Intensity distribution for waves in disordered media: deviations from Rayleigh statistics

TL;DR

This paper investigates the intensity distribution of monochromatic waves in disordered media, revealing deviations from Rayleigh statistics and identifying different asymptotic behaviors depending on source and detector placement.

Contribution

It provides new insights into the statistical behavior of wave intensities in disordered media, including deviations from classical Rayleigh statistics and the emergence of stretched-exponential regimes.

Findings

Deviations from Rayleigh statistics at high intensities.

Logarithmically-normal asymptotic behavior of P(I).

Intermediate stretched-exponential regime when source and detector are near opposite edges.

Abstract

We study the intensity distribution function, P(I), for monochromatic waves propagating in quasi one-dimensional disordered medium, assuming that a point source and a point detector are embedded in the bulk of the medium. We find deviations from the Rayleigh statistics at moderately large I and a logarithmically-normal asymptotic behavior of P(I). When the radiation source and the detector are located close to the opposite edges of the sample (on a distance much less then the sample length), an intermediate regime with a stretched-exponential behavior of P(I) emerges.