Unified Topological Dynamics of Merging Bound States in the Continuum for High-Order Topological Charges

TL;DR

This paper introduces a unified geometric framework to create high-order topological charges in bound states in the continuum within $C_4$-symmetric photonic crystals, enabling advanced light-matter interactions and high-quality Bessel OAM beams.

Contribution

It demonstrates the creation of high-order topological charges through merging processes of BICs, surpassing symmetry bounds, and introduces a geometric framework for understanding these dynamics.

Findings

High-order TCs up to ±3 achieved in $C_4$-symmetric photonic crystals.

Unified geometric framework for BIC merging dynamics.

Generation of high-quality Bessel OAM beams from high-order topological states.

Abstract

Bound states in the continuum (BICs) are polarization singularities in momentum space whose topological charges (TCs) govern advanced light-matter interactions. While lattice symmetry protects the existence of robust BICs at the $\Gamma$-point (SP-BICs), it also restricts their TCs to low-order values. Achieving high-order TCs in common crystal lattices, such as $C_4$-symmetric systems, has therefore remained an open question. Here, we systematically demonstrate that high-order TCs that surpass fundamental symmetry bounds can be created through the rich dynamics of a parameter-driven merging process of off-$\Gamma$ BICs. We introduce a unified geometric framework based on the interplay between Fabry-P\'erot interference and guided resonances, which uncovers different types of merging BICs dynamics, including near-isotropic, anisotropic, and cross-merging. Leveraging this mechanism, we realize unconventional TCs of up to $\pm3$ at either a symmetry-protected BIC or a degeneracy point in a simple $C_4$-symmetric photonic crystal slab. We further show that this high-order topology enables the generation of high-quality Bessel OAM beams, providing a physically transparent route toward engineering high-order topological photonics.