Modified Kubelka-Munk equations for localized waves inside a layered medium

Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Mar;75(3 Pt 2):036601. doi: 10.1103/PhysRevE.75.036601. Epub 2007 Mar 1.

Abstract

We present a pair of coupled partial differential equations to describe the evolution of the average total intensity and intensity flux of a wave field inside a randomly layered medium. These equations represent a modification of the Kubelka-Munk equations, or radiative transfer. Our modification accounts for wave interference (e.g., localization), which is neglected in radiative transfer. We numerically solve the modified Kubelka-Munk equations and compare the results to radiative transfer as well as to simulations of the wave equation with randomly located thin layers.