Theoretical modeling of refractive index in ion implanted LiNbO3 waveguides

Abstract

A theoretical model is developed to evaluate the roles of various mechanisms, including the molar polarization and molar volume, the spontaneous polarization and the photoelastic effect, for the modifications of refractive indices in ion-implanted LiNbO3 waveguides. Based on the model, numerical calculations of refractive indices as a function of the lattice damage level in LiNbO3 crystals of different crystalline orientations (X, Y, and Z), are performed, with results in a good agreement with experimental data. The analysis indicates that the spontaneous polarization, the molar polarization, and molar volume play important roles in determining the index profiles in ion implanted LiNbO3. In addition, the contribution of the strain-induced photoelastic effect has been identified for different damage levels.

Birefringence changes induced by thermal cycling in lithium niobate

“…The actual value is likely different because we omitted a great many defect structures, and longer-range interactions between clusters are expected to distort the lattice and have not been considered. The refractive index is affected via the quadratic electro-optic effect, namely ∆( 33 P s ∆P Yin et al (2010). Inserting values P s = 0.71 C/m 2 and g 33 = 0.09 m 4 /C 2 and n e = 2.2 for congruent LN, we estimate a change in extraordinary index of −0.6 × 10 −3 , or an expected slope of 6.5 × 10 −6 /K.…”

Theoretical modeling and experiment of refractive index change in He+ ion-implanted KTP waveguide

“…For simplicity, quadratic electro-optic coefficients, spontaneous polarization, and the photoelastic coefficient have been assumed to have linear relations with the fraction of the material being undamaged (1 − ρ) [25]: Combining these with Eq. (2) yields a new expression:…”

“…When the contribution of the molar polarization and volume has been taken into account, a simple expression [25] can be obtained:…”

“…The theoretical model on illustrating refractive index changes in ion-implanted waveguides has been studied mostly on LiNbO 3 crystal [7,[21][22][23][24][25]. The implant-induced index profile in LiNbO 3 shows apparent difference from that in the implanted KTP waveguide.…”

Refractive index profile in ion-implanted neodymium-doped yttrium vanadate waveguide: the relation between index change and lattice damage

“…According to previous research, 19,20 several factors such as spontaneous polarization, molar polarization, and molar volume are assumed to be responsible for the refractive index change in implanted crystals because implant-induced lattice damage could directly cause change of these parameters. In the case of YVO 4 crystal, the impact of spontaneous polarization on the refractive index can be ignored because its tetragonal zircon structure and high lattice symmetry represent the zero value of electro-optic coefficient.…”