Coexistence of bound states in continuum and flat bands in honeycomb scalar photonic metacrystals

Recently, significant progress has been made in the study of photonic crystals, particularly in exploring flat bands and bound states in the continuum (BICs), both of which exhibit strong confinement of photonic states. However, little research on their coexistence has been reported thus far[1]. In this study, we propose a honeycomb lattice composed of coaxial waveguide structures and analyze its band structures under perfect electric conductor (PEC) or scattering boundary conditions. We identify sets of flat bands and elucidate their formation mechanisms through the vertex-edge correspondence between the honeycomb lattice and the Kagome lattice. Our research also reveals that at the Γ-point in the Brillouin zone, all associated modes demonstrate exceptionally high quality factors (Q factors). The polarization states observed in the far-field confirm the presence of BICs at these frequencies. This discovery demonstrates the coexistence of flat bands and BICs, shedding light on designing and applying scalar photonic crystals.