A novel approach for the analysis of distributed partially proton-exchanged Ti:LiNbO₃ waveguides

Proton exchange is becoming widely accepted as a complementary technique to titanium indiffusion for the fabrication of optical waveguides on LiNbO ₃. In this paper, we propose, for the first time to our knowledge, a novel approach to analyze optical distributed waveguides formed by local index variation, combining two processes, titanium (Ti) indiffusion, and localized proton exchange (PE), yielding the distributed parameter waveguides. We present a straightforward extension of the ray-approximation method (RAM) covering the computation of a single diffusion effective index, as well as multiple successive diffusions with a specific graded index profile. The efficiency of the method is shown by varying some of the optical distributed waveguide parameters, such as the index modulation or the proton-exchanged depth. The simulation results in particular show that the evolution of the transmission spectrum is in good agreement with previous experimental results.