## Abstract

We have demonstrated the possibility that near-stoichiometric $\mathrm{Ti}:\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_{3}$ strip waveguides are fabricated by carrying out vapor transport equilibration at $1060\xb0\mathrm{C}$ for $12\text{\hspace{0.17em}}\mathrm{h}$ on a congruent $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_{3}$ substrate with photolithographically patterned $4\u20138\text{\hspace{0.17em}}\mu \mathrm{m}$ wide, $115\text{\hspace{0.17em}}\mathrm{nm}$ thick Ti strips. Optical characterizations show that these waveguides are single mode at $1.5\text{\hspace{0.17em}}\mu \mathrm{m}$ and show a waveguide loss of $1.3\text{\hspace{0.17em}}\mathrm{dB}\u2215\mathrm{cm}$ for TM mode and $1.1\text{\hspace{0.17em}}\mathrm{dB}\u2215\mathrm{cm}$ for TE mode. In the width/depth direction of the waveguide, the mode field follows the Gauss/Hermite–Gauss function. Secondary-ion-mass spectrometry (SIMS) was used to study Ti-concentration profiles in the depth direction and on the surface of the $6\text{\hspace{0.17em}}\mu \mathrm{m}$ wide waveguide. The result shows that the Ti profile follows a sum of two error functions along the width direction and a complementary error function in the depth direction. The surface Ti concentration, $1\u2215e$ width and depth, and mean diffusivities along the width and depth directions of the guide are similar to $3.0\times {10}^{21}\text{\hspace{0.17em}}{\mathrm{cm}}^{-3}$, $3.8\text{\hspace{0.17em}}\mu \mathrm{m}$, $2.6\text{\hspace{0.17em}}\mu \mathrm{m}$, 0.30 and $0.14\text{\hspace{0.17em}}\mu {\mathrm{m}}^{2}\u2215\mathrm{h}$, respectively. Micro-Raman analysis was carried out on the waveguide endface to characterize the depth profile of Li composition in the guiding layer. The results show that the depth profile of Li composition also follows a complementary error function with a $1\u2215e$ depth of $3.64\text{\hspace{0.17em}}\mu \mathrm{m}$. The mean $(\left[{\mathrm{Li}}_{\mathrm{Li}}\right]+\left[{\mathrm{Ti}}_{\mathrm{Li}}\right])\u2215(\left[{\mathrm{Nb}}_{\mathrm{Nb}}\right]+\left[{\mathrm{Ti}}_{\mathrm{Nb}}\right])$ ratio in the waveguide layer is about 0.98. The inhomogeneous Li-composition profile results in a varied substrate index in the guiding layer. A two-dimensional refractive index profile model in the waveguide is proposed by taking into consideration the varied substrate index and assuming linearity between Ti-induced index change and Ti concentration. The net waveguide surface index increments at $1545\text{\hspace{0.17em}}\mathrm{nm}$ are 0.0114 and 0.0212 for ordinary and extraordinary rays, respectively. Based upon the constructed index model, the fundamental mode field profile was calculated using the beam propagation method, and the mode sizes and effective index versus the Ti-strip width were calculated for three lower TM and TE modes using the variational method. An agreement between theory and experiment is obtained.

© 2008 Optical Society of America

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