{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:41:08Z","timestamp":1785404468801,"version":"3.56.0"},"reference-count":46,"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\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11874311"],"award-info":[{"award-number":["11874311"]}],"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":["92050102"],"award-info":[{"award-number":["92050102"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2020YFA0710100"],"award-info":[{"award-number":["2020YFA0710100"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["202006310051"],"award-info":[{"award-number":["202006310051"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["20720220134"],"award-info":[{"award-number":["20720220134"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["20720220033"],"award-info":[{"award-number":["20720220033"]}],"id":[{"id":"10.13039\/501100012226","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>\n                    The anisotropic van der Waals material \u03b1-MoO\n                    <jats:sub>3<\/jats:sub>\n                    has recently attracted considerable attention because of the ability to support ellipse and hyperbolic phonon polaritons with extreme field confinement and long lifetimes, which can be used in topological transition and transformation polaritonics. However, the dispersion theory of some phonon polaritons in complex heterojunctions often requires tedious computation, which makes it difficult to simply judge and analyze the physical process of the photonic topological transition. Here we obtain the equivalent permittivity distribution of two-dimensional (2D) heterostructures by the effective medium theory and analyze the rotation-induced topological transitions and stack-dependent topological transitions of phonon polaritons. Unlike the previous discussion, we can predict the topological transition points by a parameter \u025b\n                    <jats:sub>\n                      <jats:italic toggle=\"yes\">x<\/jats:italic>\n                      \/\n                      <jats:italic toggle=\"yes\">y<\/jats:italic>\n                    <\/jats:sub>\n                    (i.e., the permittivity ratio along the in-plane crystal axis of the equivalent medium) and design precisely the phonon polaritons in the stacked materials by controlling the equivalent permittivity after simple calculation. The feasibility of the effective medium theory is verified based on the 2D approximation model and the non-2D approximation model under the limit of an ultrathin slab. Meanwhile, we compare the field distributions and dispersions of the 2D heterostructures and the corresponding equivalent structure. The simulation suggests that the elliptic\/hyperbolic responses of the stacked materials depend on the sign of \u025b\n                    <jats:sub>\n                      <jats:italic toggle=\"yes\">x<\/jats:italic>\n                      \/\n                      <jats:italic toggle=\"yes\">y<\/jats:italic>\n                    <\/jats:sub>\n                    . The new, to the best of our knowledge, method not only provides an easier and clearer criterion for the study of photonic topological transition in anisotropic polaritons, but also shows great potential in designing some multilayer 2D heterostructures.\n                  <\/jats:p>","DOI":"10.1364\/ol.474505","type":"journal-article","created":{"date-parts":[[2022,9,23]],"date-time":"2022-09-23T13:11:52Z","timestamp":1663938712000},"page":"5433","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Criterion for photonic topological transition in two-dimensional heterostructures"],"prefix":"10.1364","volume":"47","author":[{"given":"Tao","family":"Hou","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00mcjh785","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huanyang","family":"Chen","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00mcjh785","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2022,10,14]]},"reference":[{"key":"ol-47-20-5433-R1","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1038\/nature26160","volume":"556","author":"Cao","year":"2018","journal-title":"Nature"},{"key":"ol-47-20-5433-R2","doi-asserted-by":"publisher","first-page":"076801","DOI":"10.1103\/PhysRevLett.124.076801","volume":"124","author":"Cao","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ol-47-20-5433-R3","doi-asserted-by":"publisher","first-page":"147401","DOI":"10.1103\/PhysRevLett.118.147401","volume":"118","author":"Wu","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ol-47-20-5433-R4","doi-asserted-by":"publisher","first-page":"e1701696","DOI":"10.1126\/sciadv.1701696","volume":"3","author":"Yu","year":"2017","journal-title":"Sci. Adv."},{"key":"ol-47-20-5433-R5","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1038\/s41586-019-0957-1","volume":"567","author":"Seyler","year":"2019","journal-title":"Nature"},{"key":"ol-47-20-5433-R6","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1038\/s41586-019-0975-z","volume":"567","author":"Tran","year":"2019","journal-title":"Nature"},{"key":"ol-47-20-5433-R7","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1038\/s41586-019-0976-y","volume":"567","author":"Jin","year":"2019","journal-title":"Nature"},{"key":"ol-47-20-5433-R8","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1038\/s41586-019-0986-9","volume":"567","author":"Jin","year":"2019","journal-title":"Nature"},{"key":"ol-47-20-5433-R9","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1126\/science.aav1937","volume":"366","author":"Chen","year":"2019","journal-title":"Science"},{"key":"ol-47-20-5433-R10","doi-asserted-by":"publisher","first-page":"075420","DOI":"10.1103\/PhysRevB.95.075420","volume":"95","author":"Carr","year":"2017","journal-title":"Phys. Rev. B"},{"key":"ol-47-20-5433-R11","doi-asserted-by":"publisher","first-page":"840","DOI":"10.1038\/nmat4653","volume":"15","author":"Jiang","year":"2016","journal-title":"Nat. Mater."},{"key":"ol-47-20-5433-R12","doi-asserted-by":"publisher","first-page":"1153","DOI":"10.1126\/science.aau5144","volume":"362","author":"Sunku","year":"2018","journal-title":"Science"},{"key":"ol-47-20-5433-R13","doi-asserted-by":"publisher","first-page":"4360","DOI":"10.1038\/s41467-019-12327-x","volume":"10","author":"Ni","year":"2019","journal-title":"Nat. Commun."},{"key":"ol-47-20-5433-R14","doi-asserted-by":"publisher","first-page":"233901","DOI":"10.1103\/PhysRevLett.114.233901","volume":"114","author":"Gomez-Diaz","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ol-47-20-5433-R15","doi-asserted-by":"publisher","first-page":"3217","DOI":"10.1021\/acs.nanolett.9b05319","volume":"20","author":"Hu","year":"2020","journal-title":"Nano Lett."},{"key":"ol-47-20-5433-R16","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1038\/nature14477","volume":"522","author":"High","year":"2015","journal-title":"Nature"},{"key":"ol-47-20-5433-R17","doi-asserted-by":"publisher","first-page":"892","DOI":"10.1126\/science.aaq1704","volume":"359","author":"Li","year":"2018","journal-title":"Science"},{"key":"ol-47-20-5433-R18","doi-asserted-by":"publisher","first-page":"1125","DOI":"10.1126\/science.1246833","volume":"343","author":"Dai","year":"2014","journal-title":"Science"},{"key":"ol-47-20-5433-R19","doi-asserted-by":"publisher","first-page":"5221","DOI":"10.1038\/ncomms6221","volume":"5","author":"Caldwell","year":"2014","journal-title":"Nat. Commun."},{"key":"ol-47-20-5433-R20","doi-asserted-by":"publisher","first-page":"674","DOI":"10.1038\/nphoton.2015.166","volume":"9","author":"Yoxall","year":"2015","journal-title":"Nat. Photonics"},{"key":"ol-47-20-5433-R21","doi-asserted-by":"publisher","first-page":"1901393","DOI":"10.1002\/adom.201901393","volume":"8","author":"Hu","year":"2020","journal-title":"Adv. Opt. Mater."},{"key":"ol-47-20-5433-R22","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1038\/s41586-018-0618-9","volume":"562","author":"Ma","year":"2018","journal-title":"Nature"},{"key":"ol-47-20-5433-R23","doi-asserted-by":"publisher","first-page":"6197","DOI":"10.1021\/acs.chemrev.9b00592","volume":"120","author":"Dai","year":"2020","journal-title":"Chem. Rev."},{"key":"ol-47-20-5433-R24","first-page":"21","author":"Maier","year":"2007"},{"key":"ol-47-20-5433-R25","series-title":"","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1007\/BFb0048319","volume-title":"Surface Plasmons on Smooth and Rough Surfaces and on Gratings","volume":"111","author":"Raether","year":"1988"},{"key":"ol-47-20-5433-R26","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1038\/nphoton.2009.282","volume":"4","author":"Gramotnev","year":"2010","journal-title":"Nat. Photonics"},{"key":"ol-47-20-5433-R27","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1038\/nmat2629","volume":"9","author":"Atwater","year":"2010","journal-title":"Nat. Mater."},{"key":"ol-47-20-5433-R28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s43593-020-00001-5","volume":"1","author":"Jin","year":"2021","journal-title":"eLight"},{"key":"ol-47-20-5433-R29","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1126\/science.1198258","volume":"331","author":"Boltasseva","year":"2011","journal-title":"Science"},{"key":"ol-47-20-5433-R30","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1038\/s41586-021-03581-5","volume":"597","author":"Zhang","year":"2021","journal-title":"Nature"},{"key":"ol-47-20-5433-R31","doi-asserted-by":"publisher","first-page":"211101","DOI":"10.1063\/5.0052580","volume":"118","author":"Hu","year":"2021","journal-title":"Appl. Phys. Lett."},{"key":"ol-47-20-5433-R32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s43593-022-00018-y","volume":"2","author":"Wang","year":"2022","journal-title":"eLight"},{"key":"ol-47-20-5433-R33","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1038\/s41586-020-2359-9","volume":"582","author":"Hu","year":"2020","journal-title":"Nature"},{"key":"ol-47-20-5433-R34","doi-asserted-by":"publisher","first-page":"5301","DOI":"10.1021\/acs.nanolett.0c01627","volume":"20","author":"Zheng","year":"2020","journal-title":"Nano Lett."},{"key":"ol-47-20-5433-R35","doi-asserted-by":"publisher","first-page":"5323","DOI":"10.1021\/acs.nanolett.0c01673","volume":"20","author":"Duan","year":"2020","journal-title":"Nano Lett."},{"key":"ol-47-20-5433-R36","doi-asserted-by":"publisher","first-page":"1307","DOI":"10.1038\/s41563-020-0732-6","volume":"19","author":"Chen","year":"2020","journal-title":"Nat. Mater."},{"key":"ol-47-20-5433-R37","doi-asserted-by":"publisher","first-page":"3112","DOI":"10.1021\/acs.nanolett.1c00281","volume":"21","author":"Zhang","year":"2021","journal-title":"Nano Lett."},{"key":"ol-47-20-5433-R38","doi-asserted-by":"publisher","first-page":"eabf2690","DOI":"10.1126\/sciadv.abf2690","volume":"7","author":"Duan","year":"2021","journal-title":"Sci. Adv."},{"key":"ol-47-20-5433-R39","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1021\/acsphotonics.1c01549","volume":"9","author":"\u00c1lvarez-P\u00e9rez","year":"2022","journal-title":"ACS Photonics"},{"key":"ol-47-20-5433-R40","doi-asserted-by":"publisher","first-page":"2329","DOI":"10.1515\/nanoph-2022-0034","volume":"11","author":"Bapat","year":"2022","journal-title":"Nanophotonics"},{"key":"ol-47-20-5433-R42","doi-asserted-by":"publisher","first-page":"4260","DOI":"10.1021\/acs.nanolett.2c00399","volume":"22","author":"Zeng","year":"2022","journal-title":"Nano Lett."},{"key":"ol-47-20-5433-R43","doi-asserted-by":"publisher","first-page":"3719","DOI":"10.1038\/s41467-022-31477-z","volume":"13","author":"Ruta","year":"2022","journal-title":"Nat. Commun."},{"key":"ol-47-20-5433-R44","doi-asserted-by":"publisher","first-page":"13241","DOI":"10.1021\/acsnano.2c07123","volume":"16","author":"Zheng","year":"2022","journal-title":"ACS Nano"},{"key":"ol-47-20-5433-R45","first-page":"466","volume":"2","author":"Rytov","year":"1955","journal-title":"Soviet Physics J. Exp. Theor. Phys."},{"key":"ol-47-20-5433-R46","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/0370-1573(78)90009-1","volume":"43","author":"Bergman","year":"1978","journal-title":"Phys. Rep."},{"key":"ol-47-20-5433-R47","first-page":"29","volume":"4","author":"Zhilko","year":"1995","journal-title":"Vesti Akarl. Nauk Belarusi, Ser. Fiz-Mat. Nauk"}],"container-title":["Optics Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=ol-47-20-5433&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T15:30:58Z","timestamp":1722958258000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=ol-47-20-5433"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,14]]},"references-count":46,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2022]]},"published-print":{"date-parts":[[2022]]}},"URL":"https:\/\/doi.org\/10.1364\/ol.474505","relation":{},"ISSN":["0146-9592","1539-4794"],"issn-type":[{"value":"0146-9592","type":"print"},{"value":"1539-4794","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,14]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OL.474505","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"letter","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":"2 September 2022","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"22 September 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"14 October 2022","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2022 Optica Publishing Group","name":"copyright","label":"Copyright"}]}}