Time delay in 1D disordered media with high transmission

TL;DR

This paper investigates the statistical properties of time delays in reflected and transmitted waves in highly transparent 1D disordered media, revealing Gaussian behaviors consistent with the central limit theorem through numerical simulations.

Contribution

It demonstrates that reflection amplitudes follow complex Gaussian distributions and that transmission time delays are additive with Gaussian fluctuations, extending understanding of wave propagation in disordered media.

Findings

Reflection amplitudes are complex Gaussian variables.

Transmission time delays are additive with Gaussian fluctuations.

Time delay distributions exemplify the central limit theorem.

Abstract

We study the time delay of reflected and transmitted waves in 1D disordered media with high transmission. Highly transparent and translucent random media are found in nature or can be synthetically produced. We perform numerical simulations of microwaves propagating in disordered waveguides to show that reflection amplitudes are described by complex Gaussian random variables with the remarkable consequence that the time-delay statistics in reflection of 1D disordered media are described as in random media in the diffusive regime. For transmitted waves, we show numerically that the time delay is an additive quantity and its fluctuations thus follow a Gaussian distribution. Ultimately, the distributions of the time delay in reflection and transmission are physical illustrations of the central limit theorem at work.