Extension of the Kubelka–Munk theory for fluorescent turbid media to a nonopaque layer on a background

Abstract

Photoluminescence is one of the processes by which photons are emitted after the absorption of incoming photons at a higher energy. But the yield and spectral band shape of the emission can be altered by the optical properties of the luminophore environment through scattering and absorption. To understand these effects on a photoluminescent turbid layer, the Kubelka–Munk model, which is a two-flux approximation of the radiative transfer equation, can be used. Compared to previous works, this translucent layer can be applied on a colored opaque background. The model takes into account the absorption, scattering, and luminescent properties of the layer and the reflection by the background, for both the light excitation and the light emission. The competition between these different optical interactions is studied; e.g., the model can predict the presence of an emission maximum by increasing the thickness of the luminescent layer on a light background. Moreover, the model is extended to two important cases: the presence of a photoluminescent background and the effect of a refractive index discontinuity.