{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T08:41:48Z","timestamp":1785400908942,"version":"3.56.0"},"reference-count":22,"publisher":"Optica Publishing Group","issue":"14","license":[{"start":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T00:00:00Z","timestamp":1783900800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T00:00:00Z","timestamp":1783900800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2024YFB4608100"],"award-info":[{"award-number":["2024YFB4608100"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12374350"],"award-info":[{"award-number":["12374350"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Lett."],"published-print":{"date-parts":[[2026,7,15]]},"abstract":"<jats:p>Non-Abelian braiding plays a vital role in fault-tolerant quantum computing because of its global feature. It has recently been introduced to photonic systems, but the operational modes are confined to the fundamental mode, limiting potential mode-multiplexed applications in parallel optical computing. Here, we propose an architecture for a CMOS-compatible silicon-on-insulator photonic platform that supports non-Abelian braiding of multiple high-order modes. Numerical simulations demonstrate that higher-order modes in this structure exhibit braiding evolution behavior consistent with the fundamental mode, revealing the feasibility of achieving mode-multiplexed non-Abelian braiding. We also demonstrate that the multi-mode non-Abelian braiding works in broadband. Our work extends the effective dimensionality of non-Abelian braiding from the fundamental-mode system to a multi-mode system, opening new avenues for multiplexing applications in non-Abelian integrated photonics.<\/jats:p>","DOI":"10.1364\/ol.603157","type":"journal-article","created":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T12:00:10Z","timestamp":1782734410000},"page":"4000","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Non-Abelian braiding of multiple high-order photonic modes in silicon waveguides"],"prefix":"10.1364","volume":"51","author":[{"given":"Yao","family":"Tian","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00js3aw79","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhong-Lei","family":"Shan","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00js3aw79","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5238-8885","authenticated-orcid":true,"given":"Xu-Lin","family":"Zhang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00js3aw79","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,7,13]]},"reference":[{"key":"ol-51-14-4000-R1","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1126\/science.aaz5601","type":"journal-article","volume":"368","author":"Bartolomei","year":"2020","journal-title":"Science"},{"key":"ol-51-14-4000-R2","doi-asserted-by":"publisher","first-page":"aao1707","DOI":"10.1126\/science.aao1797","type":"journal-article","volume":"362","author":"Wang","year":"2018","journal-title":"Science"},{"key":"ol-51-14-4000-R3","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1038\/s41586-023-05954-4","type":"journal-article","volume":"618","author":"Anderson","year":"2023","journal-title":"Nature"},{"key":"ol-51-14-4000-R4","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1364\/AOP.494544","type":"journal-article","volume":"15","author":"Yan","year":"2023","journal-title":"Adv. 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All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}