Prediction of space-charge density and space-charge field in thermally ion-exchanged planar surface waveguides

Using an accurate analytical expression for describing the numerical solution of the diffusion equation in planar ion-exchanged waveguides, we present normalized depth profiles for space-charge field and density as a function of the mismatch in the self diffusion coefficients of the two cations. Our results are presented in terms of analytical expressions as well as universal curves, useful for any cation pair, substrate glass, or salt. It is also shown that most of the analytical expressions for the refractive index profile used in the literature yield unphysical results.