{
  "abstract": "We present an original rigorous numerical method for calculating light diffraction by three-dimensional photonic structures with a two-dimensional periodicity. It is based on Fourier expansions in the two periodic directions and an elegant yet efficient combination of finite-difference discretization and modal treatment in the propagation direction. The Fourier finite-difference method (FFDM) is cast into an easy-to-handle, agile, and efficient matrix formalism. It uses matrix inversions instead of eigenmodes computations, a strategy that confers a clear advantage in terms of computation time for the large Fourier truncation orders that are typically used to deal with micro- and nanophotonic structures of current interest. The computational gain increases with the Fourier truncation order. It is maximal (~30) for structures with subwavelength thicknesses, since a small number of finite-difference steps is sufficient to achieve a relative accuracy of approximately 1%. Our approach is particularly well suited for the analysis of generalized grating structures and metasurfaces. A second advantage of the proposed method is the possibility of using model-order reduction techniques. We use proper orthogonal decomposition (POD) to further speed up the computation of diffraction spectra as a function of the frequency, the incident angle, or a geometric parameter.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Mondher Besbes"
    },
    {
      "name": "Yassine Ferhi"
    },
    {
      "name": "Henri Benisty"
    },
    {
      "name": "Christophe Sauvan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/70s6bjk6c88bf.bib",
  "cited_by": 0,
  "doi": "10.1364/josaa.607379",
  "fulltext_url": null,
  "id": "70s6bjk6c88bf",
  "issns": [
    "1084-7529",
    "1520-8532"
  ],
  "landing_url": "https://iogs.hal.science/hal-05339190v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "0.spi"
    ],
    [
      "hal",
      "1.phys.phys"
    ],
    [
      "hal",
      "1.spi.opti"
    ],
    [
      "hal",
      "2.phys.phys.phys-optics"
    ],
    [
      "openalex",
      "2504|Metamaterials and Metasurfaces Applications"
    ]
  ],
  "openalex": "W4417138072",
  "pdf_url": "https://iogs.hal.science/hal-05339190/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-11",
  "publisher": "Optical Society of America",
  "ris": "https://research.draconitic.com/paper/70s6bjk6c88bf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:56Z",
      "native_id": "hal-05339190",
      "source": "hal",
      "url": "https://iogs.hal.science/hal-05339190v2"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "hal:2.phys.phys.phys-optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Fourier Finite-Difference method and Proper Orthogonal Decomposition for quick spectral study of 2D periodic photonic structures",
  "title_text": "Fourier Finite-Difference method and Proper Orthogonal Decomposition for quick spectral study of 2D periodic photonic structures",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:56Z",
  "url": "https://research.draconitic.com/paper/70s6bjk6c88bf",
  "venue": "Journal of the Optical Society of America. A Optics, Image Science, and Vision",
  "versions": []
}