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Phys. Rev. E 75, 036601 (2007) [8 pages]

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

Matthew M. Haney
Geophysics Department, Sandia National Laboratories, Albuquerque, New Mexico 87185-0750, USA

Kasper van Wijk
Physical Acoustics Laboratory and Department of Geosciences, Boise State University, Boise, Idaho 83725, USA
Received 26 June 2006; revised 24 September 2006; published 1 March 2007

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.

©2007 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevE.75.036601
DOI: 10.1103/PhysRevE.75.036601
PACS: 42.25.Hz; 05.40.Fb; 72.15.Rn
  • 42.25.Hz
    Optical interference
  • 05.40.Fb
    Random walks and Levy flights
  • 72.15.Rn
    Localization effects (metals/alloys) including Anderson or weak localization
  • YEAR: 2007
KEYWORDS: radiative transfer, partial differential equations, wave equations, random processes

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