Transmission eigenvalues in random media with surface reflection

TL;DR

This paper develops a theoretical framework to understand how surface reflection influences the distribution of transmission eigenvalues in diffusive waves, revealing a nonanalytic transition at a critical reflection strength.

Contribution

The study introduces a first-principles theory for transmission eigenvalues in media with surface reflection and confirms the transition through numerical simulations.

Findings

Distribution exhibits a nonanalytic transition at a critical reflection value.

Highest transmission eigenvalue is less than one above the critical point.

Equal reflection at input and output surfaces results in a highest eigenvalue of one.

Abstract

The impact of surface reflection on the statistics of transmission eigenvalues is a largely unexplored subject of fundamental and practical importance in statistical optics. Here, we develop a first-principles theory and confirm numerically that the distribution of transmission eigenvalues of diffusive waves exhibits a nonanalytic `transition' as the strength of surface reflection at one surface passes through a critical value while that at the other is fixed. Above the critical value, the highest transmission eigenvalue is strictly smaller than unity and decreases with increasing internal reflection. When the input and output surfaces are equally reflective, the highest transmission eigenvalue is unity and the transition disappears irrespective of the strength of surface reflection.