{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T19:05:56Z","timestamp":1790103956818,"version":"4.0.1"},"reference-count":42,"publisher":"Optica Publishing Group","issue":"20","license":[{"start":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T00:00:00Z","timestamp":1790035200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T00:00:00Z","timestamp":1790035200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62165013"],"award-info":[{"award-number":["62165013"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China","award":["62365012"],"award-info":[{"award-number":["62365012"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2026,10,5]]},"abstract":"<jats:p>\n                    Bound states in the continuum (BICs) enable the support of spatially confined electromagnetic fields within the radiation continuum, exhibiting high-quality factors and nontrivial topology in the far field. This paper investigates a silicon nitride (Si\n                    <jats:sub>3<\/jats:sub>\n                    N\n                    <jats:sub>4<\/jats:sub>\n                    ) photonic crystal incorporating rotated elliptical holes. This geometric anisotropy reduces the in-plane symmetry, lifts the original mode degeneracy, and redistributes coupling to the radiation channels. The \u0393-point states remain radiative, whereas the two branches formed after degeneracy lifting separately support off-\u0393 BICs at nonzero in-plane wave vectors. The selected target branch retains a narrowband resonance, while the same perturbation splits a higher-order vortex singularity into two spatially separated first-order singularities, producing two dark regions. As the anisotropy increases, the spectral shifting and singularity splitting evolve in a correlated manner. Propagation analysis shows that the orbital angular momentum (OAM) component with l\u2009=\u2009\u2009+\u20092 remains dominant over a representative propagation range, while its mode purity varies with propagation distance. The proposed structure therefore provides a compact route to narrowband vortex-beam generation and a potential field platform for structured-light control and multiparticle optical manipulation.\n                  <\/jats:p>","DOI":"10.1364\/oe.612114","type":"journal-article","created":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T08:00:09Z","timestamp":1788854409000},"page":"37225","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Geometric-anisotropy-controlled degeneracy lifting and vortex singularity splitting with dominant +2 orbital angular momentum"],"prefix":"10.1364","volume":"34","author":[{"given":"Junfeng","family":"Zhao","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00gx3j908","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4156-1360","authenticated-orcid":true,"given":"Yunping","family":"Qi","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00gx3j908","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiayong","family":"Hu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00gx3j908","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yawei","family":"Dou","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00gx3j908","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2190-6189","authenticated-orcid":true,"given":"Xiangxian","family":"Wang","sequence":"additional","affiliation":[{"name":"Lanzhou University of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,9,22]]},"reference":[{"key":"oe-34-20-37225-R1","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/978-3-662-02781-3_19","type":"journal-article","volume":"30","author":"von Neumann","year":"1929","journal-title":"Phys. Z."},{"key":"oe-34-20-37225-R2","doi-asserted-by":"publisher","first-page":"1866","DOI":"10.1103\/PhysRev.124.1866","type":"journal-article","volume":"124","author":"Fano","year":"1961","journal-title":"Phys. Rev."},{"key":"oe-34-20-37225-R3","doi-asserted-by":"publisher","first-page":"3231","DOI":"10.1103\/PhysRevA.32.3231","type":"journal-article","volume":"32","author":"Friedrich","year":"1985","journal-title":"Phys. Rev. A"},{"key":"oe-34-20-37225-R4","doi-asserted-by":"publisher","first-page":"183902","DOI":"10.1103\/PhysRevLett.100.183902","type":"journal-article","volume":"100","author":"Marinica","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"oe-34-20-37225-R5","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1038\/nature12289","type":"journal-article","volume":"499","author":"Hsu","year":"2013","journal-title":"Nature"},{"key":"oe-34-20-37225-R6","doi-asserted-by":"publisher","first-page":"037401","DOI":"10.1103\/PhysRevLett.113.037401","type":"journal-article","volume":"113","author":"Yang","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"oe-34-20-37225-R7","doi-asserted-by":"publisher","first-page":"16048","DOI":"10.1038\/natrevmats.2016.48","type":"journal-article","volume":"1","author":"Hsu","year":"2016","journal-title":"Nat. Rev. Mater."},{"key":"oe-34-20-37225-R8","doi-asserted-by":"publisher","first-page":"31908","DOI":"10.1038\/srep31908","type":"journal-article","volume":"6","author":"Gao","year":"2016","journal-title":"Sci. Rep."},{"key":"oe-34-20-37225-R9","doi-asserted-by":"publisher","first-page":"257401","DOI":"10.1103\/PhysRevLett.113.257401","type":"journal-article","volume":"113","author":"Zhen","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"oe-34-20-37225-R10","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1038\/s41566-018-0177-5","type":"journal-article","volume":"12","author":"Doeleman","year":"2018","journal-title":"Nat. Photonics"},{"key":"oe-34-20-37225-R11","doi-asserted-by":"publisher","first-page":"1469","DOI":"10.1515\/nanoph-2020-0654","type":"journal-article","volume":"10","author":"Liu","year":"2021","journal-title":"Nanophotonics"},{"key":"oe-34-20-37225-R12","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1038\/s41566-020-0658-1","type":"journal-article","volume":"14","author":"Wang","year":"2020","journal-title":"Nat. Photonics"},{"key":"oe-34-20-37225-R13","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1038\/s41377-022-00923-4","type":"journal-article","volume":"11","author":"Kang","year":"2022","journal-title":"Light:Sci. Appl."},{"key":"oe-34-20-37225-R14","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1038\/s41377-023-01090-w","type":"journal-article","volume":"12","author":"Qin","year":"2023","journal-title":"Light:Sci. Appl."},{"key":"oe-34-20-37225-R15","doi-asserted-by":"publisher","first-page":"6014","DOI":"10.1038\/s41467-023-41068-1","type":"journal-article","volume":"14","author":"Zhang","year":"2023","journal-title":"Nat. Commun."},{"key":"oe-34-20-37225-R16","doi-asserted-by":"publisher","first-page":"27591","DOI":"10.1364\/OE.529042","type":"journal-article","volume":"32","author":"Han","year":"2024","journal-title":"Opt. Express"},{"key":"oe-34-20-37225-R17","doi-asserted-by":"publisher","first-page":"8562","DOI":"10.1364\/AO.533508","type":"journal-article","volume":"63","author":"Xu","year":"2024","journal-title":"Appl. Opt."},{"key":"oe-34-20-37225-R18","doi-asserted-by":"publisher","first-page":"9080","DOI":"10.1038\/s41467-024-53433-9","type":"journal-article","volume":"15","author":"Qin","year":"2024","journal-title":"Nat. Commun."},{"key":"oe-34-20-37225-R19","doi-asserted-by":"publisher","first-page":"2400214","DOI":"10.1002\/adma.202400214","type":"journal-article","volume":"36","author":"Xia","year":"2024","journal-title":"Adv. Mater."},{"key":"oe-34-20-37225-R20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/JSTQE.2026.3676207","type":"journal-article","volume":"32","author":"Yan","year":"2026","journal-title":"IEEE J. Sel. Top. Quantum Electron."},{"key":"oe-34-20-37225-R22","doi-asserted-by":"publisher","first-page":"245148","DOI":"10.1103\/PhysRevB.94.245148","type":"journal-article","volume":"94","author":"Ni","year":"2016","journal-title":"Phys. Rev. B"},{"key":"oe-34-20-37225-R23","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1038\/nphoton.2017.31","type":"journal-article","volume":"11","author":"Gomis-Bresco","year":"2017","journal-title":"Nat. Photonics"},{"key":"oe-34-20-37225-R24","doi-asserted-by":"publisher","first-page":"193903","DOI":"10.1103\/PhysRevLett.121.193903","type":"journal-article","volume":"121","author":"Koshelev","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"oe-34-20-37225-R25","doi-asserted-by":"publisher","first-page":"15300","DOI":"10.1021\/acs.nanolett.4c04217","type":"journal-article","volume":"24","author":"You","year":"2024","journal-title":"Nano Lett."},{"key":"oe-34-20-37225-R26","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1364\/OL.11.000288","type":"journal-article","volume":"11","author":"Ashkin","year":"1986","journal-title":"Opt. Lett."},{"key":"oe-34-20-37225-R27","doi-asserted-by":"publisher","first-page":"582","DOI":"10.1038\/ncomms1592","type":"journal-article","volume":"2","author":"Kang","year":"2011","journal-title":"Nat. Commun."},{"key":"oe-34-20-37225-R28","doi-asserted-by":"publisher","first-page":"42892","DOI":"10.1364\/OE.476031","type":"journal-article","volume":"30","author":"Wu","year":"2022","journal-title":"Opt. Express"},{"key":"oe-34-20-37225-R29","doi-asserted-by":"publisher","first-page":"1334","DOI":"10.1364\/PRJ.523874","type":"journal-article","volume":"12","author":"He","year":"2024","journal-title":"Photonics Res."},{"key":"oe-34-20-37225-R30","doi-asserted-by":"publisher","first-page":"1427","DOI":"10.1364\/PRJ.520425","type":"journal-article","volume":"12","author":"Yuan","year":"2024","journal-title":"Photonics Res."},{"key":"oe-34-20-37225-R31","doi-asserted-by":"publisher","first-page":"17227","DOI":"10.1364\/OE.26.017227","type":"journal-article","volume":"26","author":"Zhang","year":"2018","journal-title":"Opt. Express"},{"key":"oe-34-20-37225-R32","doi-asserted-by":"publisher","first-page":"7534","DOI":"10.1038\/s41467-022-35246-w","type":"journal-article","volume":"13","author":"Doiron","year":"2022","journal-title":"Nat. Commun."},{"key":"oe-34-20-37225-R33","doi-asserted-by":"publisher","first-page":"7235","DOI":"10.1364\/OL.578923","type":"journal-article","volume":"50","author":"Zhao","year":"2025","journal-title":"Opt. Lett."},{"key":"oe-34-20-37225-R34","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1038\/s41377-025-02076-6","type":"journal-article","volume":"14","author":"Allayarov","year":"2025","journal-title":"Light:Sci. Appl."},{"key":"oe-34-20-37225-R35","doi-asserted-by":"publisher","first-page":"013803","DOI":"10.1103\/PhysRevLett.134.013803","type":"journal-article","volume":"134","author":"Zhang","year":"2025","journal-title":"Phys. Rev. Lett."},{"key":"oe-34-20-37225-R36","doi-asserted-by":"publisher","first-page":"23782","DOI":"10.1364\/OE.551322","type":"journal-article","volume":"33","author":"Chiang","year":"2025","journal-title":"Opt. Express"},{"key":"oe-34-20-37225-R37","doi-asserted-by":"publisher","first-page":"754","DOI":"10.1364\/OL.545899","type":"journal-article","volume":"50","author":"Ruan","year":"2025","journal-title":"Opt. Lett."},{"key":"oe-34-20-37225-R38","doi-asserted-by":"publisher","first-page":"3962","DOI":"10.1364\/OL.560905","type":"journal-article","volume":"50","author":"Niu","year":"2025","journal-title":"Opt. Lett."},{"key":"oe-34-20-37225-R39","doi-asserted-by":"publisher","first-page":"10835","DOI":"10.1038\/s41467-025-65860-3","type":"journal-article","volume":"16","author":"Qin","year":"2025","journal-title":"Nat. Commun."},{"key":"oe-34-20-37225-R40","doi-asserted-by":"publisher","first-page":"133802","DOI":"10.1103\/PhysRevLett.134.133802","type":"journal-article","volume":"134","author":"Wang","year":"2025","journal-title":"Phys. Rev. Lett."},{"key":"oe-34-20-37225-R41","doi-asserted-by":"publisher","first-page":"1731","DOI":"10.1364\/JOSAA.398245","type":"journal-article","volume":"37","author":"Zhang","year":"2020","journal-title":"J. Opt. Soc. Am. A"},{"key":"oe-34-20-37225-R42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1117\/1.JNP.14.016005","type":"journal-article","volume":"14","author":"Sephton","year":"2020","journal-title":"J. Nanophotonics"},{"key":"oe-34-20-37225-R43","doi-asserted-by":"publisher","first-page":"385301","DOI":"10.1088\/1361-6463\/ae0598","type":"journal-article","volume":"58","author":"Zhou","year":"2025","journal-title":"J. Phys. D: Appl. Phys."}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-34-20-37225&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T18:45:53Z","timestamp":1790102753000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-34-20-37225"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,22]]},"references-count":42,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2026]]},"published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.612114","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,22]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.612114","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":"24 July 2026","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"6 September 2026","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"22 September 2026","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2026 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement","name":"copyright","label":"Copyright"}]}}