{
  "annotation_id": "92920b96-7449-4301-9973-debc5908141e",
  "date_created": "2026-03-02T18:01:55.798000Z",
  "date_modified": "2026-03-02T18:01:55.798000Z",
  "file_hash": "b089b09d5d068734a150c13526597d1de12c6fcbd39d78f93d3997e1eadeb9f4",
  "private": false,
  "record": {
    "abstract": "We work out the orthogonality relations for the set of Carniglia-Mandel\ntriple modes which provide a set of normal modes for the source-free\nelectromagnetic field in a background consisting of a passive dielectric\nhalf-space and the vacuum, respectively. Due to the inherent computational\ncomplexity of the problem, an efficient strategy to accomplish this task is\ndesirable, which is presented in the paper. Furthermore, we provide all main\nsteps for the various proofs pertaining to different combinations of triple\nmodes in the orthogonality integral.",
    "arxiv_id": "quant-ph/0212004",
    "authors": [
      "Hanno Hammer"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1080/09500340308235171",
    "journal_ref": "Journal of Modern Optics 50 (2003), 209 - 227",
    "title": "Orthogonality relations for triple modes at dielectric boundary surfaces",
    "url": "https://arxiv.org/abs/quant-ph/0212004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "246f7015-ce10-4b50-b096-b52917c726c5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}