{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T11:19:18Z","timestamp":1785410358449,"version":"3.56.0"},"reference-count":38,"publisher":"Optica Publishing Group","issue":"15","license":[{"start":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T00:00:00Z","timestamp":1753401600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2025,7,25]],"date-time":"2025-07-25T00:00:00Z","timestamp":1753401600000},"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":["12450402"],"award-info":[{"award-number":["12450402"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Innovation Program for Quantum Science and Technology","award":["2021ZD0302101"],"award-info":[{"award-number":["2021ZD0302101"]}]},{"name":"Li Ka Shing Foundation STU-GTIIT Joint Research Grants","award":["2024LKSFG02"],"award-info":[{"award-number":["2024LKSFG02"]}]},{"DOI":"10.13039\/501100010226","name":"Department of Education of Guangdong Province","doi-asserted-by":"publisher","award":["2024ZDZX1020"],"award-info":[{"award-number":["2024ZDZX1020"]}],"id":[{"id":"10.13039\/501100010226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"STU Scientific Research Foundation for Talents","award":["NTF22026"],"award-info":[{"award-number":["NTF22026"]}]},{"name":"STU Scientific Research Foundation for Talents","award":["NTF23011"],"award-info":[{"award-number":["NTF23011"]}]},{"name":"STU Scientific Research Foundation for Talents","award":["NTF23036T"],"award-info":[{"award-number":["NTF23036T"]}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2025,7,28]]},"abstract":"<jats:p>\n                    We present an\n                    <jats:italic toggle=\"yes\">ab initio<\/jats:italic>\n                    investigation of the influence of spin-orbit coupling (SOC) on high-order harmonic generation (HHG) in hydrogen atoms by numerically solving the time-dependent Schr\u00f6dinger equation including the SOC term (TDSE-SOC). We find that the SOC does not affect the HHG spectra produced by the initial ground state. However, for the excited state 2\n                    <jats:italic toggle=\"yes\">P<\/jats:italic>\n                    , and its spin-split 2\n                    <jats:italic toggle=\"yes\">P<\/jats:italic>\n                    <jats:sub>3\/2<\/jats:sub>\n                    and 2\n                    <jats:italic toggle=\"yes\">P<\/jats:italic>\n                    <jats:sub>1\/2<\/jats:sub>\n                    states which are superpositions of\n                    <jats:italic toggle=\"yes\">m<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic toggle=\"yes\">l<\/jats:italic>\n                    <\/jats:sub>\n                    \u2009=\u20090 and\n                    <jats:italic toggle=\"yes\">m<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic toggle=\"yes\">l<\/jats:italic>\n                    <\/jats:sub>\n                    \u2009=\u20091 wave functions, the harmonic yields generated from the above three states vary significantly. We developed a modified strong-field approximation theory incorporating the spin-split states to analyze the SOC effect on HHG spectra. Considering the depletion of bound states, the simulation results are qualitatively consistent with the TDSE calculations. Analysis indicates that the\n                    <jats:italic toggle=\"yes\">m<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic toggle=\"yes\">l<\/jats:italic>\n                    <\/jats:sub>\n                    \u2009=\u20090 component in the spin-split 2\n                    <jats:italic toggle=\"yes\">P<\/jats:italic>\n                    states predominantly contributes to harmonic yields, and the\n                    <jats:italic toggle=\"yes\">m<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic toggle=\"yes\">l<\/jats:italic>\n                    <\/jats:sub>\n                    \u2009=\u20091 component has a non-negligible influence on lower-energy harmonics in a linearly polarized laser field.\n                  <\/jats:p>","DOI":"10.1364\/oe.561018","type":"journal-article","created":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T07:59:15Z","timestamp":1752134355000},"page":"32603","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Effect of spin-orbit coupling on high-order harmonic generation in atoms"],"prefix":"10.1364","volume":"33","author":[{"given":"Changtong","family":"Liang","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03sxpbt26","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaopeng","family":"Yi","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03sxpbt26","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-2748-7658","authenticated-orcid":true,"given":"Shilin","family":"Hu","sequence":"additional","affiliation":[{"name":"Shantou University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"Chen","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China"},{"name":"Hefei National Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2025,7,25]]},"reference":[{"key":"oe-33-15-32603-R1","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1103\/RevModPhys.81.163","volume":"81","author":"Krausz","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"oe-33-15-32603-R2","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1038\/nphys620","volume":"3","author":"Corkum","year":"2007","journal-title":"Nat. Phys."},{"key":"oe-33-15-32603-R3","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1038\/nphoton.2013.362","volume":"8","author":"Chini","year":"2014","journal-title":"Nat. Photonics"},{"key":"oe-33-15-32603-R4","doi-asserted-by":"publisher","first-page":"27506","DOI":"10.1364\/OE.25.027506","volume":"25","author":"Gaumnitz","year":"2017","journal-title":"Opt. Express"},{"key":"oe-33-15-32603-R5","doi-asserted-by":"publisher","first-page":"1994","DOI":"10.1103\/PhysRevLett.71.1994","volume":"71","author":"Corkum","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"oe-33-15-32603-R6","doi-asserted-by":"publisher","first-page":"1599","DOI":"10.1103\/PhysRevLett.70.1599","volume":"70","author":"Schafer","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"oe-33-15-32603-R7","doi-asserted-by":"publisher","first-page":"023401","DOI":"10.1103\/PhysRevA.82.023401","volume":"82","author":"Hostetter","year":"2010","journal-title":"Phys. Rev. A"},{"key":"oe-33-15-32603-R8","doi-asserted-by":"publisher","first-page":"193901","DOI":"10.1103\/PhysRevLett.122.193901","volume":"122","author":"Li","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"oe-33-15-32603-R9","doi-asserted-by":"publisher","first-page":"233001","DOI":"10.1103\/PhysRevLett.112.233001","volume":"112","author":"Xiong","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"oe-33-15-32603-R10","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1038\/117264a0","volume":"117","author":"Uhlenbeck","year":"1926","journal-title":"Nature"},{"key":"oe-33-15-32603-R11","doi-asserted-by":"publisher","first-page":"064404","DOI":"10.1103\/PhysRevB.95.064404","volume":"95","author":"Niu","year":"2017","journal-title":"Phys. Rev. B"},{"key":"oe-33-15-32603-R12","doi-asserted-by":"publisher","first-page":"081121","DOI":"10.1103\/PhysRevB.102.081121","volume":"102","author":"Lysne","year":"2020","journal-title":"Phys. Rev. B"},{"key":"oe-33-15-32603-R13","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1038\/nphoton.2016.109","volume":"10","author":"Hartung","year":"2016","journal-title":"Nat. Photonics"},{"key":"oe-33-15-32603-R14","doi-asserted-by":"publisher","first-page":"244109","DOI":"10.1063\/5.0034807","volume":"153","author":"Lee","year":"2020","journal-title":"J. Chem. Phys."},{"key":"oe-33-15-32603-R15","doi-asserted-by":"publisher","first-page":"204020","DOI":"10.1088\/0953-4075\/47\/20\/204020","volume":"47","author":"Barth","year":"2014","journal-title":"J. Phys. B: At. Mol. Opt. Phys."},{"key":"oe-33-15-32603-R16","doi-asserted-by":"publisher","first-page":"183201","DOI":"10.1103\/PhysRevLett.131.183201","volume":"131","author":"Yang","year":"2023","journal-title":"Phys. Rev. Lett."},{"key":"oe-33-15-32603-R17","doi-asserted-by":"publisher","first-page":"124026","DOI":"10.1088\/0953-4075\/47\/12\/124026","volume":"47","author":"Pabst","year":"2014","journal-title":"J. Phys. B: At. Mol. Opt. Phys."},{"key":"oe-33-15-32603-R18","doi-asserted-by":"publisher","first-page":"173202","DOI":"10.1103\/PhysRevLett.129.173202","volume":"129","author":"Mayer","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"oe-33-15-32603-R19","doi-asserted-by":"publisher","first-page":"043202","DOI":"10.1103\/PhysRevLett.120.043202","volume":"120","author":"Trabert","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"oe-33-15-32603-R20","doi-asserted-by":"publisher","first-page":"043201","DOI":"10.1103\/PhysRevLett.120.043201","volume":"120","author":"Liu","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"oe-33-15-32603-R21","doi-asserted-by":"publisher","first-page":"053202","DOI":"10.1088\/0256-307X\/38\/5\/053202","volume":"38","author":"Li","year":"2021","journal-title":"Chin. Phys. Lett."},{"key":"oe-33-15-32603-R22","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.chemphys.2019.04.005","volume":"523","author":"Zhang","year":"2019","journal-title":"Chem. Phys."},{"key":"oe-33-15-32603-R23","doi-asserted-by":"publisher","first-page":"013404","DOI":"10.1103\/PhysRevA.95.013404","volume":"95","author":"Jordan","year":"2017","journal-title":"Phys. Rev. A"},{"key":"oe-33-15-32603-R24","doi-asserted-by":"publisher","first-page":"223001","DOI":"10.1103\/PhysRevLett.126.223001","volume":"126","author":"Ge","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"oe-33-15-32603-R25","doi-asserted-by":"publisher","first-page":"023113","DOI":"10.1103\/PhysRevA.108.023113","volume":"108","author":"Hu","year":"2023","journal-title":"Phys. Rev. A"},{"key":"oe-33-15-32603-R26","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1038\/nphoton.2014.108","volume":"8","author":"Fleischer","year":"2014","journal-title":"Nat. Photonics"},{"key":"oe-33-15-32603-R27","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1002\/qua.24582","volume":"114","author":"Hu","year":"2014","journal-title":"Int. J. Quan. Chem."},{"key":"oe-33-15-32603-R28","doi-asserted-by":"publisher","first-page":"033104","DOI":"10.1103\/PhysRevA.107.033104","volume":"107","author":"Hu","year":"2023","journal-title":"Phys. Rev. A"},{"key":"oe-33-15-32603-R29","doi-asserted-by":"publisher","first-page":"1815","DOI":"10.1088\/0034-4885\/64\/12\/205","volume":"64","author":"Bachau","year":"2001","journal-title":"Rep. Prog. Phys."},{"key":"oe-33-15-32603-R30","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/BF02127704","volume":"6","author":"Crank","year":"1996","journal-title":"Adv. Comput. Math."},{"key":"oe-33-15-32603-R31","doi-asserted-by":"publisher","first-page":"4553","DOI":"10.1103\/PhysRevA.57.4553","volume":"57","author":"Gaarde","year":"1998","journal-title":"Phys. Rev. A"},{"key":"oe-33-15-32603-R32","doi-asserted-by":"publisher","first-page":"063430","DOI":"10.1103\/PhysRevA.81.063430","volume":"81","author":"Han","year":"2010","journal-title":"Phys. Rev. A"},{"key":"oe-33-15-32603-R33","doi-asserted-by":"publisher","first-page":"021802","DOI":"10.1103\/PhysRevA.61.021802","volume":"61","author":"Tong","year":"2000","journal-title":"Phys. Rev. A"},{"key":"oe-33-15-32603-R34","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/S0301-0104(97)00063-3","volume":"217","author":"Tong","year":"1997","journal-title":"Chem. Phys."},{"key":"oe-33-15-32603-R35","doi-asserted-by":"publisher","first-page":"063412","DOI":"10.1103\/PhysRevA.72.063412","volume":"72","author":"Wang","year":"2005","journal-title":"Phys. Rev. A"},{"key":"oe-33-15-32603-R36","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1016\/j.optcom.2017.09.100","volume":"410","author":"Guo","year":"2018","journal-title":"Opt. Commun."},{"key":"oe-33-15-32603-R37","doi-asserted-by":"publisher","first-page":"2117","DOI":"10.1103\/PhysRevA.49.2117","volume":"49","author":"Lewenstein","year":"1994","journal-title":"Phys. Rev. A"},{"key":"oe-33-15-32603-R38","doi-asserted-by":"publisher","first-page":"041402","DOI":"10.1103\/PhysRevA.75.041402","volume":"75","author":"Chen","year":"2007","journal-title":"Phys. Rev. A"}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-33-15-32603&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,26]],"date-time":"2025-07-26T03:07:27Z","timestamp":1753499247000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-33-15-32603"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,25]]},"references-count":38,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2025]]},"published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.561018","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,25]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.561018","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":"3 March 2025","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"9 June 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"25 July 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"}]}}