{
  "abstract": "In a lossless periodic structure, a bound state in the continuum (BIC) corresponds to a real zero and a local maximum of the imaginary part of a complex dispersion relation $k = k(β)$, where $β$ is the Bloch wave number. A perturbation of the structure deforms the dispersion curve and may destroy, move or split the BIC, as demonstrated in existing studies involving lossless symmetry-preserving perturbations, symmetry-breaking perturbations and dissipative perturbations. We present a comprehensive perturbation theory, emphasizing the evolution of the real zeros and extreme points of $\\mathrm{Im}[k(β)]$ under various structural perturbations. In particular, our theory reveals the existence of lasing threshold modes (LTMs), which are also zeros of $\\mathrm{Im}[k(β)]$ when the perturbation involves gain with or without balanced loss. Using local Taylor expansions and Puiseux series, we determine the number, locations, and leading-order scaling of real zeros and extreme points for various types of BICs under different types of structural perturbations. The theory recovers known results and predicts new behavior for super-BICs under $\\mathcal{PT}$-symmetric perturbations. Specifically, a propagating super-BIC corresponding to a fourth-order zero of $\\mathrm{Im}[k(β)]$ splits into two real zeros representing either two BICs or two LTMs, and a symmetric standing wave splits into two BIC-LTM pairs. Our theory provides a general framework for studying BICs and nearby resonant modes in both lossless and non-Hermitian periodic structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28321",
  "author_total": 2,
  "authors": [
    {
      "name": "Lijun Yuan"
    },
    {
      "name": "Ya Yan Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6pra8fcwtq96q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28321",
  "fulltext_url": null,
  "id": "6pra8fcwtq96q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28321",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.optics"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Non-Hermitian Physics"
    ]
  ],
  "openalex": "W7204835924",
  "pdf_url": "https://arxiv.org/pdf/2608.28321",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6pra8fcwtq96q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2608.28321",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28321"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Structural perturbation theory for bound states in the continuum via bifurcation of zeros and extrema of the dispersion relation",
  "title_text": "Structural perturbation theory for bound states in the continuum via bifurcation of zeros and extrema of the dispersion relation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:22Z",
  "url": "https://research.draconitic.com/paper/6pra8fcwtq96q",
  "venue": "arXiv",
  "versions": []
}