On the optical thickness of disordered particulate media

In this work ray-tracing theory is employed to determine the amount of propagating incident optical energy, characterized by the Poynting vector, that is reflected and the amount that is absorbed by aggregates of randomly dispersed particles. It is assumed that any absorbed optical energy becomes entirely trapped within the particles, and is not re-emitted. Of particular interest is to ascertain the dependence of the overall scattering on the volume fraction of the particles and the ratio of the refractive indices of the ambient medium and the particles. Both analytical and numerical studies are performed to study the volume fractions and reflectivity of the particles needed to achieve optically thick systems, i.e. systems where, in an overall averaged sense, no incident electromagnetic radiation penetrates through the aggregate collection of particles.