Modeling of the index change in K(+)-Na(+) ion-exchanged glass

We have measured the surface index change and birefringence in K(+)-Na(+) ion-exchanged waveguides and compared the results with theory. The contribution to the index change caused by the polarizability/volume changes (Deltan(p)) is calculated using two theoretical models which use empirical relations based on the glass composition. In both cases, we encounter large discrepancies between the predicted and measured values which are attributed to the inherent deficiency in the models, which assume free expansion of the glass in calculating the volume changes. Recognizing that the net volume change is much smaller, we accurately measure its value and show that both models can be used to predict Deltan(p) with the same accuracy, provided that the correct volume change is used. We show that the limitation in accuracy is dictated by measurement errors and uncertainties in the values of the ionic radii and polarizabilities. We also present a unique and systematic method for determining the compressive stress generated in the glass resulting from ion exchange.