An H+/Li+ exchange model is found to be applicable to describe the diffusion of protons when optical waveguides are formed in LiNbO3 by proton exchange methods where the proton doped crystal structure stays in the pure \alpha phase. The H+ and Li+ self-diffusion coefficients in the ion exchange model are determined as a function of the proton exchange temperature both for x-cut and z-cut LiNbO3. In this way a very useful tool for predicting the proton concentration profiles and hence the refractive index profiles of \alpha phase proton exchange LiNbO3 waveguides is achieved.
Torben Veng and Torben Skettrup, "Ion Exchange Model for \alpha Phase Proton Exchange Waveguides in LiNbO3," J. Lightwave Technol. 16, 646- (1998)