Broadband mean free path of diffuse light in polydisperse ensembles of scatterers for white light-emitting diode lighting

We study the diffuse transport of light through polymer slabs containing TiO₂ scattering particles. The slabs are diffuser plates typical of a commercial white light-emitting diode (LED) module (Fortimo). We have measured the diffuse transmission and reflection properties over a broad wavelength range (470–840 nm) from which we derive the transport mean free path using the theory of light diffusion. With increasing scatterer density, the mean free path becomes shorter. The mean free path increases with wavelength; hence, blue light is scattered more strongly than red light. To interpret the results, we propose an ab initio model without adjustable parameters for the mean free path by using Mie theory. We include inhomogeneous broadening as a result of the size distribution of the scattering particles asmeasured by dynamic light scattering. Surprisingly, the calculatedmean free path decreases with wavelength, at variance with our experiments, which is caused by particles with radii R in excess of 0.25 μm. Close inspection of the scatterers by electron microscopy reveals that large particles (R > 0.4 μm) consist of clusters of small particles (R < 0.13 μm). Therefore, we have improved our model by only taking into account the individual scatterers within the clusters. This model predicts mean free paths in good agreement with our experimental results. We discuss consequences of our results to white LED lighting modules.