Relationship Between Refractive Index Change and Ti Concentration in Bulk Ti-Doped $\hbox{LiNbO}_{3}$ 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 keff of Ti ions varies within 0.47-0.74 and there exists a transition region near 6.0 mol%, below which the keff varies within 0.47-0.56 and above which the keff 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.