Theoretical modeling of refractive index in ion implanted $LiNbO3$ waveguides

A theoretical model is developed to evaluate the roles of various mechanisms, including the molar polarization and molar volume, the spontaneous polarization and the photoelastic effect, for the modifications of refractive indices in ion-implanted $LiNbO3$ waveguides. Based on the model, numerical calculations of refractive indices as a function of the lattice damage level in $LiNbO3$ crystals of different crystalline orientations (X, Y, and Z), are performed, with results in a good agreement with experimental data. The analysis indicates that the spontaneous polarization, the molar polarization, and molar volume play important roles in determining the index profiles in ion implanted $LiNbO3$⁠. In addition, the contribution of the strain-induced photoelastic effect has been identified for different damage levels.