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arXiv · 2605.17479

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

Keren Wang·Lujun Huang·Wei Wang
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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.

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Keren Wang, Lujun Huang, Wei Wang. 2026-05-17. Unified Topological Dynamics of Merging Bound States in the Continuum for High-Order Topological Charges. https://arxiv.org/abs/2605.17479

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