Multiple flatbands and localized states in photonic super-Kagome lattices.

We demonstrate multiple flatbands and compact localized states (CLSs) in a photonic super-Kagome lattice (SKL) that exhibits coexistence of singular and nonsingular flatbands within its unique band structure. Specifically, we find that the upper two flatbands of an SKL are singular-characterized by singularities due to band touching with their neighboring dispersive bands at the Brillouin zone center. Conversely, the lower three degenerate flatbands are nonsingular and remain spectrally isolated from other dispersive bands. The existence of such two distinct types of flatbands is experimentally demonstrated by observing stable evolution of the CLSs with various geometrical shapes in a laser-written SKL. We also discuss the classification of the flatbands in momentum space, using band-touching singularities of the Bloch wave functions. Furthermore, we validate this classification in real space based on unit cell occupancy of the CLSs in a single SKL plaquette. These results may provide insights for the study of flatband transport, dynamics, and nontrivial topological phenomena in other relevant systems.