Coupling characteristics of a diffused channel-waveguide directional coupler

We present a theoretical model to calculate the coupling constant of a diffused channel-waveguide directional coupler, taking into account the variation of refractive index both along the surface and perpendicular to the surface of the waveguide. We discuss the theoretical dependence of the coupling length on various fabrication parameters. The results show good agreement with the experimental data for a Ti-diffused LiNbO_3 directional coupler.