Porosity and pore size dependence of the real in-line transmission of YAG and alumina ceramics

Based on the exact Mie solution for spheres and several approximations known from scattering theory (Rayleigh, Fraunhofer, Rayleigh-Gans-Debye), including the less well known van de Hulst approximation and a new closed-form expression (using scaling of the Rayleigh result), the real in-line transmission (RIT) of porous YAG, porous alumina and dense YAG-alumina composites is analyzed. In particular, pore size and inclusion size dependences of the RIT are calculated for these materials at wavelengths 695, 1031 and 2940 nm. It is shown that the van de Hulst approximation is superior to all other approximations when the refractive indices are close as in the case of almost-index-matching inclusions at low concentrations, but our closed-form expression, although in this very special case slightly less precise than the van de Hulst approximation, is always the safer choice for estimating the RIT. Both approaches are superior to any of the other approximations.