Analytical modeling of light transport in scattering materials with strong absorption

Abstract

We have investigated the transport of light through slabs that both scatter and strongly absorb, a situation that occurs in diverse application fields ranging from biomedical optics, powder technology, to solid-state lighting. In particular, we study the transport of light in the visible wavelength range between $420$ and $700$ nm through silicone plates filled with YAG:Ce$^{3+}$ phosphor particles, that even re-emit absorbed light at different wavelengths. We measure the total transmission, the total reflection, and the ballistic transmission of light through these plates. We obtain average single particle properties namely the scattering cross-section $\sigma_s$, the absorption cross-section $\sigma_a$, and the anisotropy factor $\mu$ using an analytical approach, namely the P3 approximation to the radiative transfer equation. We verify the extracted transport parameters using Monte-Carlo simulations of the light transport. Our approach fully describes the light propagation in phosphor diffuser plates that are used in white LEDs and that reveal a strong absorption ($L/\ell_{\mathrm{a}} > 1$) up to $L/\ell_{\mathrm{a}} = 4$, where $L$ is the slab thickness, $\ell_{\mathrm{a}}$ is the absorption mean free path. In contrast, the widely used diffusion theory fails to describe this parameter range. Our approach is a suitable analytical tool for industry, since it provides a fast yet accurate determination of key transport parameters, and since it introduces predictive power into the design process of white light emitting diodes.