Absorption of collimated incident radiation in a semitransparent strongly scattering medium: Computational analysis and explanation of red algae blooming in snow

Abstract

The study of directional radiation absorption in weakly absorbing and strongly scattering media is of interest for a variety of important applications, including laser hyperthermia of human tumors in a therapeutic window of transparency, determination of the optical and thermal properties of highly porous ceramics, and calculations of the deep solar heating of snow cover in polar regions and mountains. In such problems, multiple scattering of radiation can lead to a non-monotonic variation of the absorbed radiation power with distance from the illuminated surface of the medium and to the appearance of the absorption maximum at some depth below the surface. This effect has a known physical explanation and can be predicted using the suggested analytical solution based on the transport approximation for the scattering phase function and the two-flux approximation for the diffuse component of the radiation intensity. The range of illumination angles at which the absorption maximum inside an optically thick medium is observed is determined. The position and magnitude of this maximum are also obtained. In the present work, the verification of this approximate solution using reference numerical calculations is carried out for the first time. It is shown that the simple analytical model is acceptable for regular calculations. Computational results for pure snow illuminated by the Sun showed that red light gives the strongest absorption maximum at a small distance from the snow surface. This is a basis of the presented physical explanation for the intense photosynthesis of red microalgae responsible for the well-known ``snow blood'' phenomenon.