Controlling transmission eigenchannels in random media by edge reflection

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, $\rho (\mathcal{T}\to 1)\sim (1-\mathcal{T}{)}^{-\frac{1}{2}}$. At the threshold, $\rho (\mathcal{T})$ exhibits critical statistics with a distinct singularity $\sim (1-\mathcal{T}{)}^{-\frac{1}{3}}$; above it the high transmission eigenchannels disappear and $\rho (\mathcal{T})$ vanishes for $\mathcal{T}$ 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.

17 pages, 12 figures

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• Universal optimal transmission of light through disordered materials
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• Modification of light transmission channels by inhomogeneous absorption in random media
• Supersymmetric field theory of local light diffusion in semi-infinite media
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Cited by in corpus (8)

• Control of mesoscopic transport by modifying transmission channels in opaque media
• Optical transmission matrix as a probe of the photonic interaction strength
• Impact of non-Hemiticity on modal strength and correlation in transmission through random open cavities
• Invariance principle for wave propagation inside inhomogeneously disordered materials
• Diffusion in translucent media
• Super-universality of eigenchannel structures and possible optical applications
• Energy-leaky modes in partially measured scattering matrices of disordered media
• Impact of surface reflection on transmission eigenvalue statistics and energy distributions inside random media