Notice of Retraction: Relationship between refractive index change and Ti concentration in bulk Ti-doped LiNbO₃ crystal

Relationship between refractive index change and Ti concentration in bulk Ti-doped congruent LiNbO₃ crystal is studied. A series of bulk Ti-doped congruent LiNbO₃ crystals with different Ti concentrations up to 12 mol% in crystal were grown. The Ti concentration in crystal was determined by neutron activation analysis. The results show that the distribution coefficient k_eff of Ti ions varies within 0.47-0.74 and there exists a transition region near 6.0 mol%, below which the k_eff varies within 0.47-0.56 and above which the k_eff steps up to 0.74. The ordinary and extraordinary refractive indices of the crystals were measured and correlated with Ti concentration. The results show that the ordinary/extraordinary index change and Ti concentration follow an exponential/linear relationship, which is similar to that of congruent Ti:LiNbO₃ waveguide but different from that of either Ti-doped near-stoichiometric bulk material or waveguide. It is concluded that the relationship changes with material composition but does not change from bulk material to waveguide structure.