Fault-tolerant bandstructure of two-dimensional square photonic crystals with different dielectric rod shapes

Based on simulations using the plane-wave expansion method, we show that the position of the first bandgap for TM polarized electromagnetic radiation in a high-filling ratio two-dimensional square photonic crystal is practically insensitive to the shape of dielectric rods with the same cross-sectional area. The width of this bandgap depends on the rod shape, but the difference between photonic crystals with circular and regular polygonal rod shapes with a number of edges higher than six can be neglected. For higher-order bandgaps the difference is larger. These results suggest that the fabrication tolerances related to the shape of dielectric rods in a PBG are not as strict as previously thought.