Circularly polarized states and propagating bound states in the continuum in a periodic array of cylinders

TL;DR

This paper investigates how symmetry-breaking perturbations in a periodic array of cylinders affect bound states in the continuum (BICs), revealing the emergence of circularly polarized states and elucidating their topological charge conservation.

Contribution

It demonstrates that breaking in-plane inversion symmetry in a periodic cylinder array leads to the formation of circularly polarized states, linking symmetry breaking to topological charge dynamics.

Findings

Breaking in-plane inversion symmetry destroys propagating BICs.

Emergence of circularly polarized states with conserved topological charge.

Transition of BICs to CPSs through symmetry perturbations.

Abstract

Bound states in the continuum (BICs) in a periodic structure sandwiched between two homogeneous media have interesting properties and useful applications in photonics. The topological nature of BICs was previously revealed based on a topological charge related to the far-field polarization vector of the surrounding resonant states. Recently, it was established that when a symmetry-protected BIC (with a nonzero topological charge) is destroyed by a generic symmetry-breaking perturbation, a pair of circularly polarized resonant states (CPSs) emerge and the net topological charge is conserved. A periodic structure can also support propagating BICs with a nonzero wavevector. These BICs are not protected by symmetry in the sense of symmetry mismatch, but they need symmetry for their robust existence. Based on a highly accurate computational method for a periodic array of slightly noncircular cylinders, we show that a propagating BIC is typically destroyed by a structural perturbation that breaks only the in-plane inversion symmetry, and when this happens, a pair of CPSs of opposite handedness emerge so that the net topological charge is conserved. We also study the generation and annihilation of CPSs when a structural parameter is varied. It is shown that two CPSs with opposite topological charge and same handedness, connected to two BICs or in a continuous branch from one BIC, may collapse and become a CPS with a zero charge. Our study clarifies the important connection between symmetry and topological charge conservation.