Localized states emerging from singular and nonsingular flat bands in a frustrated fractal-like photonic lattice

TL;DR

This paper investigates flat bands in a fractal-like photonic lattice, demonstrating the existence of localized states that propagate without diffraction, revealing new insights into geometrical frustration and flat band phenomena.

Contribution

It introduces a photonic lattice with singular and nonsingular flat bands, experimentally demonstrating diffractionless propagation of localized states due to geometrical frustration.

Findings

Nonsingular flat bands can be spanned by compact localized states

Localized states propagate diffractionless in the lattice

Interplay between frustration, flat bands, and localized states is revealed

Abstract

We report on singular and nonsingular flat bands in a Sierpinski fractal-like photonic lattice. We demonstrate that the 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. We experimentally prove these states to propagate diffractionless in the photonic lattice. Our 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.