Designing finite-height photonic crystal waveguides: confinement of light and dispersion relations

Guidelines are obtained for characteristic design parameters of finite-height photonic crystal waveguides using diagrams of photonic bandgaps for infinite-height photonic crystals. This is achieved by requiring photonic crystal designs with bandgaps well below a fundamental upper frequency limit for leakage-free guidance of light related to the properties of the media above/below the finite-height photonic crystal waveguide. The approach has the advantage that it can be applied to a large number of diagrams for infinite-height crystals that are already available in the literature, and furthermore the approach is not computer intensive compared to more rigorous numerical approaches to three-dimensional structures. We consider optical waveguide designs based on introducing a line defect in photonic crystals with air holes arranged on a triangular lattice in a silicon slab. For the media above/below the slab we consider the choices of silica and air. Dispersion relations are calculated for various waveguide designs. The analysis reveals a complex distribution of bands related to guided modes and provides information on how the guidance properties are modified as the waveguide width is changed. Furthermore, the analysis reveals the existence of bandgaps that are almost omni-directional. For a specific choice of photonic crystal waveguide placed on a silica substrate these bandgaps that have previously been overlooked gives the only possibility of leakage-free bandgap guidance of TM-polarized light.