Determination of internal reflectance for photonic glasses

We experimentally show that the angular distribution of diffusely transmitted light from highly scattering dense media, such as photonic glasses, deviates significantly from Fresnel's law. We model a system of a photonic glass on a substrate by introducing an optical boundary layer that is sandwiched between the bulk effective medium and the substrate. Based on the model, we calculate the extrapolation length ratio, the photon transport/scattering mean-free paths, and the angular distribution of transmitted light intensity. The internal reflectance of the photonic glass is accurately determined by considering the diffuse scattering in the boundary layer. The modeling results agree well with the experimentally measured angular distribution and transport mean-free path. Our modeling also reaffirms that the real physical process of light scattering near the interface between photonic glass and the substrate cannot be simply described as internal reflection from a flat surface. The extrapolation length ratio of a photonic glass calculated from our boundary layer model is considerably larger than that from Fresnel's law. This indicates that the transport mean-free paths determined in other reported experiments for highly scattering dense media may have included significant errors and that the boundary layer analysis could be a good replacement to accurately describe the internal reflectance for photonic glasses.