Distribution of light inside three-dimensional scattering slabs: Comparison of radiative transfer and electromagnetic theory

Abstract

In this study, we examine the energy density distribution inside laterally infinitely extended turbid slabs due to perpendicular and oblique plane illumination with monochromatic light. We solve the scalar radiative transfer equation analytically for the fluence rate inside a slab to obtain the normalized energy density and compare it to the average energy density resulting from full vectorial numerical solutions of Maxwell’s equations. The scattering slabs have a dimensionless thickness of 300 (∼48 wavelengths) and contain monodisperse spherical particles submerged in the background medium of the slab. The volume fractions under study are up to 30%. Additionally, various angles of illumination are evaluated. The absolute value for the energy density of both theories is in agreement with <27% relative deviation for the investigated slabs. Our study shows that the scalar radiative transfer theory with the effective refractive index as a homogeneous background medium can predict the correct absolute behavior of the energy density inside the investigated scattering slabs within a few percent relative deviation, if the volume concentration of the scatterers is <20%.