{"id":"https://openalex.org/W1978612880","doi":"https://doi.org/10.1364/ao.29.002460","title":"Effective medium equivalent to a symmetric multilayer at oblique incidence","display_name":"Effective medium equivalent to a symmetric multilayer at oblique incidence","publication_year":1990,"publication_date":"1990-06-01","ids":{"openalex":"https://openalex.org/W1978612880","doi":"https://doi.org/10.1364/ao.29.002460","mag":"1978612880","pmid":"https://pubmed.ncbi.nlm.nih.gov/20563190"},"language":"en","primary_location":{"id":"doi:10.1364/ao.29.002460","doi":"https://doi.org/10.1364/ao.29.002460","is_oa":false,"landing_page_url":"https://doi.org/10.1364/ao.29.002460","pdf_url":null,"source":{"id":"https://openalex.org/S4210211917","display_name":"Applied Optics","issn_l":"0003-6935","issn":["0003-6935","1539-4522","1540-8981","1559-128X","2155-3165"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","dongbi-c","jufo-1","medline","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315679","host_organization_name":"Optica Publishing Group","host_organization_lineage":["https://openalex.org/P4310315679"],"host_organization_lineage_names":["Optica Publishing Group"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Optics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068656123","display_name":"J. Lafait","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405264447","display_name":"Universit\u00e9 Pierre-et-Marie-Curie","ror":"https://ror.org/01yvrd251","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081","https://openalex.org/I4405264447"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J. Lafait","raw_affiliation_strings":["The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, \nFrance","The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, #N#France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, \nFrance","institution_ids":["https://openalex.org/I4405264447"]},{"raw_affiliation_string":"The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, #N#France","institution_ids":["https://openalex.org/I4405264447"]}]},{"author_position":"middle","author":{"id":null,"display_name":"T. Yamaguchi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405264447","display_name":"Universit\u00e9 Pierre-et-Marie-Curie","ror":"https://ror.org/01yvrd251","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081","https://openalex.org/I4405264447"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"T. Yamaguchi","raw_affiliation_strings":["The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, \nFrance","The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, #N#France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, \nFrance","institution_ids":["https://openalex.org/I4405264447"]},{"raw_affiliation_string":"The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, #N#France","institution_ids":["https://openalex.org/I4405264447"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084653019","display_name":"Jean\u2010Marc Frig\u00e9rio","orcid":"https://orcid.org/0000-0003-0471-2075","observed_orcids":["https://orcid.org/0000-0003-0471-2075"]},"institutions":[{"id":"https://openalex.org/I4405264447","display_name":"Universit\u00e9 Pierre-et-Marie-Curie","ror":"https://ror.org/01yvrd251","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081","https://openalex.org/I4405264447"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J. M. Frigerio","raw_affiliation_strings":["The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, \nFrance","The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, #N#France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, \nFrance","institution_ids":["https://openalex.org/I4405264447"]},{"raw_affiliation_string":"The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, #N#France","institution_ids":["https://openalex.org/I4405264447"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040870382","display_name":"A. Bichri","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405264447","display_name":"Universit\u00e9 Pierre-et-Marie-Curie","ror":"https://ror.org/01yvrd251","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081","https://openalex.org/I4405264447"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A. Bichri","raw_affiliation_strings":["The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, \nFrance","The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, #N#France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, \nFrance","institution_ids":["https://openalex.org/I4405264447"]},{"raw_affiliation_string":"The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, #N#France","institution_ids":["https://openalex.org/I4405264447"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074617174","display_name":"Kouider Driss-Khodja","orcid":"https://orcid.org/0000-0001-7403-5802","observed_orcids":["https://orcid.org/0000-0001-7403-5802"]},"institutions":[{"id":"https://openalex.org/I4405264447","display_name":"Universit\u00e9 Pierre-et-Marie-Curie","ror":"https://ror.org/01yvrd251","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081","https://openalex.org/I4405264447"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"K. Driss-Khodja","raw_affiliation_strings":["The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, \nFrance","The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, #N#France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, \nFrance","institution_ids":["https://openalex.org/I4405264447"]},{"raw_affiliation_string":"The authors are with Universit\u00e9 Pierre et Marie Curie, Laboratoire d\u2019Optique des Solides, 4 place Jussieu, F-75252 Paris CEDEX 05, #N#France","institution_ids":["https://openalex.org/I4405264447"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4405264447"],"apc_list":null,"apc_paid":null,"fwci":0.7442,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.60386775,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"29","issue":"16","first_page":"2460","last_page":"2460"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11723","display_name":"Optical Coatings and Gratings","score":0.6898999810218811,"subfield":{"id":"https://openalex.org/subfields/2508","display_name":"Surfaces, Coatings and Films"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11723","display_name":"Optical Coatings and Gratings","score":0.6898999810218811,"subfield":{"id":"https://openalex.org/subfields/2508","display_name":"Surfaces, Coatings and Films"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12050","display_name":"Optical Polarization and Ellipsometry","score":0.13590000569820404,"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/T10245","display_name":"Metamaterials and Metasurfaces Applications","score":0.07029999792575836,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/effective-medium-theory","display_name":"effective medium theory","score":0.8840000033378601},{"id":"https://openalex.org/keywords/multilayer-films","display_name":"multilayer films","score":0.7580000162124634},{"id":"https://openalex.org/keywords/oblique-incidence","display_name":"oblique incidence","score":0.9520000219345093},{"id":"https://openalex.org/keywords/dielectric-tensor","display_name":"dielectric tensor","score":0.9259999990463257},{"id":"https://openalex.org/keywords/effective-thickness","display_name":"effective thickness","score":0.9539999961853027},{"id":"https://openalex.org/keywords/absorbing-films","display_name":"absorbing films","score":0.7519999742507935},{"id":"https://openalex.org/keywords/incident-angle-dependence","display_name":"incident angle dependence","score":0.9120000004768372}],"concepts":[{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.7645329236984253},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.6161965131759644},{"id":"https://openalex.org/C133386390","wikidata":"https://www.wikidata.org/wiki/Q184996","display_name":"Dielectric","level":2,"score":0.5861425399780273},{"id":"https://openalex.org/C161326058","wikidata":"https://www.wikidata.org/wiki/Q7245073","display_name":"Principal axis theorem","level":2,"score":0.5598764419555664},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4838465750217438},{"id":"https://openalex.org/C182610534","wikidata":"https://www.wikidata.org/wiki/Q633620","display_name":"Ray","level":2,"score":0.47252824902534485},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26317089796066284},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25748294591903687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.15936097502708435},{"id":"https://openalex.org/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","level":1,"score":0.09913554787635803}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1364/ao.29.002460","doi":"https://doi.org/10.1364/ao.29.002460","is_oa":false,"landing_page_url":"https://doi.org/10.1364/ao.29.002460","pdf_url":null,"source":{"id":"https://openalex.org/S4210211917","display_name":"Applied Optics","issn_l":"0003-6935","issn":["0003-6935","1539-4522","1540-8981","1559-128X","2155-3165"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","dongbi-c","jufo-1","medline","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315679","host_organization_name":"Optica Publishing Group","host_organization_lineage":["https://openalex.org/P4310315679"],"host_organization_lineage_names":["Optica Publishing Group"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Optics","raw_type":"journal-article"},{"id":"pmid:20563190","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/20563190","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":"Applied optics","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1666853924","https://openalex.org/W1984255985","https://openalex.org/W2047445241","https://openalex.org/W2157032767","https://openalex.org/W2609902715"],"related_works":["https://openalex.org/W2046983846","https://openalex.org/W1865378804","https://openalex.org/W2070917553","https://openalex.org/W1579836078","https://openalex.org/W2045443400","https://openalex.org/W2915243663","https://openalex.org/W2276192987","https://openalex.org/W1992269174","https://openalex.org/W2077530322","https://openalex.org/W1920354129"],"abstract_inverted_index":{"It":[0,66],"is":[1,11,67,78,93,121],"shown":[2],"that":[3],"a":[4,14],"multilayer":[5],"with":[6],"repeated":[7],"symmetric":[8],"unit":[9,72,113],"structure":[10,73,114],"equivalent":[12,76,119],"to":[13,30,36,42,86,96],"homogeneous":[15],"and":[16,40,49,57,89,105],"optically":[17],"biaxial":[18],"medium":[19,77,120],"for":[20],"obliquely":[21],"incident":[22,50],"light,":[23],"the":[24,31,37,43,54,58,75,81,87,90,97,106,117],"three":[25],"principal":[26],"axes":[27],"being":[28,84],"normal":[29,35,41,85],"plane":[32],"of":[33,53,108,112,116],"incidence,":[34],"film":[38],"plane,":[39],"other":[44],"two.":[45],"Unit":[46],"thickness":[47,60,92],"dependence":[48,52],"angle":[51],"dielectric":[55],"tensor":[56],"effective":[59,91],"are":[61,102],"calculated":[62],"using":[63],"exact":[64],"formulas.":[65],"found":[68],"that,":[69],"at":[70],"small":[71],"thickness,":[74],"almost":[79],"uniaxial,":[80],"optical":[82],"axis":[83],"film,":[88],"very":[94],"close":[95],"mechanical":[98],"one.":[99],"Absorbing":[100],"films":[101],"also":[103],"envisaged":[104],"domain":[107],"validity":[109],"(in":[110],"terms":[111],"thickness)":[115],"uniaxial":[118],"defined":[122],"by":[123],"numerical":[124],"examples.":[125]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-06T10:28:23.643775","created_date":"2016-06-24T00:00:00"}
