Filtering Random Matrices: The Effect of Incomplete Channel Control in Multiple Scattering

TL;DR

This paper develops an analytic random matrix theory to understand how incomplete control over input and output channels affects the statistical properties of the scattering matrix in disordered media, revealing a transition from coherent diffusion to uncorrelated behavior.

Contribution

It introduces a new theoretical framework describing the impact of partial channel control on scattering matrix eigenvalues in disordered media.

Findings

Density of transmission eigenvalues shifts from bimodal to Gaussian distribution as control decreases.

Loss of correlation leads to reduced access to open eigenchannels.

Information capacity per channel increases with incomplete control.

Abstract

We present an analytic random matrix theory for the effect of incomplete channel control on the measured statistical properties of the scattering matrix of a disordered multiple-scattering medium. When the fraction of the controlled input channels, m1, and output channels, m2, is decreased from unity, the density of the transmission eigenvalues is shown to evolve from the bimodal distribution describing coherent diffusion, to the distribution characteristic of uncorrelated Gaussian random matrices, with a rapid loss of access to the open eigenchannels. The loss of correlation is also reflected in an increase in the information capacity per channel of the medium. Our results have strong implications for optical and microwave experiments on diffusive scattering media.