{
  "annotation_id": "45e7d6de-20a2-4602-92b8-4887677741bc",
  "date_created": "2026-03-02T18:01:11.450000Z",
  "date_modified": "2026-03-02T18:01:11.450000Z",
  "file_hash": "e279ce78b392f66ff55d00b5e487f4c74f413d22d33904fe7d55945bf6d4a11c",
  "private": false,
  "record": {
    "abstract": "We report on a matrix-based diffraction integral that evaluates the focal\nfield of any diffraction-limited axisymmetric complex system. This diffraction\nformula is a generalization of the Debye integral applied to apertured focused\nbeams, which may be accommodated to broadband problems. Longitudinal chromatic\naberration may limit the convenience of the Debye formulation and,\nadditionally, spatial boundaries of validity around the focal point are\nprovided. Fresnel number is reformulated in order to guarantee that the focal\nregion is entirely into the region of validity of the Debye approximation when\nthe Fresnel number of the focusing geometry largely exceeds unity. We have\napplied the matrix-based Debye integral to several examples. Concretely, we\npresent an optical system for beam focusing with strong angular dispersion and\nfree of longitudinal chromatic aberration. This simple formalism leaves an open\ndoor for analysis and design of focused beams with arbitrary angular\ndispersion. Our results are valid for ultrashort pulsed and polychromatic\nincoherent sources.",
    "arxiv_id": "physics/0609030",
    "authors": [
      "Carlos J. Zapata-Rodriguez"
    ],
    "categories": [
      "physics.optics"
    ],
    "doi": "10.1364/JOSAA.24.000675",
    "title": "Debye representation of dispersive focused waves",
    "url": "https://arxiv.org/abs/physics/0609030"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ff58b4c7-d342-4aca-b8f8-6c217f0c70e5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}