{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:16:57Z","timestamp":1785403017159,"version":"3.56.0"},"reference-count":48,"publisher":"Optica Publishing Group","issue":"20","license":[{"start":{"date-parts":[[2022,10,14]],"date-time":"2022-10-14T00:00:00Z","timestamp":1665705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2022,10,14]],"date-time":"2022-10-14T00:00:00Z","timestamp":1665705600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of Hunan Province","doi-asserted-by":"publisher","award":["2021JJ30001"],"award-info":[{"award-number":["2021JJ30001"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61835004"],"award-info":[{"award-number":["61835004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Lett."],"published-print":{"date-parts":[[2022,10,15]]},"abstract":"<jats:p>We theoretically propose topological spatial differentiators by the normal-incidence reflection of light. Firstly, a three-dimensional propagation model is established for the light normally incident on the interface between two media. It is found that due to the spin\u2013orbit interaction of light, a given circularly polarized light always induces oppositely polarized light carrying a topological charge, so the two intrinsic spin components are separated radially or azimuthally. Moreover, the normally reflected fields are approximately proportional to two kinds of second-order spatial differentiations of the input circularly and linearly polarized fields. Further results applying to the two-dimensional image processing for edge detection validate the two topological spatial differentiators.<\/jats:p>","DOI":"10.1364\/ol.473999","type":"journal-article","created":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T14:00:30Z","timestamp":1664373630000},"page":"5425","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Topological spatial differentiators upon reflection of the normally incident light"],"prefix":"10.1364","volume":"47","author":[{"given":"Heng","family":"Li","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05htk5m33","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenhao","family":"Xu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05htk5m33","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8537-3361","authenticated-orcid":true,"given":"Weixing","family":"Shu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05htk5m33","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2022,10,14]]},"reference":[{"key":"ol-47-20-5425-R1","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1126\/science.1242818","volume":"343","author":"Silva","year":"2014","journal-title":"Science"},{"key":"ol-47-20-5425-R2","doi-asserted-by":"publisher","first-page":"704","DOI":"10.1038\/nphoton.2015.208","volume":"9","author":"Solli","year":"2015","journal-title":"Nat. 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