{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T11:38:22Z","timestamp":1785411502011,"version":"3.56.0"},"reference-count":45,"publisher":"Optica Publishing Group","issue":"21","license":[{"start":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T00:00:00Z","timestamp":1727395200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T00:00:00Z","timestamp":1727395200000},"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":["12074307"],"award-info":[{"award-number":["12074307"]}],"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":["12304372"],"award-info":[{"award-number":["12304372"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["xzy012022023"],"award-info":[{"award-number":["xzy012022023"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2022M712553"],"award-info":[{"award-number":["2022M712553"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shaanxi Fundamental Science Research Project for Mathematics and Physics","award":["22JSZ004"],"award-info":[{"award-number":["22JSZ004"]}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2024,10,7]]},"abstract":"<jats:p>\n                    We demonstrate analytically and numerically that the reverse energy flow is able to appear around the optical axis in the focal region of tightly focused hybrid vector beams. Theoretically, we derive and obtain the general expression of the longitudinal component of the Poynting vector in the focal plane for hybrid vector beams having circular polarization mapping tracks on the Poincar\u00e9 sphere under\n                    <jats:italic>xy<\/jats:italic>\n                    basis vectors. Following from the obtained expression and the numerical simulation results, the on-axis and near-axis reverse energy flow behaviors are proved. We also reveal that the relative phase of\n                    <jats:italic>xy<\/jats:italic>\n                    basis vectors can be adopted to conveniently control the reverse energy flow. Furthermore, we show that the concerned hybrid vector beams can meanwhile induce the nonzero transverse energy flow in the focal plane, while the previously reported cases with locally linear polarization states cannot. More strikingly, further simulation results indicate that one can observe the reverse energy flow phenomena for the hybrid vector beams under circular and elliptical polarization basis vectors. The results provide a fresh method for achieving and controlling the reverse energy flow.\n                  <\/jats:p>","DOI":"10.1364\/oe.536888","type":"journal-article","created":{"date-parts":[[2024,9,24]],"date-time":"2024-09-24T00:00:08Z","timestamp":1727136008000},"page":"36865","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Controllable reverse energy flow in the focus of tightly focused hybrid vector beams"],"prefix":"10.1364","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2726-8125","authenticated-orcid":true,"given":"Lei","family":"Han","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/017zhmm22","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiale","family":"Qi","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/017zhmm22","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chuchu","family":"Gao","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/017zhmm22","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fuli","family":"Li","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/017zhmm22","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2024,9,27]]},"reference":[{"key":"oe-32-21-36865-R1","author":"Griffiths","year":"2023"},{"key":"oe-32-21-36865-R2","author":"Born","year":"2013"},{"key":"oe-32-21-36865-R3","author":"Bohren","year":"2008"},{"key":"oe-32-21-36865-R4","doi-asserted-by":"publisher","first-page":"2844","DOI":"10.1364\/JOSAA.24.002844","volume":"24","author":"Novitsky","year":"2007","journal-title":"J. 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