Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals

The photonic band structures of two-dimensional photonic crystals consisting of lattices with different symmetries and scatterers of various shapes, orientations, and sizes are studied numerically. Specifically, four types of lattices (triangular, hexagonal, square, and rectangular) and five different shapes of scatterers (hexagon, circle, square, rectangle, and ellipse) are considered. The scatterers are either dielectric rods in air, or air rods in dielectric media. The lattice symmetry and all these properties of the scatterers can affect the band gap size. Given a lattice symmetry, the largest absolute photonic band gap is achieved by selecting a scatterer of the same symmetry; e.g., hexagonal rods in triangular or honeycomb lattices, square rods in square lattices, and rectangular rods in rectangular lattices. The band gap can be further maximized by adjusting the orientation and size of the scatterers; but no simple, systematic rules can be drawn.