Topological properties of nearly flat bands in two-dimensional photonic crystals

Based on exact numerical calculations and physical analyses, we have demonstrated that there are two types of flat band in two-dimensional (2D) magnetic photonic crystals (PhCs). One has trivial topology with a zero Chern number, and the other has a nontrivial topology with a nonzero Chern number. The former originates from resonant scatterings of single scatters or cavity modes encircled by scatters in PhCs with complex lattices, while the latter comes from strong coupling interactions of fields among neighboring unit cells. Two types of flat bands exhibit very different topological properties. When a point source with the frequency corresponding to the trivial flat band is placed inside the PhCs, its radiation is easily cloaked by metal obstacles. In contrast, a topological flat band state can bypass the obstacles.