Statistics and control of waves in disordered media

TL;DR

This paper reviews the fundamental concepts and recent advances in understanding wave propagation in disordered media, focusing on transmission matrix analysis, statistical properties, and energy distribution within random systems.

Contribution

It provides a comprehensive review of the use of the transmission matrix in analyzing wave behavior in disordered media, combining experimental, theoretical, and simulation approaches.

Findings

Transmission matrix describes wave scaling and fluctuations.

Statistics of transmission and focusing are characterized.

Energy density distribution of eigenchannels is analyzed.

Abstract

Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to describe the scaling, fluctuations, delay time, density of states, and control of waves propagating through and within disordered systems. Microwave measurements, random matrix theory calculations, and computer simulations are employed to study the statistics of transmission and focusing in single samples and the scaling of the probability distribution of transmission and transmittance in random ensembles. Finally, we explore the disposition of the energy density of transmission eigenchannels inside random media.