Unconventional Flatband Line States in Photonic Lieb Lattices

TL;DR

This paper demonstrates the existence of unconventional extended flatband line states in photonic Lieb lattices, which are topologically nontrivial and cannot be described by traditional localized states, with experimental realization using laser writing.

Contribution

It introduces a new class of flatband states—line states with nontrivial topology—in photonic Lieb lattices, expanding understanding of flatband phenomena.

Findings

Unconventional flatband line states are observed experimentally.

These states are topologically nontrivial and extend around the lattice.

The states are robust to excitation imperfections.

Abstract

Flatband systems typically host "compact localized states"(CLS) due to destructive interference and macroscopic degeneracy of Bloch wave functions associated with a dispersionless energy band. Using a photonic Lieb lattice(LL), we show that conventional localized flatband states are inherently incomplete, with the missing modes manifested as extended line states which form non-contractible loops winding around the entire lattice. Experimentally, we develop a continuous-wave laser writing technique to establish a finite-sized photonic LL with specially-tailored boundaries, thereby directly observe the unusually extended flatband line states.Such unconventional line states cannot be expressed as a linear combination of the previously observed CLS but rather arise from the nontrivial real-space topology.The robustness of the line states to imperfect excitation conditions is discussed, and their potential applications are illustrated.