Global Framework for Dynamics and Criticality of Bound States in the Continuum

@misc{wang2026global,
  title = {{Global Framework for Dynamics and Criticality of Bound States in the Continuum}},
  author = {Keren Wang and Lujun Huang and Wei Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28934},
  eprint = {2609.28934},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28934},
}

TY  - UNPB
TI  - Global Framework for Dynamics and Criticality of Bound States in the Continuum
AU  - Keren Wang
AU  - Lujun Huang
AU  - Wei Wang
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.28934
UR  - https://arxiv.org/abs/2609.28934
AB  - Bound states in the continuum (BICs) exhibit rich momentum-space dynamics, including merging, annihilation, and reconnection across symmetry directions and bands. Yet these phenomena have largely been explained case by case, without a unified framework to classify or predict them. Here we develop a global symmetry-equivariant theory for the dynamics of nondegenerate and degenerate BICs. We show that BIC dynamics can be classified into α-, β-, and γ-processes according to root motion, which not only encompass the reported dynamics in C_2v, C_4v, and C_6v systems but also include previously unrecognized ones. More importantly, we reveal that distinct dynamics are bridged by the criticality of BICs through a \emph{merging of merging}, in which selected direction--band branches acquire higher-order radiation zeros. Such a theory predicts which branches become critical and how to tune system parameters to realize them. Following this framework, we construct high-order BICs in full-wave calculations, realizing Q∼ k^−10 nondegenerate criticality and Q∼ k^−8 single-branch and band-paired degenerate criticalities. Our framework provides a systematic route to understanding, discovering, and selectively controlling BIC dynamics and high-Q states.
ER  -