Effective medium theories for composite optical materials in spectral ranges of weak absorption: the case of Nb2O5–SiO2 mixtures

Abstract

The validity of effective medium theories (EMTs) for mixtures of dielectric materials in weak absorption regions is studied. Based on the Bergman spectral representation, it is possible to show that for any EMT the absorption properties of a mixture consist basically of scaling of the absorption properties of the material with highest absorption. The real part of the dielectric function remains unaffected by the absorption properties. Thin films consisting of Nb2O5–SiO2 mixtures are characterized using optical measurements and the results are compared with the calculations of EMTs. The large discrepancies between the absorption properties observed experimentally and those calculated using EMTs are justified by the failure of these theories to predict a compositional dependence of relevant structural parameters, such as the band-gap energy or the width of localized states. This failure, however, affects the calculation of the refractive index in the weak absorption regions to a less significant degree.