{"id":"https://openalex.org/W2004103591","doi":"https://doi.org/10.1103/physrevlett.106.093902","title":"PT -Symmetry Breaking and Laser-Absorber Modes in Optical Scattering Systems","display_name":"PT -Symmetry Breaking and Laser-Absorber Modes in Optical Scattering Systems","publication_year":2011,"publication_date":"2011-03-02","ids":{"openalex":"https://openalex.org/W2004103591","doi":"https://doi.org/10.1103/physrevlett.106.093902","mag":"2004103591","pmid":"https://pubmed.ncbi.nlm.nih.gov/21405622"},"language":"en","primary_location":{"id":"doi:10.1103/physrevlett.106.093902","doi":"https://doi.org/10.1103/physrevlett.106.093902","is_oa":true,"landing_page_url":"https://doi.org/10.1103/physrevlett.106.093902","pdf_url":"http://link.aps.org/pdf/10.1103/PhysRevLett.106.093902","source":{"id":"https://openalex.org/S24807848","display_name":"Physical Review Letters","issn_l":"0031-9007","issn":["0031-9007","1079-7114","1092-0145"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-2","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Letters","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2004103591"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"http://link.aps.org/pdf/10.1103/PhysRevLett.106.093902","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068898941","display_name":"Y. D. Chong","orcid":"https://orcid.org/0000-0002-8649-7884","observed_orcids":["https://orcid.org/0000-0002-8649-7884"]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Y. D. Chong","raw_affiliation_strings":["Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100447677","display_name":"Li Ge","orcid":"https://orcid.org/0000-0002-1922-4464","observed_orcids":["https://orcid.org/0000-0002-1922-4464"]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Li Ge","raw_affiliation_strings":["Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070859860","display_name":"A. Douglas Stone","orcid":"https://orcid.org/0000-0002-0037-2950","observed_orcids":["https://orcid.org/0000-0002-0037-2950"]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Douglas Stone","raw_affiliation_strings":["Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068898941","https://openalex.org/A5100447677"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":{"value":3750,"currency":"USD","value_usd":3750},"apc_paid":null,"fwci":24.5091,"has_fulltext":true,"cited_by_count":987,"citation_normalized_percentile":{"value":0.99838408,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"106","issue":"9","first_page":"093902","last_page":"093902"},"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":0.9984999895095825,"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":0.9984999895095825,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11996","display_name":"Random lasers and scattering media","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pt-symmetry","display_name":"PT symmetry","score":0.9179999828338623},{"id":"https://openalex.org/keywords/pt-symmetry-breaking","display_name":"PT symmetry breaking","score":0.6919999718666077},{"id":"https://openalex.org/keywords/light-scattering","display_name":"light scattering","score":0.7379999756813049},{"id":"https://openalex.org/keywords/scattering-matrix","display_name":"scattering matrix","score":0.859000027179718},{"id":"https://openalex.org/keywords/coherent-perfect-absorption","display_name":"coherent perfect absorption","score":0.972000002861023},{"id":"https://openalex.org/keywords/norm-preservation","display_name":"norm preservation","score":0.4869999885559082},{"id":"https://openalex.org/keywords/pole-zero-cancellation","display_name":"pole-zero cancellation","score":0.5879999995231628}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6249674558639526},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.613734245300293},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.6016454100608826},{"id":"https://openalex.org/C204795200","wikidata":"https://www.wikidata.org/wiki/Q903282","display_name":"Symmetry breaking","level":2,"score":0.47987309098243713},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.45045074820518494},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.4241282641887665},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.4103415608406067},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.38532429933547974},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3435787260532379},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.17515552043914795},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1103/physrevlett.106.093902","doi":"https://doi.org/10.1103/physrevlett.106.093902","is_oa":true,"landing_page_url":"https://doi.org/10.1103/physrevlett.106.093902","pdf_url":"http://link.aps.org/pdf/10.1103/PhysRevLett.106.093902","source":{"id":"https://openalex.org/S24807848","display_name":"Physical Review Letters","issn_l":"0031-9007","issn":["0031-9007","1079-7114","1092-0145"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-2","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Letters","raw_type":"journal-article"},{"id":"pmid:21405622","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21405622","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical review letters","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:1008.5156","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1008.5156","pdf_url":"https://arxiv.org/pdf/1008.5156","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/101037","doi":null,"is_oa":false,"landing_page_url":"https://hdl.handle.net/10356/101037","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},{"id":"doi:10.48550/arxiv.1008.5156","doi":"https://doi.org/10.48550/arxiv.1008.5156","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1008.5156","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1103/physrevlett.106.093902","doi":"https://doi.org/10.1103/physrevlett.106.093902","is_oa":true,"landing_page_url":"https://doi.org/10.1103/physrevlett.106.093902","pdf_url":"http://link.aps.org/pdf/10.1103/PhysRevLett.106.093902","source":{"id":"https://openalex.org/S24807848","display_name":"Physical Review Letters","issn_l":"0031-9007","issn":["0031-9007","1079-7114","1092-0145"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-2","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Letters","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2635374589","display_name":"MRSEC: Materials Research Science and Engineering Center for Research on Interface Structures and Phenomena","funder_award_id":"0520495","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2798704468","display_name":"Semiclassical and Quantum Theory of Open and Complex Lasers","funder_award_id":"0908437","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308380","display_name":"Yale University","ror":"https://ror.org/03v76x132"},{"id":"https://openalex.org/F4320333422","display_name":"Materials Research Science and Engineering Center, Harvard University","ror":"https://ror.org/01qa5ep47"},{"id":"https://openalex.org/F4320337367","display_name":"Division of Materials Research","ror":"https://ror.org/01pc7k308"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2004103591.pdf","grobid_xml":"https://content.openalex.org/works/W2004103591.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1531935167","https://openalex.org/W1665371518","https://openalex.org/W1968235873","https://openalex.org/W2040825465","https://openalex.org/W2047699813","https://openalex.org/W2067123857","https://openalex.org/W2072774600","https://openalex.org/W2077809553","https://openalex.org/W2078628709","https://openalex.org/W2086334850","https://openalex.org/W2097234381","https://openalex.org/W2140726841","https://openalex.org/W2159798643","https://openalex.org/W2166223485","https://openalex.org/W2168499099"],"related_works":["https://openalex.org/W1497992227","https://openalex.org/W2099575773","https://openalex.org/W2320420844","https://openalex.org/W779353799","https://openalex.org/W2236470637","https://openalex.org/W2331392819","https://openalex.org/W2399609215","https://openalex.org/W2606551067","https://openalex.org/W3135041018","https://openalex.org/W1929314672"],"abstract_inverted_index":{"Using":[0],"a":[1,18,31,67,82],"scattering":[2,9,35],"matrix":[3,89],"formalism,":[4],"we":[5],"derive":[6],"the":[7,28,78,87],"general":[8],"properties":[10],"of":[11,20,30,44,86],"optical":[12],"structures":[13],"that":[14],"are":[15,38],"symmetric":[16],"under":[17],"combination":[19],"parity":[21],"and":[22,41,49,69,84],"time":[23],"reversal":[24],"(PT).":[25],"We":[26],"demonstrate":[27],"existence":[29],"transition":[32],"between":[33],"PT-symmetric":[34],"eigenstates,":[36],"which":[37,62],"norm":[39],"preserving,":[40],"symmetry-broken":[42],"pairs":[43],"eigenstates":[45],"exhibiting":[46],"net":[47],"amplification":[48],"loss.":[50],"The":[51],"system":[52],"proposed":[53],"by":[54],"Longhi":[55],"[Phys.":[56],"Rev.":[57],"A":[58],"82,":[59],"031801":[60],"(2010).],":[61],"can":[63],"act":[64],"simultaneously":[65],"as":[66],"laser":[68],"coherent":[70],"perfect":[71],"absorber,":[72],"occurs":[73],"at":[74],"discrete":[75],"points":[76],"in":[77],"broken-symmetry":[79],"phase,":[80],"when":[81],"pole":[83],"zero":[85],"S":[88],"coincide.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":48},{"year":2025,"cited_by_count":43},{"year":2024,"cited_by_count":50},{"year":2023,"cited_by_count":56},{"year":2022,"cited_by_count":68},{"year":2021,"cited_by_count":87},{"year":2020,"cited_by_count":70},{"year":2019,"cited_by_count":86},{"year":2018,"cited_by_count":78},{"year":2017,"cited_by_count":84},{"year":2016,"cited_by_count":91},{"year":2015,"cited_by_count":66},{"year":2014,"cited_by_count":69},{"year":2013,"cited_by_count":39},{"year":2012,"cited_by_count":39}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}
