Hole geometry effect on stop-band characteristics of photonic crystal in Ti-diffused LiNbO₃ waveguide

Effects of finite hole depth and non-cylindrical hole shape on stop-band characteristics of photonic crystal formed by air-hole square lattice in Ti-diffused LiNbO₃ strip waveguide were studied theoretically. The study shows that hole depth determines the contrast of stop-band, and the hole radius and conical angle determine the bandgap and location. Cylindrical holes must be sufficiently deep so as to overlap most of waveguide mode and hence obtain a stop-band with high contrast, sharp edge and broad bandgap. Non-cylindrical holes seriously affect the stop-band features. Conical holes cause low contrast and narrow bandgap, and the stop-band shifts with the conical angle. For the cylindrical-conical hybrid holes, the cylindrical portion determines the desired features. Given the difficulty in fabricating high aspect-ratio cylindrical holes, we propose to fabricate the holes at the bottom of a shallow trench, which is introduced into waveguide surface prior to the hole milling.