Third Cumulant of the total Transmission of diffuse Waves

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, $⟨⟨T_a^3⟩⟩$, to the normalized second cumulant $⟨⟨T_a^2⟩⟩$. For a broad Gaussian beam profile it is found that $⟨⟨T_a^3⟩⟩=\frac{16}{5}⟨⟨T_a^2⟩{⟩}^2$. This is in good agreement with data of optical experiments.

16 pages revtex, 8 separate postscript figures