Symmetrical analysis of complex two-dimensional hexagonal photonic crystals

We study complex hexagonal photonic crystals with unit cells that include different dielectric cylinders. A general symmetrical perturbation approach for a hexagonal lattice with up to three basis rods is presented that systematically develops other structural derivatives including comblike structures. We show how the band spectrum of these complex structures evolves from the most symmetrical prophase. The results are in agreement with the plane-wave calculations of the band spectrum.