A novel approach for the analysis of Ti-PE: LiNbO₃ distributed parameter waveguides

Proton exchange is becoming widely accepted as a complementary technique to titanium indiffusion for the fabrication of integrated optical waveguides in LiNbO₃. In this paper, we propose, for the first time to our knowledge, a novel approach to analyze the optical distributed waveguides formed by local index variation, combining two processes, titanium indiffusion (Ti), and a localized patterned proton exchange (PE), yielding to the Ti-PE: LiNbO₃ distributed parameter waveguides. We present a straightforward extension of the Wentzel Kramers and Brillouin (WKB) technique covering the computation of a single diffusion's effective index, to multiple successive diffusions having a specific graded-index profile. The efficiency of the method is shown by varying some of its parameters, like the index modulation or the proton exchanged depth, for example. The simulation's result proves that the evolution of the reflectivity's spectrum has been found to be in a good agreement with prediction.