{"id":"https://openalex.org/W1998557095","doi":"https://doi.org/10.1007/s00340-011-4628-7","title":"Classical simulation of relativistic quantum mechanics in periodic optical structures","display_name":"Classical simulation of relativistic quantum mechanics in periodic optical structures","publication_year":2011,"publication_date":"2011-07-08","ids":{"openalex":"https://openalex.org/W1998557095","doi":"https://doi.org/10.1007/s00340-011-4628-7","mag":"1998557095"},"language":"en","primary_location":{"id":"doi:10.1007/s00340-011-4628-7","doi":"https://doi.org/10.1007/s00340-011-4628-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00340-011-4628-7","pdf_url":null,"source":{"id":"https://openalex.org/S182865820","display_name":"Applied Physics B","issn_l":"0721-7269","issn":["0721-7269","0946-2171","1432-0649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Physics B","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1111.3461","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001137611","display_name":"Stefano Longhi","orcid":"https://orcid.org/0000-0002-8739-3542","observed_orcids":["https://orcid.org/0000-0002-8739-3542"]},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"S. Longhi","raw_affiliation_strings":["Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, 20133, Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, 20133, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001137611"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":{"value":4090,"currency":"USD","value_usd":4090},"apc_paid":null,"fwci":4.0648,"has_fulltext":true,"cited_by_count":73,"citation_normalized_percentile":{"value":0.94748304,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"104","issue":"3","first_page":"453","last_page":"468"},"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":0.75,"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":0.75,"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":0.03849999979138374,"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"}},{"id":"https://openalex.org/T10490","display_name":"Orbital Angular Momentum in Optics","score":0.02319999970495701,"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/relativistic-quantum-mechanics","display_name":"relativistic quantum mechanics","score":0.7639999985694885},{"id":"https://openalex.org/keywords/photonic-lattices","display_name":"photonic lattices","score":0.9269999861717224},{"id":"https://openalex.org/keywords/bragg-gratings","display_name":"Bragg gratings","score":0.9539999961853027},{"id":"https://openalex.org/keywords/zitterbewegung","display_name":"Zitterbewegung","score":0.8820000290870667},{"id":"https://openalex.org/keywords/klein-tunneling","display_name":"Klein tunneling","score":0.9980000257492065},{"id":"https://openalex.org/keywords/vacuum-decay","display_name":"vacuum decay","score":0.9409999847412109},{"id":"https://openalex.org/keywords/pair-production","display_name":"pair production","score":0.9539999961853027},{"id":"https://openalex.org/keywords/dirac-oscillator","display_name":"Dirac oscillator","score":0.9980000257492065},{"id":"https://openalex.org/keywords/non-hermitian-physics","display_name":"non-Hermitian physics","score":0.8059999942779541}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8817999958992004},{"id":"https://openalex.org/C2779577033","wikidata":"https://www.wikidata.org/wiki/Q206604","display_name":"Zitterbewegung","level":3,"score":0.8118000030517578},{"id":"https://openalex.org/C68717125","wikidata":"https://www.wikidata.org/wiki/Q735602","display_name":"Quantum optics","level":2,"score":0.5401999950408936},{"id":"https://openalex.org/C51493423","wikidata":"https://www.wikidata.org/wiki/Q2486351","display_name":"Superluminal motion","level":2,"score":0.5296000242233276},{"id":"https://openalex.org/C81263218","wikidata":"https://www.wikidata.org/wiki/Q7330289","display_name":"Relativistic quantum chemistry","level":2,"score":0.4851999878883362},{"id":"https://openalex.org/C103862110","wikidata":"https://www.wikidata.org/wiki/Q1151533","display_name":"Optical physics","level":3,"score":0.4724000096321106},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4602000117301941},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.42179998755455017},{"id":"https://openalex.org/C20788544","wikidata":"https://www.wikidata.org/wiki/Q467054","display_name":"Photonics","level":2,"score":0.4131999909877777},{"id":"https://openalex.org/C168997771","wikidata":"https://www.wikidata.org/wiki/Q2022629","display_name":"Relativistic particle","level":3,"score":0.39910000562667847},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3725999891757965},{"id":"https://openalex.org/C2780167933","wikidata":"https://www.wikidata.org/wiki/Q1550652","display_name":"Pulse (music)","level":3,"score":0.34880000352859497},{"id":"https://openalex.org/C140673361","wikidata":"https://www.wikidata.org/wiki/Q7310838","display_name":"Relativistic wave equations","level":3,"score":0.3472999930381775},{"id":"https://openalex.org/C66601787","wikidata":"https://www.wikidata.org/wiki/Q7049210","display_name":"Nonclassical light","level":3,"score":0.3441999852657318},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.33739998936653137},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C163862864","wikidata":"https://www.wikidata.org/wiki/Q724183","display_name":"Relativistic speed","level":4,"score":0.3330000042915344},{"id":"https://openalex.org/C154236941","wikidata":"https://www.wikidata.org/wiki/Q942347","display_name":"Physical optics","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C149773537","wikidata":"https://www.wikidata.org/wiki/Q12969754","display_name":"Electromagnetic radiation","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C2778907946","wikidata":"https://www.wikidata.org/wiki/Q637725","display_name":"Bloch oscillations","level":3,"score":0.32839998602867126},{"id":"https://openalex.org/C113362759","wikidata":"https://www.wikidata.org/wiki/Q7098889","display_name":"Optical radiation","level":3,"score":0.32519999146461487},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.31949999928474426},{"id":"https://openalex.org/C520434653","wikidata":"https://www.wikidata.org/wiki/Q38867","display_name":"Laser","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C74939445","wikidata":"https://www.wikidata.org/wiki/Q5055185","display_name":"Cavity quantum electrodynamics","level":4,"score":0.28619998693466187},{"id":"https://openalex.org/C57476683","wikidata":"https://www.wikidata.org/wiki/Q3332147","display_name":"Relativistic quantum mechanics","level":4,"score":0.26919999718666077},{"id":"https://openalex.org/C206611041","wikidata":"https://www.wikidata.org/wiki/Q4393075","display_name":"Relativistic mechanics","level":3,"score":0.2653999924659729},{"id":"https://openalex.org/C124657808","wikidata":"https://www.wikidata.org/wiki/Q1133068","display_name":"Quantum dot","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C2777813233","wikidata":"https://www.wikidata.org/wiki/Q1527816","display_name":"Grating","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.2549000084400177},{"id":"https://openalex.org/C69746256","wikidata":"https://www.wikidata.org/wiki/Q193068","display_name":"Wave\u2013particle duality","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00340-011-4628-7","doi":"https://doi.org/10.1007/s00340-011-4628-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00340-011-4628-7","pdf_url":null,"source":{"id":"https://openalex.org/S182865820","display_name":"Applied Physics B","issn_l":"0721-7269","issn":["0721-7269","0946-2171","1432-0649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Physics B","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1111.3461","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1111.3461","pdf_url":"https://arxiv.org/pdf/1111.3461","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":"doi:10.48550/arxiv.1111.3461","doi":"https://doi.org/10.48550/arxiv.1111.3461","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1111.3461","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":"pmh:oai:arXiv.org:1111.3461","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1111.3461","pdf_url":"https://arxiv.org/pdf/1111.3461","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1998557095.pdf","grobid_xml":"https://content.openalex.org/works/W1998557095.grobid-xml"},"referenced_works_count":154,"referenced_works":["https://openalex.org/W79001361","https://openalex.org/W212270999","https://openalex.org/W625715774","https://openalex.org/W1531935167","https://openalex.org/W1544234979","https://openalex.org/W1545180657","https://openalex.org/W1589914989","https://openalex.org/W1661960065","https://openalex.org/W1665371518","https://openalex.org/W1963820638","https://openalex.org/W1964489191","https://openalex.org/W1964850626","https://openalex.org/W1968537230","https://openalex.org/W1968859093","https://openalex.org/W1970514171","https://openalex.org/W1970947221","https://openalex.org/W1972951295","https://openalex.org/W1974418311","https://openalex.org/W1975264848","https://openalex.org/W1976677893","https://openalex.org/W1977871904","https://openalex.org/W1978582765","https://openalex.org/W1980138601","https://openalex.org/W1982510647","https://openalex.org/W1984141379","https://openalex.org/W1984220188","https://openalex.org/W1984367344","https://openalex.org/W1986216607","https://openalex.org/W1986816479","https://openalex.org/W1989966984","https://openalex.org/W1990107322","https://openalex.org/W1990557380","https://openalex.org/W1992376231","https://openalex.org/W1992465120","https://openalex.org/W1994533889","https://openalex.org/W1996547609","https://openalex.org/W1997323544","https://openalex.org/W1999750768","https://openalex.org/W1999925585","https://openalex.org/W2000650215","https://openalex.org/W2003051976","https://openalex.org/W2003409983","https://openalex.org/W2003593341","https://openalex.org/W2004103591","https://openalex.org/W2005797215","https://openalex.org/W2008931389","https://openalex.org/W2009918492","https://openalex.org/W2011152117","https://openalex.org/W2011967582","https://openalex.org/W2012434079","https://openalex.org/W2013039846","https://openalex.org/W2014135237","https://openalex.org/W2014788644","https://openalex.org/W2018938134","https://openalex.org/W2018942861","https://openalex.org/W2020476780","https://openalex.org/W2021018489","https://openalex.org/W2021442722","https://openalex.org/W2024923839","https://openalex.org/W2026205980","https://openalex.org/W2026801623","https://openalex.org/W2027718107","https://openalex.org/W2028785431","https://openalex.org/W2032066624","https://openalex.org/W2033148600","https://openalex.org/W2033357739","https://openalex.org/W2033874072","https://openalex.org/W2035846715","https://openalex.org/W2037856736","https://openalex.org/W2038670463","https://openalex.org/W2038985364","https://openalex.org/W2040735443","https://openalex.org/W2042000192","https://openalex.org/W2042073190","https://openalex.org/W2043649748","https://openalex.org/W2044053619","https://openalex.org/W2044185713","https://openalex.org/W2044209773","https://openalex.org/W2046670825","https://openalex.org/W2047455383","https://openalex.org/W2047491919","https://openalex.org/W2048492878","https://openalex.org/W2049756287","https://openalex.org/W2050024221","https://openalex.org/W2050686679","https://openalex.org/W2057201898","https://openalex.org/W2057595669","https://openalex.org/W2057684188","https://openalex.org/W2058404058","https://openalex.org/W2058550585","https://openalex.org/W2058692466","https://openalex.org/W2059235004","https://openalex.org/W2059885503","https://openalex.org/W2060251425","https://openalex.org/W2061653218","https://openalex.org/W2062331957","https://openalex.org/W2063659230","https://openalex.org/W2065312566","https://openalex.org/W2065499715","https://openalex.org/W2067123857","https://openalex.org/W2068824512","https://openalex.org/W2068873395","https://openalex.org/W2069672988","https://openalex.org/W2071849475","https://openalex.org/W2072020654","https://openalex.org/W2072216248","https://openalex.org/W2072374571","https://openalex.org/W2073899528","https://openalex.org/W2076169073","https://openalex.org/W2077193646","https://openalex.org/W2077666279","https://openalex.org/W2079341640","https://openalex.org/W2080856445","https://openalex.org/W2083433309","https://openalex.org/W2086749336","https://openalex.org/W2087504958","https://openalex.org/W2087891782","https://openalex.org/W2088192059","https://openalex.org/W2088480740","https://openalex.org/W2088931175","https://openalex.org/W2089857892","https://openalex.org/W2093212801","https://openalex.org/W2101463303","https://openalex.org/W2105685140","https://openalex.org/W2108375990","https://openalex.org/W2108634308","https://openalex.org/W2112930989","https://openalex.org/W2115969249","https://openalex.org/W2117062221","https://openalex.org/W2122057592","https://openalex.org/W2123614369","https://openalex.org/W2125284466","https://openalex.org/W2126665790","https://openalex.org/W2129843869","https://openalex.org/W2137781770","https://openalex.org/W2140726841","https://openalex.org/W2143841922","https://openalex.org/W2155711475","https://openalex.org/W2159950825","https://openalex.org/W2163160733","https://openalex.org/W2164611922","https://openalex.org/W2166757146","https://openalex.org/W2166978948","https://openalex.org/W2167648595","https://openalex.org/W2168850143","https://openalex.org/W2268965330","https://openalex.org/W2488460509","https://openalex.org/W2799118597","https://openalex.org/W2949965471","https://openalex.org/W2951308009","https://openalex.org/W2951635196","https://openalex.org/W4213086593","https://openalex.org/W4253375318","https://openalex.org/W6604007578"],"related_works":["https://openalex.org/W2068873395","https://openalex.org/W2609800056","https://openalex.org/W2065499715","https://openalex.org/W6949546856","https://openalex.org/W4413942585","https://openalex.org/W102430513","https://openalex.org/W2918023906","https://openalex.org/W2370203977","https://openalex.org/W2046670825","https://openalex.org/W2890650537"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
