Disorder-Induced Coherence Enables Control of Wave Transport

Abstract

The transmission matrix of a disordered medium, experimentally accessible for classical waves and central to the theory of mesoscopic electronic transport, supports transmission eigenchannels ranging from complete to vanishing transmission. This range reflects wave coherence, yet the evolution of coherence with depth across eigenchannels has not been examined. Using microwave measurements and numerical simulations, we show how wave interference evolves with depth within the sample to produce constructive or destructive interference in high- and low-transmission eigenchannels, respectively. In the highest-transmission eigenchannel, the alignment of modal contributions from the waveguide modes of an incident eigenchannel can become nearly perfect as the sample length increases, allowing transmission to remain high despite extensive multiple scattering. Although the contributions in low-transmission eigenchannels are somewhat reduced relative to those in high-transmission channels, they remain appreciable, and transmission is suppressed by their destructive interference rather than by their small magnitude. Because these contributions remain appreciable, it is possible to measure eigenchannel transmission far below the noise floor of conventional transmission and more than nine orders of magnitude below the highest transmission eigenvalue when the frequency is tuned through a transmission zero. In simulations, we determine the forward- and backward-propagating modal contributions to each eigenchannel throughout the sample and extract the corresponding flux, energy density, and velocity, whose mutual consistency validates the analysis. These results reveal how modal alignment evolves throughout disordered media and underlies the contrasting characteristics of transmission eigenchannels.