Symmetrical perturbation analysis of complex two-dimensional photonic crystals

We study complex photonic crystals with unit cells that include different dielectric cylinders. A symmetrical perturbation approach is developed here which predicts how the band spectrum of the complex structures evolves from the most symmetrical prophase. As a specific example, we apply this symmetrical approach to the analysis of square lattices with alternating layers of dielectric cylinders perpendicular to one selected diagonal of the prophase unit cell. The results are shown to be in agreement with the plane wave calculations of the band spectrum.