Bandgap engineering and defect modes in photonic crystals with rotated hexagonal holes

We study the bandgap structure of two-dimensional photonic crystals created by a triangular lattice of rotated hexagonal holes, and explore the effects of the reduced symmetry in the unit-cell geometry on the value of the absolute bandgap and the frequencies of localized defect modes. We reveal that a maximum absolute bandgap for this structure is achieved for an intermediate rotation angle of the holes. This angle depends on the radius of the holes and the refractive index of the background material. We also study the properties of the defect modes created by missing holes, and discuss the mode tunability in such structures.