{
  "abstract": "We investigate the Bloch spectrum for transverse electric (TE) modes in a 2D high-contrast dielectric metamaterial. Our analysis focuses on the high-frequency regime where the propagating wavelength is commensurate with the microstructural period $d$, and the permittivity within the inclusions scales as $d^{-2}$. Using operator factorization and Sobolev space decomposition, we demonstrate that Bloch eigenvalues $ω^2$ can be analytically continued and represented as a power series in $d^2$. We establish a rigorous upper bound on the microstructural length scale $d$, defined by the inclusion geometry, under which this expansion remains valid. Furthermore, we provide a definitive proof for the opening of band gaps in the frequency spectrum for all periods below a critical length scale, i.e., for all $d < \\overline{d}$. The threshold is explicitly characterized as a geometric function determined by the interaction between Dirichlet eigenvalues and the spectrum of the associated Neumann-Poincaré operator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04925",
  "author_total": 3,
  "authors": [
    {
      "name": "Silvia Jiménez Bolaños"
    },
    {
      "name": "Robert P. Lipton"
    },
    {
      "name": "Robert Viator"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvydyhfe0ax44.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04925",
  "fulltext_url": null,
  "id": "fvydyhfe0ax44",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04925",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04925",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvydyhfe0ax44.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04925",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04925"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Bandgaps at high frequency from highly oscillatory metamaterials",
  "title_text": "Bandgaps at high frequency from highly oscillatory metamaterials",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/fvydyhfe0ax44",
  "venue": "arXiv",
  "versions": []
}