues at the threshold.

Mapping of the eigenvalue transition to resonator shuffling in Anderson localization.

Abstract

Transmission eigenchannels and associated eigenvalues, that give a full account of wave propagation in random media, have recently emerged as a major theme in theoretical and applied optics. Here we demonstrate, both analytically and numerically, that in quasi one-dimensional ($1$D) diffusive samples, their behavior is governed mostly by the asymmetry in the reflections of the sample edges rather than by the absolute values of the reflection coefficients themselves. We show that there exists a threshold value of the asymmetry parameter, below which high transmission eigenchannels exist, giving rise to a singularity in the distribution of the transmission eigenvalues, $\rho({\cal T}\rightarrow 1)\sim(1-{\cal T})^{-\frac{1}{2}}$. At the threshold, $\rho({\cal T})$ exhibits critical statistics with a distinct singularity $\sim(1-{\cal T})^{-\frac{1}{3}}$; above it the high transmission eigenchannels disappear and $\rho({\cal T})$ vanishes for ${\cal T}$ exceeding a maximal transmission eigenvalue. We show that such statistical behavior of the transmission eigenvalues can be explained in terms of effective cavities (resonators), analogous to those in which the states are trapped in $1$D strong Anderson localization. In particular, the $\rho ( \mathcal{T}) $-transition can be mapped onto the shuffling of the resonator with perfect transmittance from the sample center to the edge with stronger reflection. We also find a similar transition in the distribution of resonant transmittances in $1$D layered samples. These results reveal a physical connection between high transmission eigenchannels in diffusive systems and $1$D strong Anderson localization. They open up a fresh opportunity for practically useful application: controlling the transparency of opaque media by tuning their coupling to the environment.