Accurate semi-empirical model for annealed proton exchanged waveguides in z-cut lithium niobate

This study develops an accurate method to estimate the proton dose after proton exchange (PE) by applying a soft anneal step, typically 10-30 hours at 210°C, which solves the problems of instability and multi-phase composition of PE waveguides. The soft anneal process slows down with time and practically self-terminates once the refractive index step at 633 nm drops below 0.105, corresponding to a concentration x = 0.44 in the film H_xLi_1-xNbO₃. Proton dose estimate after soft anneal can be done with 0.25 to 0.5% precision by prism coupling measurements allowing control of the waveguide nonlinear optical frequency converters (WNOFC) quasi-phase-matching (QPM) wavelength with 0.5-1 nm accuracy.