{
  "abstract": "Paper I of this series (arXiv:2610.29336) solves, via the retarded Green's functions, the local differential equations governing light propagation in a plane-parallel dielectric slab, obtaining a pair of retarded integral equations that represent, at the continuum level, the microscopic multiple-scattering picture underlying the local formulation. The two formulations are thus proven to be analytically equivalent. The local system of differential equations is then solved numerically with a finite-difference time-domain scheme (FDTD-ADE). This report closes the loop by solving the retarded integral equations directly, without passing through the local formulation, and comparing the result with the FDTD-ADE solution under the same physical and material conditions. The two independently implemented, structurally different numerical schemes agree within 0.02-1.3% for the reported reflected and transmitted energy fractions; the absorbed fraction, computed independently in both schemes from the Lorentz damping term rather than merely inferred from 1-R-T, agrees closely between the two methods, to the precision reported. Both solutions are also compared with an exact reference, the Airy formula weighted over the pulse spectrum: the direct solution reproduces it to within 0.3%, and its Richardson extrapolation to all digits shown. The agreement persists for a few-cycle pulse and for a sub-wavelength slab, where naive fixed-point iteration of the integral equations is not a practical convergent strategy. A complementary set of movie-style, nine-frame visualizations is also presented, illustrating the same equivalence directly in the field rather than only in integrated observables. To the author's knowledge, a direct numerical cross-validation of these two formulations in this genuinely time-dependent regime has not previously been reported.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30833",
  "author_total": 1,
  "authors": [
    {
      "name": "Giancarlo Reali"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkj7jwvzxqw0t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30833",
  "fulltext_url": null,
  "id": "dkj7jwvzxqw0t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30833",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.optics"
    ],
    [
      "openalex",
      "2208|Electromagnetic Simulation and Numerical Methods"
    ]
  ],
  "openalex": "W7223297359",
  "pdf_url": "https://arxiv.org/pdf/2610.30833",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dkj7jwvzxqw0t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.30833",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30833"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Light pulse propagation through a dielectric slab. II. Two roads to the same field: numerical cross-validation of local (FDTD-ADE) and non-local (retarded integral-equation) solutions",
  "title_text": "Light pulse propagation through a dielectric slab. II. Two roads to the same field: numerical cross-validation of local (FDTD-ADE) and non-local (retarded integral-equation) solutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:34Z",
  "url": "https://research.draconitic.com/paper/dkj7jwvzxqw0t",
  "venue": "arXiv",
  "versions": []
}