Photonic bands and gap maps in a photonic crystal slab

The photonic bands of a two-dimensional (2-D) lattice patterned in a planar waveguide are calculated by expanding the magnetic: field on the basis of waveguide modes. The method yields both the truly guided modes of the structure as well as the quasi-guided modes (or guided resonances) which lie above the light line in the first Brillouin zone. Representative results for the photonic bands are shown in the cases of strong- and weak-confinement waveguides patterned with a triangular lattice of holes. The gap maps as a function of hole radius are calculated and show significant differences with respect to the ideal 2-D case. A comparison of the photonic bands with those extracted from the calculated surface reflectance shows very good agreement, thereby indicating the reliability of the approach.