Bound States in the Continuum in Multipolar Lattices

TL;DR

This paper develops a theory for bound states in the continuum (BICs) in multipolar lattices, revealing their robustness, symmetry protection, and topological properties, advancing understanding and engineering of high-Q resonant states.

Contribution

It introduces a comprehensive theoretical framework for BICs in multipolar lattices, linking topological charge with Q-factor behavior and demonstrating their robustness and symmetry protection.

Findings

BICs are robust to lattice parameter changes and remain pinned in specific k-space directions.

Some multipolar lattices host BICs forming continuous lines in k-space with zero topological charge.

The topological charge of BICs relates directly to the asymptotic Q-factor behavior.

Abstract

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.