Relationship between refractive index increase and Ti⁴⁺ concentration in Ti: LiNbO₃ waveguide fabricated by Ti⁴⁺ diffusion in near-stoichiometric LiNbO₃ substrate

Multi-mode Ti:LiNbO₃ planar waveguide was fabricated by in-diffusion of 100-nm-thick Ti-metal film coated onto a near-stoichiometric LiNbO₃ substrate prepared by vapor transport equilibration. The crystalline phase and composition in the waveguide were characterized. The guided modes in the planar waveguide were characterized by prism coupling technique. The refractive index profile is constructed from the measured mode indices using the inverse Wentzel-Krames-Brillouin method, and correlated with the Ti⁴⁺- concentration profile, which was obtained from secondary-ion-mass-spectroscopy analysis. The results show that the waveguide still retains the LiNbO₃ phase, its composition is near-stoichiometric. The index change and Ti⁴⁺-concentration follow an exponential relationship with a power index 0.4 for an ordinary ray and 1.07 for an extraordinary ray. A comparison of various congruent and near-stoichiometric bulk materials or waveguides allows to conclude that the relationship is different from congruent to near-stoichiometric composition, from one fabrication method to another, and from bulk material to waveguide configuration. The difference is explained qualitatively.