Electro-optic coefficients r₁₃ and r₃₃ of singly Er³⁺-doped and In³⁺/Er³⁺-codoped LiNbO₃ crystals

A series of singly Er³⁺-doped and doubly In³⁺/Er³⁺-doped congruent LiNbO₃ crystals were grown by Czochralski method. The Er³⁺-only doped crystals were grown from the growth melts doped with different concentrations of Er₂O₃ up to 1 mol%, and the In³⁺/Er³⁺-codoped crystals from the melts doped with fixed 0.5 mol% Er₂O₃ while varied In₂O₃ contents of 0.0, 0.5, 1.0 and 1.5 mol%. The electro-optic coefficients γ₁₃ and γ₃₃ of these doped crystals were measured by Mach-Zehnder interferometry. Both clamped and unclamped coefficients were measured. The results show that both γ₁₃ and γ₃₃ reveal small Er³⁺ and In³⁺ doping effects. In the Er³⁺-only doping case, γ₁₃ almost does not change within the experimental error of 3%, γ₃₃ reveals a degradation tendency with a rise in Er³⁺ doping level, but the degradation is no more than 5% in the considered Er³⁺ concentration range 0–3.0 mol% (in crystal). In the In³⁺/Er³⁺-codoping case, both γ₁₃ and γ₃₃ can be regarded as unchanged in the studied In³⁺ concentration range of 0–2.6 mol% (in crystal) within the error. The small Er³⁺ or In³⁺ doping effect is desired in light of electro-optic application of these crystals. It is qualitatively explained on the basis of EO coefficient model and doping effect on defect structure of LiNbO₃.