Localized States Emerging from Singular and Nonsingular Flat Bands in a Frustrated Fractal-Like Photonic Lattice

Abstract

Singular and nonsingular flat bands in a Sierpinski fractal-like photonic lattice are reported. It is demonstrated that the lowest two bands, being isolated and degenerate due to geometrical frustration, are nonsingular and thus can be spanned by a complete set of compact localized states. These states are experimentally proven to propagate diffractionless in the photonic lattice. The results reveal the interplay between geometrical frustration, degenerate flat bands, and compact localized states in a single photonic lattice, and pave the way to photonic spin liquid ground states.