Reflectance Fluctuations in an Absorbing Random Waveguide

TL;DR

This paper investigates the statistical behavior of reflectance in disordered waveguides with weak absorption, revealing universal fluctuation regimes and crossover behaviors as waveguide length varies.

Contribution

It identifies two distinct regimes of reflectance fluctuations in absorbing disordered waveguides and characterizes their crossover behaviors with respect to absorption strength and waveguide length.

Findings

Universal fluctuations in high absorption regime.

Crossover in reflectance variance with waveguide length.

Asymmetric reflectance distribution in low absorption regime.

Abstract

We study the statistics of the reflectance (the ratio of reflected and incident intensities) of an $N$-mode disordered waveguide with weak absorption $\gamma$ per mean free path. Two distinct regimes are identified. The regime $\gamma N^2\gg1$ shows universal fluctuations. With increasing length $L$ of the waveguide, the variance of the reflectance changes from the value $2/15 N^2$, characteristic for universal conductance fluctuations in disordered wires, to another value $1/8 N^2$, characteristic for chaotic cavities. The weak-localization correction to the average reflectance performs a similar crossover from the value $1/3 N$ to $1/4 N$. In the regime $\gamma N^2\ll1$, the large-$L$ distribution of the reflectance $R$ becomes very wide and asymmetric, $P(R)\propto (1-R)^{-2}$ for $R\ll 1-\gamma N$.