Notice of Retraction: Relation of refractive index change to ti-concentration in ti-diffused LiNbO₃ waveguide doped with Sc³⁺

Multimode Ti⁴⁺-diffused LiNbO₃ planar waveguide doped with Sc³⁺ ions was fabricated by codiffusion of stacked Sc ₂O₃ and Ti-metal thin film coated onto Z-cut congruent LiNbO₃ substrate at 1060 °C in wet O₂. The Ti ⁴⁺-concentration was profiled by secondary ion mass spectrometry. The refractive index profile is constructed from measured mode index, and correlated with the Ti⁴⁺ profile. Other two related issues including the contribution of Sc $^{3+}{\hbox{-}}$doping to substrate refractive index and Li₂O out-diffusion were also studied. The results show that the Sc³⁺-doping has little contribution to the substrate index and the Li₂O out-diffusion was effectively suppressed. The index change and Ti⁴⁺-concentration follow an exponential relationship with a power index 0.54/0.79 for the ordinary/extraordinary ray. The relationship is similar to that of conventional Ti:LiNbO₃ waveguide because of little contribution of Sc ³⁺-doping to the substrate index and effective suppression for Li ₂O out-diffusion. Some considerations for fabricating an optical-damage-resistant Ti:Sc:LiNbO₃ waveguide are given.