  Two-dimensional (2D) honeycomb photonic crystals with cylinders and
connecting walls have the potential to have a large full band gap. In
experiments, 2D photonic crystals do not have an infinite height, and
therefore, we investigate the effects of the thickness of the walls, the height
of the slabs and the type of the substrates on the photonic bands and gap maps
of 2D honeycomb photonic crystal slabs. The band structures are calculated by
the plane wave expansion method and the supercell approach. We find that the
slab thickness is a key parameter affecting the band gap size while on the
other hand the wall thickness hardly affact the gap size. For symmetric
photonic crystal slabs with lower dielectric claddings, the height of the slabs
needs to be sufficiently large to maintain a band gap. For asymmetric
claddings, the projected band diagrams are similar to that of symmetric slabs
as long as the dielectric constants of the claddings do not differ greatly.
