{
  "annotation_id": "0a72ed8e-9807-4761-b739-b0aa6657f4ce",
  "date_created": "2026-03-02T18:00:39.758000Z",
  "date_modified": "2026-03-02T18:00:39.758000Z",
  "file_hash": "cb24b37b4c050aae060c00c5d5c0681992fdd39aefd8466390d9583471cf674a",
  "private": false,
  "record": {
    "abstract": "Exploiting the similarities between the Helmholtz wave equation and the\nKlein-Gordon equation, the former is linearized using the Feschbach-Villars\nprocedure used for linearizing the Klein-Gordon equation. Then the\nFoldy-Wouthuysen iterative diagonalization technique is applied to obtain a\nHamiltonian description for a system with varying refractive index. Besides\nreproducing all the traditional quasiparaxial terms, this method leads to\nadditional terms, which are dependent on the wavelength, in the optical\nHamiltonian. This alternate prescription to obtain the aberration expansion is\napplied to the axially symmetric graded index fiber. This results in the\nwavelength-dependent modification of the paraxial behaviour and the aberration\ncoefficients. Explicit expression for the modified coefficients of the\naberration to third-order are presented. Sixth and eighth order Hamiltonians\nare derived for this system.",
    "arxiv_id": "physics/0210001",
    "authors": [
      "Sameen Ahmed Khan"
    ],
    "categories": [
      "physics.optics",
      "physics.acc-ph",
      "physics.gen-ph",
      "quant-ph"
    ],
    "doi": "10.1007/s10773-005-1488-0",
    "journal_ref": "Int.J.Theor.Phys.44:95-125,2005",
    "title": "An alternate way to obtain the aberration expansion in Helmholtz Optics",
    "url": "https://arxiv.org/abs/physics/0210001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5ef5cea8-fa73-4a9a-94e0-00372b8b3379",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}