{
  "abstract": "This paper develops a quantitative theory of second-harmonic generation (SHG) in hollow plasmonic nanowires, distinguishing geometric symmetry breaking from cavity effects. We consider a centrosymmetric material with a concentric circular cavity and a slightly perturbed outer boundary. Relative to the solid nanowire in~\\cite{liu2026quantitative}, the cavity introduces a topological defect by changing the cross-section from a disk to a doubly connected domain, whereas the outer-boundary perturbation breaks geometric symmetry. Local inversion-symmetry breaking at the interfaces induces nonlinear surface polarization. Using layer potentials and boundary-perturbation asymptotics, we derive explicit leading- and first-order formulas for the fundamental and second-harmonic fields. For a circular outer boundary, the leading-order second-harmonic field is purely quadrupolar; its amplitude differs from the solid-wire case by $O(γ^2)$ as $γ=r_i/r_e\\to0$ and decays as $O(r_e-r_i)$ in the nonresonant thin-shell limit. For perturbations proportional to $\\cos(nθ)$, $n\\ge3$, the first-order second-harmonic correction contains only modes $n-2$, $n$, and $n+2$, yielding dipolar, quadrupolar, or higher-order radiation for $n=3$, $n=4$, or $n\\ge5$, respectively, provided the lowest-order modal coefficient is nonzero. We derive plasmonic resonance conditions at both frequencies and estimate the singular orders of single and simultaneous resonances, including possible higher-order singularities from coincident resonance factors. Thus geometric symmetry determines the multipolar modes, whereas the cavity radius controls their amplitudes and resonant enhancement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35307",
  "author_total": 4,
  "authors": [
    {
      "name": "Qi Lei"
    },
    {
      "name": "Hongyu Liu"
    },
    {
      "name": "Zhi-Qiang Miao"
    },
    {
      "name": "Guang-Hui Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b0mm2f0a6f3d7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35307",
  "fulltext_url": null,
  "id": "b0mm2f0a6f3d7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35307",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2204|Plasmonic and Surface Plasmon Research"
    ]
  ],
  "openalex": "W7223926011",
  "pdf_url": "https://arxiv.org/pdf/2610.35307",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b0mm2f0a6f3d7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35307",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35307"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative Analysis of Second-Harmonic Generation in Plasmonic Nanowires: Symmetry Breaking and a Topological Defect",
  "title_text": "Quantitative Analysis of Second-Harmonic Generation in Plasmonic Nanowires: Symmetry Breaking and a Topological Defect",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/b0mm2f0a6f3d7",
  "venue": "arXiv",
  "versions": []
}