dorsal/arxiv
View SchemaBeams of electromagnetic radiation carrying angular momentum: The Riemann-Silberstein vector and the classical-quantum correspondence
| Authors | Iwo Bialynicki-Birula, Zofia Bialynicka-Birula |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511011 |
| URL | https://arxiv.org/abs/quant-ph/0511011 |
| DOI | 10.1016/j.optcom.2005.11.071 |
Abstract
All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann-Silberstein vector -- a complex combination of the electric and magnetic field vectors -- that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. Bessel beams, exact Laguerre-Gauss beams, and other related beams of electromagnetic radiation can be described in a unified fashion. The appropriate photon quantum numbers for these beams are identified. Special emphasis is put on the angular momentum of a single photon and its connection with the angular momentum of the beam.
{
"annotation_id": "fc2fd7d0-2c6e-4896-bc50-b424d35b0171",
"date_created": "2026-03-02T18:02:20.744000Z",
"date_modified": "2026-03-02T18:02:20.744000Z",
"file_hash": "80ec80a60e9d3ce5bcad4f06ec41c1b3024eb6fc4052d965894c89deb6f12f42",
"private": false,
"record": {
"abstract": "All beams of electromagnetic radiation are made of photons. Therefore, it is\nimportant to find a precise relationship between the classical properties of\nthe beam and the quantum characteristics of the photons that make a particular\nbeam. It is shown that this relationship is best expressed in terms of the\nRiemann-Silberstein vector -- a complex combination of the electric and\nmagnetic field vectors -- that plays the role of the photon wave function. The\nWhittaker representation of this vector in terms of a single complex function\nsatisfying the wave equation greatly simplifies the analysis. Bessel beams,\nexact Laguerre-Gauss beams, and other related beams of electromagnetic\nradiation can be described in a unified fashion. The appropriate photon quantum\nnumbers for these beams are identified. Special emphasis is put on the angular\nmomentum of a single photon and its connection with the angular momentum of the\nbeam.",
"arxiv_id": "quant-ph/0511011",
"authors": [
"Iwo Bialynicki-Birula",
"Zofia Bialynicka-Birula"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.optcom.2005.11.071",
"title": "Beams of electromagnetic radiation carrying angular momentum: The Riemann-Silberstein vector and the classical-quantum correspondence",
"url": "https://arxiv.org/abs/quant-ph/0511011"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "6001d085-2ace-45ad-9c34-17ae50e4ffe1",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}