Design of full-k-space flat bands in photonic crystals beyond the tight-binding picture

Based on a band engineering method, we propose a theoretical prescription to create a full-k-space flat band in dielectric photonic crystals covering the whole Brillouin Zone. With wave functions distributed in air instead of in the dielectrics, such a flat band represents a unique mechanism for achieving flat dispersions beyond the tight-binding picture, which can enormously reduce the requirement of permittivity contrast in the system. Finally, we propose and numerically demonstrate a unique application based on the full-k-space coverage of the flat band: ultra-sensitive detection of small scatterers.