Approximate calculation of leaky-mode loss coefficients for Ti-diffused LiNbO₃waveguides

A hybrid-mode model is developed which allows analytical calculation of the leaky-mode loss coefficient in Ti-diffused LiNbO3waveguides. Field representations correspond to the approximation of geometrical optics. Hybrid-mode effective indexes are approximated utilizing the known anisotropy of LiNbO3. ForX- orY-cut waveguides the leaky mode is shown to be an extraordinary-like hybrid mode with a small ordinary field component which arises from extraordinary to ordinary power conversion at the abrupt index boundary. This ordinary index component is not bound by the graded index boundary, giving rise to the power loss. The theoretical dependence of the loss coefficient on propagation direction is in agreement with experiment.