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

TL;DR

This paper introduces modified Kubelka-Munk equations that incorporate wave interference effects like localization, providing a more accurate description of wave behavior inside layered media compared to traditional radiative transfer models.

Contribution

The authors develop a new set of coupled PDEs that extend the classical Kubelka-Munk equations to include wave interference, enabling better modeling of localized waves in layered structures.

Findings

Modified equations match wave simulations more closely than classical models.

Numerical solutions demonstrate the importance of interference effects.

Enhanced understanding of wave localization in layered media.

Abstract

We present a pair of coupled partial differential equations to describe the evolution of the average total intensity and intensity flux of a wavefield 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.