{
  "id": "2303.18199",
  "version": "v1",
  "published": "2023-03-30T03:49:42.000Z",
  "updated": "2023-03-30T03:49:42.000Z",
  "title": "SU(2) Symmetry of Coherent Photons and Application to Poincaré Rotator",
  "authors": [
    "Shinichi Saito"
  ],
  "categories": [
    "physics.optics"
  ],
  "abstract": "Lie algebra is a hidden mathematical structure behind various quantum systems realised in nature. Here, we consider $SU(2)$ wavefunctions for polarisation states of coherent photons emitted from a laser source, and discuss the relationship to spin expectation values with SO(3) symmetry based on isomorphism theorems. In particular, we found rotated half-wave-plates correspond to mirror reflections in the Poincar\\'e sphere, which do not form a subgroup in the projected O(2) plane due to anti-hermitian property. This could be overcome experimentally by preparing another half-wave-plate to realise a pristine rotator in $SU(2)$, which allows arbitrary rotation angles determined by the physical rotation. By combining another 2 quarter-wave-plates, we could also construct a genuine phase-shifter, thus, realising passive control over the full Poincar\\'e sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-30T03:49:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coherent photons",
      "application",
      "full poincare sphere",
      "arbitrary rotation angles",
      "spin expectation values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}