Photonic crystal structure with square symmetry within each layer and a three-dimensional band gap

We present a layered photonic crystal structure having a connectivity that is different from diamond which possesses square symmetry within each layer. This structure has a complete photonic band gap of 18% of the midgap frequency with a dielectric contrast of 12:1, and is a structure with layered square symmetry having a gap greater than 10%. We demonstrate a waveguide in this crystal created by removing a row of rods from a single layer.