{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T11:32:34Z","timestamp":1774351954354,"version":"3.50.1"},"reference-count":50,"publisher":"Wiley","issue":"21","license":[{"start":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T00:00:00Z","timestamp":1667260800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T00:00:00Z","timestamp":1667260800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100000675","name":"Institution of Engineering and Technology","doi-asserted-by":"publisher","award":["AF Harvey Prize"],"award-info":[{"award-number":["AF Harvey Prize"]}],"id":[{"id":"10.13039\/501100000675","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["award 733700 (Simons Collaboration in Mathematics)"],"award-info":[{"award-number":["award 733700 (Simons Collaboration in Mathematics)"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nanophotonics"],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Here, we investigate the nonreciprocal propagation and amplification of surface plasmons in drift\u2010current biased graphene, using both Galilean and relativistic\u2010type Doppler shift transformations of the graphene\u2019s conductivity. Consistent with previous studies, both conductivity models predict strongly nonreciprocal propagation of surface plasmons due to the drag effect caused by the drifting electrons. In particular, the Galilean Doppler shift model leads to stronger spectral asymmetries in the plasmon dispersion with regimes of unidirectional propagation. Remarkably, it is shown that both conductivity models predict regimes of nonreciprocal plasmon amplification in a wide angular sector of in\u2010plane directions when the drift\u2010current biased graphene sheet is coupled to a plasmonic substrate (namely, SiC), with the plasmon amplification rate being substantially higher for the relativistic Doppler shift model.<\/jats:p>","DOI":"10.1515\/nanoph-2022-0451","type":"journal-article","created":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T18:56:33Z","timestamp":1667242593000},"page":"4929-4936","source":"Crossref","is-referenced-by-count":12,"title":["Directional dependence of the plasmonic gain and nonreciprocity in drift\u2010current biased graphene"],"prefix":"10.1002","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8500-9885","authenticated-orcid":false,"given":"Tiago A.","family":"Morgado","sequence":"first","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es Department of Electrical Engineering University of Coimbra 3030\u2010290 Coimbra Portugal"}]},{"given":"M\u00e1rio G.","family":"Silveirinha","sequence":"additional","affiliation":[{"name":"University of Lisbon\u2013Instituto Superior T\u00e9cnico and Instituto de Telecomunica\u00e7\u00f5es Avenida Rovisco Pais, 1 1049\u2010001 Lisboa Portugal"}]}],"member":"311","published-online":{"date-parts":[[2022,11,1]]},"reference":[{"key":"e_1_2_5_2_1","doi-asserted-by":"publisher","DOI":"10.1103\/revmodphys.17.343"},{"key":"e_1_2_5_3_1","doi-asserted-by":"publisher","DOI":"10.1088\/0034\u20104885\/67\/5\/r03"},{"key":"e_1_2_5_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aop.2011.10.013"},{"key":"e_1_2_5_5_1","doi-asserted-by":"publisher","DOI":"10.1103\/physrevapplied.10.047001"},{"key":"e_1_2_5_6_1","doi-asserted-by":"publisher","DOI":"10.3390\/sym11040486"},{"key":"e_1_2_5_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/tmag.1968.1066210"},{"key":"e_1_2_5_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/22.989957"},{"key":"e_1_2_5_9_1","doi-asserted-by":"publisher","DOI":"10.1364\/josab.22.000240"},{"key":"e_1_2_5_10_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1261243"},{"key":"e_1_2_5_11_1","doi-asserted-by":"publisher","DOI":"10.1038\/nphoton.2008.273"},{"key":"e_1_2_5_12_1","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.109.033901"},{"key":"e_1_2_5_13_1","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms3407"},{"key":"e_1_2_5_14_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41566\u2010017\u20100051\u2010x"},{"key":"e_1_2_5_15_1","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.123.206101"},{"key":"e_1_2_5_16_1","doi-asserted-by":"publisher","DOI":"10.1117\/1.ap.4.1.014002"},{"key":"e_1_2_5_17_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.3615688"},{"key":"e_1_2_5_18_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1210923109"},{"key":"e_1_2_5_19_1","doi-asserted-by":"publisher","DOI":"10.1364\/oe.20.007672"},{"key":"e_1_2_5_20_1","doi-asserted-by":"publisher","DOI":"10.1038\/nphoton.2016.161"},{"key":"e_1_2_5_21_1","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.110.223602"},{"key":"e_1_2_5_22_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1246957"},{"key":"e_1_2_5_23_1","doi-asserted-by":"publisher","DOI":"10.1103\/physreva.94.033810"},{"key":"e_1_2_5_24_1","doi-asserted-by":"publisher","DOI":"10.1103\/physrevb.99.045407"},{"key":"e_1_2_5_25_1","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.124.257403"},{"key":"e_1_2_5_26_1","doi-asserted-by":"publisher","DOI":"10.1103\/physrevlett.128.013902"},{"key":"e_1_2_5_27_1","unstructured":"T. G.Rappoport T. A.Morgado S.Lanneb\u00e8re M. G.Silveirinha \u201cEngineering transistor\u2010like optical gain in two\u2010dimensional materials with Berry curvature dipoles \u201d arXiv:2206.04023."},{"key":"e_1_2_5_28_1","doi-asserted-by":"publisher","DOI":"10.1103\/physreva.82.043803"},{"key":"e_1_2_5_29_1","doi-asserted-by":"publisher","DOI":"10.1088\/1367\u20102630\/13\/3\/033025"},{"key":"e_1_2_5_30_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1214383"},{"key":"e_1_2_5_31_1","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms9359"},{"key":"e_1_2_5_32_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41928\u2010018\u20100025\u20100"},{"key":"e_1_2_5_33_1","doi-asserted-by":"publisher","DOI":"10.1109\/lawp.2018.2868044"},{"key":"e_1_2_5_34_1","unstructured":"D. S.Borgnia T. V.Phan L. 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