Bound states in the continuum in multipolar lattices

We develop a theory of bound states in the continuum (BICs) in multipolar lattices – periodic arrays of resonant multipoles. We predict that BICs are completely robust to changes in lattice parameters remaining pinned to specific directions in the k-space. The lack of radiation for BICs in such structures is protected by the symmetry of multipoles forming the lattice. We also show that some multipolar lattices can host BICs forming a continuous line in the k-space and such BICs carry zero topological charge. The developed approach sets a direct fundamental relation between the topological charge of BIC and the asymptotic behavior of the Q-factor in its vicinity. We believe that our theory is a significant step towards gaining deeper insight into the physics of BICs and the engineering of high-Q states in all-dielectric metasurfaces.