{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:40:55Z","timestamp":1785544855347,"version":"3.56.0"},"reference-count":32,"publisher":"Optica Publishing Group","issue":"9","license":[{"start":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T00:00:00Z","timestamp":1745452800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T00:00:00Z","timestamp":1745452800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12474291"],"award-info":[{"award-number":["12474291"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11974101"],"award-info":[{"award-number":["11974101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006407","name":"Natural Science Foundation of Henan Province","doi-asserted-by":"publisher","award":["242300421386"],"award-info":[{"award-number":["242300421386"]}],"id":[{"id":"10.13039\/501100006407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2025,5,5]]},"abstract":"<jats:p>The broken symmetry of the optical beam\u2019s intrinsic structure can lead to the spin-orbit coupling and induce the optical spin Hall effect which displays the spin-dependent transverse deflection of the light. In this paper, we theoretically investigate the optical spin Hall effect in the tight focusing of the radially polarized beam with the trigonometric-function vortex phase, whose intrinsic orbital angular momentum (OAM) structure and the total OAM can be modulated by its trigonometric-function vortex phase. We show that, the broken symmetry of vortex phase structure will lead to the optical spin Hall effect in the focal field, which displays a decentered spatial separation of the different spin angular momentum (SAM) states. More interestingly, with the change of the initial phase of the trigonometric-function vortex phase, the decentered transverse deflection of the different SAM distributions rotates around the optical axis, and the periodic reversion between the positive and the negative SAM states occurs simultaneously. The is because that the total OAM and the intrinsic OAM structure are changed by modulating the parameters of the trigonometric-function vortex phase. Our results provide an effective modulation way of the optical spin Hall effect in the tight focusing of the vortex beams.<\/jats:p>","DOI":"10.1364\/oe.560612","type":"journal-article","created":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T08:00:39Z","timestamp":1744790439000},"page":"19295","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Optical spin Hall effect controlled by tunable orbital angular momentum structure"],"prefix":"10.1364","volume":"33","author":[{"given":"Xishang","family":"Shi","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05d80kz58","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dong","family":"Xu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05d80kz58","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6426-4043","authenticated-orcid":true,"given":"Xinzhong","family":"Li","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05d80kz58","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2347-1393","authenticated-orcid":true,"given":"Hehe","family":"Li","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05d80kz58","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2025,4,24]]},"reference":[{"key":"oe-33-9-19295-R1","doi-asserted-by":"publisher","first-page":"796","DOI":"10.1038\/nphoton.2015.201","volume":"9","author":"Yu Bliokh","year":"2015","journal-title":"Nat. Photonics"},{"key":"oe-33-9-19295-R2","doi-asserted-by":"publisher","first-page":"5199","DOI":"10.1103\/PhysRevA.46.5199","volume":"46","author":"Liberman","year":"1992","journal-title":"Phys. Rev. A"},{"key":"oe-33-9-19295-R3","doi-asserted-by":"publisher","first-page":"035108","DOI":"10.1103\/PhysRevB.72.035108","volume":"72","author":"Yu","year":"2005","journal-title":"Phys. Rev. B"},{"key":"oe-33-9-19295-R4","doi-asserted-by":"publisher","first-page":"026605","DOI":"10.1103\/PhysRevE.70.026605","volume":"70","author":"Yu","year":"2004","journal-title":"Phys. Rev. E"},{"key":"oe-33-9-19295-R5","doi-asserted-by":"publisher","first-page":"10434","DOI":"10.1364\/OE.485247","volume":"31","author":"Liu","year":"2023","journal-title":"Opt. Express"},{"key":"oe-33-9-19295-R6","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1126\/science.1152697","volume":"319","author":"Hosten","year":"2008","journal-title":"Science"},{"key":"oe-33-9-19295-R7","doi-asserted-by":"publisher","first-page":"033515","DOI":"10.1103\/PhysRevA.103.033515","volume":"103","author":"Ling","year":"2021","journal-title":"Phys. Rev. A"},{"key":"oe-33-9-19295-R8","doi-asserted-by":"publisher","first-page":"2803","DOI":"10.1515\/nanoph-2021-0794","volume":"11","author":"Kim","year":"2022","journal-title":"Nanophotonics"},{"key":"oe-33-9-19295-R9","doi-asserted-by":"publisher","first-page":"2200046","DOI":"10.1002\/lpor.202200046","volume":"17","author":"Kim","year":"2023","journal-title":"Laser Photonics Rev."},{"key":"oe-33-9-19295-R10","doi-asserted-by":"publisher","first-page":"2200534","DOI":"10.1002\/lpor.202200534","volume":"17","author":"Sheng","year":"2023","journal-title":"Laser Photonics Rev."},{"key":"oe-33-9-19295-R11","doi-asserted-by":"publisher","first-page":"2200681","DOI":"10.1002\/lpor.202200681","volume":"17","author":"Chen","year":"2023","journal-title":"Laser Photonics Rev."},{"key":"oe-33-9-19295-R12","doi-asserted-by":"publisher","first-page":"2200783","DOI":"10.1002\/lpor.202200783","volume":"17","author":"Ling","year":"2023","journal-title":"Laser Photonics Rev."},{"key":"oe-33-9-19295-R13","doi-asserted-by":"publisher","first-page":"10783","DOI":"10.1021\/acs.nanolett.4c01931","volume":"24","author":"Fu","year":"2024","journal-title":"Nano Lett."},{"key":"oe-33-9-19295-R14","doi-asserted-by":"publisher","first-page":"023819","DOI":"10.1103\/PhysRevA.101.023819","volume":"101","author":"Shu","year":"2020","journal-title":"Phys. Rev. A"},{"key":"oe-33-9-19295-R15","doi-asserted-by":"publisher","first-page":"128548","DOI":"10.1016\/j.optcom.2022.128548","volume":"520","author":"Ma","year":"2022","journal-title":"Opt. Commun."},{"key":"oe-33-9-19295-R16","doi-asserted-by":"publisher","first-page":"2166","DOI":"10.1364\/OL.457507","volume":"47","author":"Khonina","year":"2022","journal-title":"Opt. Lett."},{"key":"oe-33-9-19295-R17","doi-asserted-by":"publisher","first-page":"253601","DOI":"10.1103\/PhysRevLett.104.253601","volume":"104","author":"Rodrguez-Herrera","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"oe-33-9-19295-R18","doi-asserted-by":"publisher","first-page":"034001","DOI":"10.1117\/1.AP.3.3.034001","volume":"3","author":"Yang","year":"2021","journal-title":"Adv. Photonics"},{"key":"oe-33-9-19295-R19","doi-asserted-by":"publisher","first-page":"043809","DOI":"10.1103\/PhysRevA.85.043809","volume":"85","author":"Zhou","year":"2012","journal-title":"Phys. Rev. A"},{"key":"oe-33-9-19295-R20","doi-asserted-by":"publisher","first-page":"251602","DOI":"10.1063\/1.4772502","volume":"101","author":"Zhou","year":"2012","journal-title":"Appl. Phys. Lett."},{"key":"oe-33-9-19295-R21","doi-asserted-by":"publisher","first-page":"034043","DOI":"10.1103\/PhysRevApplied.11.034043","volume":"11","author":"Zhu","year":"2019","journal-title":"Phys. Rev. Appl."},{"key":"oe-33-9-19295-R22","doi-asserted-by":"publisher","first-page":"11137","DOI":"10.1073\/pnas.1820636116","volume":"116","author":"Zhou","year":"2019","journal-title":"Proc. Natl. Acad. Sci."},{"key":"oe-33-9-19295-R23","doi-asserted-by":"publisher","first-page":"034045","DOI":"10.1103\/PhysRevApplied.21.034045","volume":"21","author":"He","year":"2024","journal-title":"Phys. Rev. Appl."},{"key":"oe-33-9-19295-R24","doi-asserted-by":"publisher","first-page":"724","DOI":"10.1126\/science.1234892","volume":"340","author":"Shitrit","year":"2013","journal-title":"Science"},{"key":"oe-33-9-19295-R25","doi-asserted-by":"publisher","first-page":"1405","DOI":"10.1126\/science.1231758","volume":"339","author":"Yin","year":"2013","journal-title":"Science"},{"key":"oe-33-9-19295-R26","doi-asserted-by":"publisher","first-page":"063813","DOI":"10.1103\/PhysRevA.83.063813","volume":"83","author":"Wang","year":"2011","journal-title":"Phys. Rev. A"},{"key":"oe-33-9-19295-R27","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1007\/s00340-022-07902-y","volume":"128","author":"Ma","year":"2022","journal-title":"Appl. Phys. B"},{"key":"oe-33-9-19295-R28","doi-asserted-by":"publisher","first-page":"8120","DOI":"10.1364\/OE.482303","volume":"31","author":"Ma","year":"2023","journal-title":"Opt. Express"},{"key":"oe-33-9-19295-R29","doi-asserted-by":"publisher","first-page":"013511","DOI":"10.1103\/PhysRevA.110.013511","volume":"110","author":"Zhang","year":"2024","journal-title":"Phys. Rev. A"},{"key":"oe-33-9-19295-R30","doi-asserted-by":"publisher","first-page":"2409","DOI":"10.1364\/OL.488701","volume":"48","author":"Zhang","year":"2023","journal-title":"Opt. Lett."},{"key":"oe-33-9-19295-R31","doi-asserted-by":"publisher","first-page":"S7","DOI":"10.1088\/1464-4266\/4\/2\/361","volume":"4","author":"Barnett","year":"2002","journal-title":"J. Opt. B:Quantum Semiclassical Opt."},{"key":"oe-33-9-19295-R32","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1098\/rspa.1959.0200","volume":"253","author":"Richards","year":"1959","journal-title":"Proc. R. Soc. London"}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-33-9-19295&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T11:20:31Z","timestamp":1745493631000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-33-9-19295"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,24]]},"references-count":32,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025]]},"published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.560612","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,24]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.560612","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"25 February 2025","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"14 April 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"24 April 2025","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement","name":"copyright","label":"Copyright"}]}}