Abstract: We study the band-gap 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 band gap and the frequencies of localized defect modes. We reveal that a maximum absolute band gap for this structure is achieved for an intermediate rotation an-le of the holes. This angle depends on the radius of the holes and the refractive index of the back-round material. We also study the properties of the defect modes created by missing holes and discuss the mode tunability in such structures.

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