Design of waveguides, bends and splitters in photonic crystal slabs with hexagonal holes in a triangular lattice

Waveguides in photonic crystal slabs (PCS) can be obtained by omitting a row of holes (Wl-waveguides). In general the propagation properties in such waveguides suffer from the unavoidable periodic sidewall corrugation caused by the remaining parts of the crystal. The corrugation acts as a Bragg reflector, causing the occurrence of so-called mini stopbands in the transmission of the waveguide. The effect is quite strong in PCS with circular holes, but it can be significantly reduced if correctly oriented hexagonal holes are used. This so-called hexagon-type PCS allows the design of waveguides, bends and splitters having a relatively high group velocity and a wide transmission window in the PCS stopband for modes having their magnetic field oriented mainly perpendicular to the slab.