Getting beneath the surface of opaque media: universal structure of transmission eigenchannels

TL;DR

This paper derives a universal expression for the spatial energy distribution of transmission eigenchannels in diffusive media, revealing their complex structure and enabling control over wave propagation inside opaque materials.

Contribution

It introduces a universal formula for the average energy profile of transmission eigenchannels, linking them to localization lengths and solving a generalized diffusion equation.

Findings

Eigenchannels have a universal spatial energy distribution.

The energy profile is described by a generalized diffusion equation.

Results enable wave control inside random media.

Abstract

Because the desire to explore opaque materials is ordinarily frustrated by multiple scattering of waves, attention has focused on the transmission matrix of the wave field. This matrix gives the fullest account of transmission and conductance and enables the control of the transmitted flux; however, it cannot address the fundamental issue of the spatial profile of eigenchannels of the transmission matrix inside the sample. Here we obtain a universal expression for the average disposition of energy of transmission eigenchannels for diffusive waves in terms of auxiliary localization lengths determined by the corresponding transmission eigenvalues. The spatial profile of each eigenchannel is shown to be a solution of a generalized diffusion equation. These results reveal the rich structure of transmission eigenchannels and enable the control of wave propagation and the energy distribution inside random media.