Shape-dependence of transmission, reflection and absorption eigenvalue densities in disordered waveguides with dissipation

TL;DR

This paper investigates how absorption and geometry influence the distribution of transmission, reflection, and absorption eigenvalues in disordered waveguides, revealing geometry-dependent behaviors and transitions in eigenvalue densities.

Contribution

It demonstrates that absorption and waveguide asymmetry alter eigenvalue densities, challenging the universal bimodal distribution in lossless systems and enabling new control strategies.

Findings

Eigenvalue densities depend on waveguide geometry with absorption.

Absorption eigenvalue density transitions from single-peak to double-peak.

Reflection and absorption eigenvalues depend on incident side in asymmetric waveguides.

Abstract

The universal bimodal distribution of transmission eigenvalues in lossless diffusive systems un- derpins such celebrated phenomena as universal conductance fluctuations, quantum shot noise in condensed matter physics and enhanced transmission in optics and acoustics. Here, we show that in the presence of absorption, density of the transmission eigenvalues depends on the confinement geometry of scattering media. Furthermore, in an asymmetric waveguide, densities of the reflection and absorption eigenvalues also depend of the side from which the waves are incident. With increas- ing absorpotion, the density of absorption eigenvalues transforms from single-peak to double-peak function. Our findings open a new avenue for coherent control of wave transmission, reflection and absorption in random media.