Beyond Fourier harmonics: Anapole-engineered flat-band quasi–bound states in the continuum in dielectric metasurfaces

We present a theoretical and numerical study of wide-angle photonic flatbands in an all-dielectric metasurface consisting of horizontally aligned dimer resonators. While conventional strategies for realizing bound states in the continuum (BICs) typically rely on suppressing specific Fourier harmonics, we show that robust quasi-BIC flatbands can persist well beyond this restrictive condition. By employing a dimer-based unit cell, the lattice periodicity is effectively doubled, resulting in Brillouin zone folding that maps guided modes from the zone edge to the $\mathrm{\ensuremath{\Gamma}}$ point, where they couple to free-space radiation. Through multipolar decomposition of the scattered fields, we demonstrate that radiative losses are suppressed via far-field destructive interference between the total electric dipole and magnetic quadrupole moments, leading to high-$Q$ quasi-BICs with remarkable angular tolerance. Analytical modeling confirms that the observed flat dispersion stems not only from tailored Fourier harmonics but also from the intrinsic symmetry and phase coherence of the interfering multipoles. Full-wave simulations validate the emergence of ultraflat photonic bands exhibiting minimal angular dispersion, achieved by controlling the dimer separation. These findings establish a versatile and robust framework wherein Brillouin zone folding provides the momentum-space conditions and multipolar interference ensures angle-insensitive quasi-BIC flatbands, opening avenues for practical applications in slow-light devices, low-threshold nanolasers, and nonlinear photonic platforms.