{"id":"https://openalex.org/W4393935027","doi":"https://doi.org/10.3390/sym16040430","title":"Modeling the Non-Hermitian Infinity-Loop Micro-Resonator over a Free Spectral Range Reveals the Characteristics for Operation at an Exceptional Point","display_name":"Modeling the Non-Hermitian Infinity-Loop Micro-Resonator over a Free Spectral Range Reveals the Characteristics for Operation at an Exceptional Point","publication_year":2024,"publication_date":"2024-04-04","ids":{"openalex":"https://openalex.org/W4393935027","doi":"https://doi.org/10.3390/sym16040430"},"language":"en","primary_location":{"id":"doi:10.3390/sym16040430","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym16040430","pdf_url":"https://www.mdpi.com/2073-8994/16/4/430/pdf?version=1712220935","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/4/430/pdf?version=1712220935","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017033852","display_name":"Tianrui Li","orcid":"https://orcid.org/0009-0000-1416-8806"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tianrui Li","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Photon Science Institute, The University of Manchester, Oxford Rd., Manchester M13 9PL, UK"],"raw_orcid":"https://orcid.org/0009-0000-1416-8806","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Photon Science Institute, The University of Manchester, Oxford Rd., Manchester M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090696133","display_name":"Matthew P. Halsall","orcid":"https://orcid.org/0000-0001-7441-4247"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Matthew P. Halsall","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Photon Science Institute, The University of Manchester, Oxford Rd., Manchester M13 9PL, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Photon Science Institute, The University of Manchester, Oxford Rd., Manchester M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064012207","display_name":"Iain F. Crowe","orcid":"https://orcid.org/0000-0001-8797-3582"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Iain F. Crowe","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Photon Science Institute, The University of Manchester, Oxford Rd., Manchester M13 9PL, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Photon Science Institute, The University of Manchester, Oxford Rd., Manchester M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064012207"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.324,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54418151,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"16","issue":"4","first_page":"430","last_page":"430"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10988","display_name":"Advanced Fiber Laser Technologies","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/free-spectral-range","display_name":"Free spectral range","score":0.7821980118751526},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.7438002228736877},{"id":"https://openalex.org/keywords/resonator","display_name":"Resonator","score":0.7012029886245728},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.657189130783081},{"id":"https://openalex.org/keywords/coupled-mode-theory","display_name":"Coupled mode theory","score":0.48696741461753845},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.46989819407463074},{"id":"https://openalex.org/keywords/photonic-crystal","display_name":"Photonic crystal","score":0.43377113342285156},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.39666759967803955},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.33339089155197144},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.30396199226379395},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1471605896949768},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.1044427752494812}],"concepts":[{"id":"https://openalex.org/C2776015930","wikidata":"https://www.wikidata.org/wiki/Q1454132","display_name":"Free spectral range","level":3,"score":0.7821980118751526},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7438002228736877},{"id":"https://openalex.org/C97126364","wikidata":"https://www.wikidata.org/wiki/Q349669","display_name":"Resonator","level":2,"score":0.7012029886245728},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.657189130783081},{"id":"https://openalex.org/C2781181084","wikidata":"https://www.wikidata.org/wiki/Q5178020","display_name":"Coupled mode theory","level":3,"score":0.48696741461753845},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.46989819407463074},{"id":"https://openalex.org/C75302062","wikidata":"https://www.wikidata.org/wiki/Q900150","display_name":"Photonic crystal","level":2,"score":0.43377113342285156},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.39666759967803955},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33339089155197144},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.30396199226379395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1471605896949768},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.1044427752494812},{"id":"https://openalex.org/C42067758","wikidata":"https://www.wikidata.org/wiki/Q174102","display_name":"Refractive index","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym16040430","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym16040430","pdf_url":"https://www.mdpi.com/2073-8994/16/4/430/pdf?version=1712220935","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire/bd8416f2-7039-4a74-978b-12c5b8c4adcd","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/bd8416f2-7039-4a74-978b-12c5b8c4adcd","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Li, T, Halsall, M P & Crowe, I F 2024, 'Modeling the Non-Hermitian Infinity-Loop Micro-Resonator over a Free Spectral Range Reveals the Characteristics for Operation at an Exceptional Point', Symmetry, vol. 16, no. 4, 430. https://doi.org/10.3390/sym16040430","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:852fb64c34a44a89b341f952131619fc","is_oa":true,"landing_page_url":"https://doaj.org/article/852fb64c34a44a89b341f952131619fc","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 4, p 430 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/16/4/430/","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16040430","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym16040430","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym16040430","pdf_url":"https://www.mdpi.com/2073-8994/16/4/430/pdf?version=1712220935","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.9100000262260437}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393935027.pdf","grobid_xml":"https://content.openalex.org/works/W4393935027.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1531935167","https://openalex.org/W1911969426","https://openalex.org/W2102489731","https://openalex.org/W2565894717","https://openalex.org/W2787598948","https://openalex.org/W2883094646","https://openalex.org/W3014141222","https://openalex.org/W3031293393","https://openalex.org/W3144678762","https://openalex.org/W3203521431","https://openalex.org/W3215189266","https://openalex.org/W4205977323","https://openalex.org/W4225821417","https://openalex.org/W4281745367","https://openalex.org/W4293237704","https://openalex.org/W4378083756"],"related_works":["https://openalex.org/W2087696644","https://openalex.org/W2160749150","https://openalex.org/W2216211804","https://openalex.org/W2506639017","https://openalex.org/W2064530639","https://openalex.org/W1993094484","https://openalex.org/W1991015334","https://openalex.org/W2284759267","https://openalex.org/W1773929059","https://openalex.org/W1524435170"],"abstract_inverted_index":{"We":[0,34,100],"develop":[1],"a":[2,21,59,70],"4":[3],"\u00d7":[4],"4-matrix":[5],"model":[6,77],"based":[7,26],"on":[8,27],"temporal":[9],"coupled":[10,42],"mode":[11],"theory":[12],"(TCMT)":[13],"to":[14,38,58,107],"elucidate":[15],"the":[16,28,36,52,79,94,103,108,115,125],"intricate":[17],"energy":[18],"exchange":[19],"within":[20,69],"non-Hermitian,":[22],"resonant":[23,43,126],"photonic":[24],"structure,":[25],"recently":[29],"described":[30],"infinity-loop":[31],"micro-resonator":[32],"(ILMR).":[33],"consider":[35],"structure":[37],"consist":[39],"of":[40,117,120],"four":[41],"modes,":[44],"with":[45,63],"clockwise":[46],"and":[47,66],"counterclockwise":[48],"propagating":[49],"optical":[50],"fields,":[51],"interplay":[53],"between":[54,124],"which":[55],"gives":[56],"rise":[57],"rich":[60],"spectral":[61,73,97],"form":[62],"both":[64],"overlapping":[65],"non-overlapping":[67],"resonances":[68,92],"single":[71],"free":[72,96],"range":[74,98],"(FSR).":[75,99],"Our":[76],"clarifies":[78],"precise":[80],"conditions":[81,109],"for":[82,110],"exceptional":[83],"points":[84],"(EPs)":[85],"in":[86],"this":[87],"system":[88,104],"by":[89],"examining":[90],"neighboring":[91],"over":[93],"device":[95],"find":[101],"that":[102],"is":[105],"robust":[106],"observing":[111],"an":[112],"EP,":[113],"despite":[114],"presence":[116],"non-zero":[118],"coupling":[119],"signals,":[121],"or":[122],"crosstalk,":[123],"modes.":[127]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-12-26T23:08:49.675405","created_date":"2025-10-10T00:00:00"}