{
  "abstract": "A metasurface is an electrically thin interface that controls the phase, amplitude and polarization of a wave, upon reflection or transmission. Printed on a grounded dielectric substrate and spatially modulated across the aperture, it converts a guided surface wave into a radiated leaky wave, a mechanism used in holographic metasurface antennas. Controlling this conversion requires synthesizing a prescribed distribution of admittance tensors, each derived from the homogenization of a subwavelength unit cell. Many numerical and semi-analytical methods have been proposed to relate the geometry of a meta-atom to the tensor it produces. This paper presents, to the author's knowledge, the first analytical model, restricted to elliptical meta-atoms on a uniform lattice. The Galerkin method is applied directly to the geometry of the patches, without spatial meshing. An affine transformation maps any rotated ellipse onto the unit disk, so that a single formulation covers every configuration. A wideband response takes from minutes to tens of minutes with a periodic full-wave solver, while the proposed model evaluates it in a few tens of milliseconds on the same workstation, roughly three orders of magnitude faster. The predicted admittance agrees with a method-of-moments reference up to the fundamental resonance and captures the guided-mode anomaly of the substrate. Beyond the physical insight it brings, the model is a differentiable function of the geometry, which makes the quasi-real-time design of optimized metasurfaces possible.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08166",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Fromentèze"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/12prf9cmgk6vv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08166",
  "fulltext_url": null,
  "id": "12prf9cmgk6vv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08166",
  "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.class-ph"
    ],
    [
      "arxiv",
      "physics.optics"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08166",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/12prf9cmgk6vv.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2611.08166",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08166"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Analytical Modeling of the Admittance Tensor of Periodic Elliptical Meta-Atoms",
  "title_text": "Analytical Modeling of the Admittance Tensor of Periodic Elliptical Meta-Atoms",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:30Z",
  "url": "https://research.draconitic.com/paper/12prf9cmgk6vv",
  "venue": "arXiv",
  "versions": []
}