The impact of finite-depth cylindrical and conical holes in lithium niobate photonic crystals

Abstract

The performance of lithium niobate (LN) photonic crystals (PhCs) is theoretically analyzed with transmission spectra and band diagrams as calculated by the 3-D Finite-Difference Time Domain (FDTD) method. For a square lattice of holes fabricated in the top surface of an Annealed Proton-Exchange (APE) waveguide, we investigate the influence of both finite hole depth and non-cylindrical hole shape, using a full treatment of the birefringent gradient index profile. As expected, cylindrical holes which are sufficiently deep to overlap the APE waveguide mode (centered at 2.5μm below the surface) produce transmission spectra closely resembling those predicted by simple 2-D modeling. As the hole depth decreases without any change in the cylindrical shape, the contrast between the photonic pass- and stop-bands and the sharpness of the band-edge are slowly lost. We show that this loss of contrast is due to the portion of the buried APE waveguide mode that passes under the holes. However, conical holes of any depth fail to produce well-defined stop-bands in either the transmission spectra or band diagrams. Deep conical holes act as a broad-band attenuator due to refraction of the mode out of the APE region down into the bulk. Experimental results confirming this observation are shown. The impact of holes which are cylindrical at the top and conical at their bottom is also investigated. Given the difficulty of fabricating high aspect-ratio cylindrical holes in lithium niobate, we propose a partial solution to improve the overlap between shallow holes and the buried mode, in which the PhC holes are fabricated at the bottom of a wide, shallow trench previously introduced into the APE waveguide surface. © 2008 Optical Society of America.