Transmission statistics and focusing in single disordered samples

TL;DR

This study demonstrates that in disordered samples, the transmission statistics and focusing capabilities are governed by a single parameter, the participation number of the transmission matrix eigenvalues, applicable in microwave experiments and random matrix models.

Contribution

It introduces the participation number as a key parameter controlling transmission statistics and focusing in disordered samples, linking experimental results with theoretical models.

Findings

Participation number M determines transmission statistics.

Inverse of M equals the variance of relative total transmission.

Contrast in maximal focusing equals M.

Abstract

We show in microwave experiments and random matrix calculations that in samples with a large number of channels the statistics of transmission for different incident channels relative to the average transmission is determined by a single parameter, the participation number of the eigenvalues of the transmission matrix, M. Its inverse, M-1, is equal to the variance of relative total transmission of the sample, while the contrast in maximal focusing is equal to M. The distribution of relative total transmission changes from Gaussian to negative exponential over the range in which M-1 changes from 0 to 1. This provides a framework for transmission and imaging in single samples.