Third Cumulant of the total Transmission of diffuse Waves

TL;DR

This paper develops a theoretical framework relating the third cumulant to the second cumulant of total wave transmission in multiple scattering, validated by optical experimental data.

Contribution

It introduces a diagrammatic theory connecting the third and second cumulants of transmission, providing analytical predictions for diffuse wave scattering.

Findings

The third cumulant is proportional to the square of the second cumulant.

The theory's predictions agree well with optical experiment data.

Provides a new analytical relation for cumulants in wave scattering.

Abstract

The probability distribution of the total transmission is studied for waves multiple scattered from a random, static configuration of scatterers. A theoretical study of the second and third cumulant of this distribution is presented. Within a diagrammatic approach a theory is developed which relates the third cumulant normalized to the average, $\langle \langle T_a^3 \rangle \rangle$, to the normalized second cumulant $\langle \langle T_a^2 \rangle \rangle$. For a broad Gaussian beam profile it is found that $\langle \langle T_a^3 \rangle \rangle= \frac{16}{5} \langle \langle T_a^2 \rangle \rangle^2 $. This is in good agreement with data of optical experiments.