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

The optical performance of transparent ceramics, as quantified e.g. via the real in-linetransmission, is strongly dependent on the microstructure of these ceramics. While low porosity is always a necessary condition, half a century ago it was conjectured that translucency, and even more so transparency, could only be achieved with a large grain size. However, research from the 1970s onwards has clearly shown that ceramics with a high degree of transparency can also be prepared if the grain size (and pore size) is smaller than the wavelength of light. With the advance of nanotechnology the preparation of these ceramics has become feasible, so that ceramics with real in-line transmissions approaching the theoretical maxima can now be either very fine-grained or rather coarse-grained, i.e. significantly smaller or larger than the wavelength of light. Nevertheless, successful quantitative estimates of porosity and pore size effects have become available only in the last decade. This contribution recalls Mie scattering theory and its approximations for small and large pores (Rayleigh scattering, Fraunhofer diffraction and geometrical ray optics), and the effective medium theory proposed by Apetz and van Bruggen in combination with the Rayleigh-Gans-Debye approximation for modeling the grain size dependence of the real in-line transmission for ceramics with anisotropic (and thus birefringent) crystallites. These approaches are applied here to the pore size dependence of the transmission of YAG and alumina ceramics and to the grain and inclusion size dependence of the transmission of alumina and YAG-alumina composites. We explicitly reconsider the assumptions made in these predictions and compare approximate results obtained via a recently proposed closed-form expression for the porosity and pore size dependence of the real in-line transmission with the results of exact Mie calculations for YAG and alumina ceramics. It is shown that our simple closed-form expression is a remarkably powerful tool, leading to results close to the Mie solution. Due to the relatively similar refractive indices (064.0 =?n and the fact that the birefringence of alumina is low 008.0 =?n), the porosity and pore size dependences of the real in-line transmission are very similar for YAG and alumina, and the idea might arise to prepare composites of YAG and alumina, which would have improved thermal and mechanical properties and might imply a future possibility of "composite lasers" (e.g. combining the Cr-doped ruby laser and the Nd- or Yb-doped YAG laser). This idea is briefly discussed. Modeling of the inclusion size dependence of the real in-line transmission, however, seems to indicate that (for reasonable volume fractions of the order tens of percent) the grain size of the inclusions would have to be below approximately 10 nm to guarantee sufficient transmission. Composites of this type are currently out of sight, but future nanotechnology might be able to realize materials of this type