Theoretical expression for change of extraordinary refractive index in annealed proton exchanged LiNbO3 optical waveguides

A general expression for the change in extraordinary refractive index of the annealed proton exchanged LiNbO₃ waveguide has been deduced. The expression deduced explains the experimental results of decrease in change of extraordinary refractive index with annealing. The effect of annealing time has also been incorporated following Cao's model (Cao, Ramaswamy, Srivastava, J. Lightwave Technol. 10 (1992) 1302–1313). The concentration profile of protons in the annealed waveguide has been deduced theoretically, which is consistent with the previous results. The spontaneous polarization has been considered as the central mechanism for change in extraordinary refractive index due to proton exchange with annealing.