Rayleigh scattering with material dispersion for low volume fraction transparent glass ceramics

Abstract

In this report we review the literature concerning the theory of scattering in transparent glass ceramics (TGCs). The parameters dictating scattering are all relational and include the size of the scatterers relative to the wavelength of propagating light, the volume fraction of crystals relative to the vitreous matrix and the refractive index difference between crystal and glass. We extend the theory by including material dispersion for the case of low, i.e., <5% volume fraction of nanocrystals relative to the vitreous matrix where Rayleigh scattering is appropriate. We examine five crystal-glass sets and calculate the scattering coefficient from the visible to the mid-infrared. We show that for all combinations, the scattering coefficient departs from the fixed refractive index case by as much as 48% at 2.5 µm for BaF2 nanocrystals in an aluminosilictate glass. For every case studied, the addition of material dispersion reduces the dependence on wavelength from the standard λ−p where p = 4 to as much as p = 4.8 for the case of PbF2 nanocrystals in an aluminosilictate glass. For the accurate estimation of the Rayleigh scattering coefficient in a TGC, knowledge of material dispersion is therefore essential.