{
  "annotation_id": "5dffb132-4894-422b-b33b-9aa626e33f2d",
  "date_created": "2026-03-02T18:00:42.798000Z",
  "date_modified": "2026-03-02T18:00:42.798000Z",
  "file_hash": "574f7fd91d06a5c855c9f0f219d9ba4350dad8fcf6bacfd06899bfb36eb95b79",
  "private": false,
  "record": {
    "abstract": "We reelaborate on the basic properties of lossless multilayers by using\nbilinear transformations. We study some interesting properties of the\nmultilayer transfer function in the unit disk, showing that hyperbolic geometry\nturns out to be an essential tool for understanding multilayer action. We use a\nsimple trace criterion to classify multilayers into three classes that\nrepresent rotations, translations, or parallel displacements. Moreover, we show\nthat these three actions can be decomposed as a product of two reflections in\nhyperbolic lines. Therefore, we conclude that hyperbolic reflections can be\nconsidered as the basic pieces for a deeper understanding of multilayer optics.",
    "arxiv_id": "physics/0305040",
    "authors": [
      "A. G. Barriuso",
      "J. J. Monzon",
      "L. L. Sanchez-Soto",
      "J. F. Carinena"
    ],
    "categories": [
      "physics.optics"
    ],
    "doi": "10.1364/JOSAA.20.001812",
    "title": "Hyperbolic reflections as fundamental building blocks for multilayer   optics",
    "url": "https://arxiv.org/abs/physics/0305040"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5c5386b9-2420-491b-a689-faa118f58c4b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}