Breakdown of light transport models in photonic scattering slabs with strong absorption and anisotropy

Ozan Akdemir*, Ad Lagendijk, Willem L. Vos

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
63 Downloads (Pure)


The radiative transfer equation (RTE) models the transport of light inside photonic scattering samples such as paint, foam, and tissue. Analytic approximations to solve the RTE fail for samples with strong absorption and dominant anisotropic scattering and predict unphysical negative energy densities and the diffuse flux in the wrong direction. Here we fully characterize the unphysical regions of three popular approximations to the RTE for a slab, namely the P1 approximation (or diffusion approximation), the P3 approximation, and a popular modification to P3 that corrects the forward scattering in the approximation. We find that the δ function correction to P3 eliminates the unphysical range in the forward scattering. In addition, we compare the predictions of these analytical methods to exact Monte Carlo simulations for the physical and unphysical regions. We present maps of relative errors for the albedo and the anisotropy of the scatterers for a realistic index contrast typical of a polymer slab in air and optical thickness. The relative error maps provide a guideline for the accuracy of the analytical methods to interpret experiments on light transport in photonic scattering slabs. Our results show that the P1 approximation is significantly inaccurate to extract transport parameters unless the sample scatters purely isotropic and elastic. The P3 approximation exceeds P1 in terms of accuracy in its physical range for moderate absorption, and the P3 with the δ function correction is the most accurate approximation considered here for the forward direction.

Original languageEnglish
Article number033517
JournalPhysical Review A
Issue number3
Early online date21 Mar 2022
Publication statusPublished - Mar 2022


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