{
  "abstract": "We establish analytical bounds on the normalized longitudinal propagation constants $β=k_z/k_0$ of modes in lossless dielectric diffraction gratings. If $ε_{\\max}$ denotes the maximum relative permittivity, we show that regular modes ($β^2\\in\\mathbb{R}$) satisfy $β^2\\leε_{\\max}$ despite the lack of a scalar dispersion relation. We further show that the so-called ghost modes ($β^2\\notin\\mathbb{R}$), admitted by the non-Hermitian nature of the associated eigenproblem, satisfy $|\\mathrm{Re}(β)|\\le\\sqrt{ε_{\\max}}/2$. Both bounds are obtained directly from the Fourier-series formulation of the fully coupled vectorial eigenproblem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05052",
  "author_total": 1,
  "authors": [
    {
      "name": "Ehsan Faghihifar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/40aq0r8rma500.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05052",
  "fulltext_url": null,
  "id": "40aq0r8rma500",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05052",
  "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",
      "physics.optics"
    ],
    [
      "openalex",
      "2504|Metamaterials and Metasurfaces Applications"
    ]
  ],
  "openalex": "W7211872399",
  "pdf_url": "https://arxiv.org/pdf/2609.05052",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/40aq0r8rma500.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2609.05052",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05052"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Bounds on Propagation Constants in Dielectric Gratings",
  "title_text": "Bounds on Propagation Constants in Dielectric Gratings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:36Z",
  "url": "https://research.draconitic.com/paper/40aq0r8rma500",
  "venue": "arXiv",
  "versions": []
}