{
  "annotation_id": "9e4a10e8-e441-4861-95b4-92c8e4d168c3",
  "date_created": "2026-03-02T18:01:00.009000Z",
  "date_modified": "2026-03-02T18:01:00.009000Z",
  "file_hash": "245f171b7f1ff317470c779ad4692568db9d9dfef9657dfd7c536a75ebc838e1",
  "private": false,
  "record": {
    "abstract": "We reconsider the basic properties of ray-transfer matrices for first-order\noptical systems from a geometrical viewpoint. In the paraxial regime of scalar\nwave optics, there is a wide family of beams for which the action of a\nray-transfer matrix can be fully represented as a bilinear transformation on\nthe upper complex half-plane, which is the hyperbolic plane. Alternatively,\nthis action can be also viewed in the unit disc. In both cases, we use a simple\ntrace criterion that arranges all first-order systems in three classes with a\nclear geometrical meaning: they represent rotations, translations, or parallel\ndisplacements. We analyze in detail the relevant example of an optical\nresonator.",
    "arxiv_id": "physics/0506112",
    "authors": [
      "A. G. Barriuso",
      "J. J. Monzon",
      "L. L. Sanchez-Soto",
      "J. F. Carinena"
    ],
    "categories": [
      "physics.optics"
    ],
    "doi": "10.1088/1464-4258/7/9/002",
    "title": "Geometrical aspects of first-order optical systems",
    "url": "https://arxiv.org/abs/physics/0506112"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d508fbc5-9bb8-4371-ad64-18ebfacfcd9f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}