{"id":"https://openalex.org/W2004308494","doi":"https://doi.org/10.1090/s0002-9947-2011-05334-1","title":"Unique determination of periodic polyhedral structures by scattered electromagnetic fields","display_name":"Unique determination of periodic polyhedral structures by scattered electromagnetic fields","publication_year":2011,"publication_date":"2011-04-19","ids":{"openalex":"https://openalex.org/W2004308494","doi":"https://doi.org/10.1090/s0002-9947-2011-05334-1","mag":"2004308494"},"language":"en","primary_location":{"id":"doi:10.1090/s0002-9947-2011-05334-1","doi":"https://doi.org/10.1090/s0002-9947-2011-05334-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-2011-05334-1","pdf_url":"https://www.ams.org/tran/2011-363-09/S0002-9947-2011-05334-1/S0002-9947-2011-05334-1.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/tran/2011-363-09/S0002-9947-2011-05334-1/S0002-9947-2011-05334-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018497995","display_name":"Gang Bao","orcid":"https://orcid.org/0000-0003-1591-8095","observed_orcids":["https://orcid.org/0000-0003-1591-8095"]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gang Bao","raw_affiliation_strings":["Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027","Department of Mathematics Michigan , State University East Lansing , Michigan, 48824-1027"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Mathematics Michigan , State University East Lansing , Michigan, 48824-1027","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100457335","display_name":"Hai Feng Zhang","orcid":"https://orcid.org/0000-0002-5494-001X","observed_orcids":["https://orcid.org/0000-0002-5494-001X","https://orcid.org/0000-0001-9520-9840"]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hai Zhang","raw_affiliation_strings":["Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027","Department of Mathematics Michigan , State University East Lansing , Michigan, 48824-1027"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Mathematics Michigan , State University East Lansing , Michigan, 48824-1027","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090609331","display_name":"Jun Zou","orcid":"https://orcid.org/0000-0002-4809-7724","observed_orcids":["https://orcid.org/0000-0002-4809-7724"]},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jun Zou","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.387,"has_fulltext":true,"cited_by_count":43,"citation_normalized_percentile":{"value":0.9830237,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"363","issue":"9","first_page":"4527","last_page":"4551"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9897000193595886,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9897000193595886,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.0027000000700354576,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.002300000051036477,"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/global-uniqueness","display_name":"global uniqueness","score":0.8769999742507935},{"id":"https://openalex.org/keywords/diffraction-gratings","display_name":"diffraction gratings","score":0.8529999852180481},{"id":"https://openalex.org/keywords/electromagnetic-scattering","display_name":"electromagnetic scattering","score":0.6930000185966492},{"id":"https://openalex.org/keywords/inverse-scattering","display_name":"inverse scattering","score":0.6779999732971191},{"id":"https://openalex.org/keywords/incident-plane-wave","display_name":"incident plane wave","score":0.6330000162124634}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8388940095901489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6614145040512085},{"id":"https://openalex.org/C207114421","wikidata":"https://www.wikidata.org/wiki/Q133900","display_name":"Diffraction","level":2,"score":0.6041781902313232},{"id":"https://openalex.org/C2777813233","wikidata":"https://www.wikidata.org/wiki/Q1527816","display_name":"Grating","level":2,"score":0.552773118019104},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.523813784122467},{"id":"https://openalex.org/C40308292","wikidata":"https://www.wikidata.org/wiki/Q122518","display_name":"Plane wave","level":2,"score":0.5200369358062744},{"id":"https://openalex.org/C149773537","wikidata":"https://www.wikidata.org/wiki/Q12969754","display_name":"Electromagnetic radiation","level":2,"score":0.5199854969978333},{"id":"https://openalex.org/C28843909","wikidata":"https://www.wikidata.org/wiki/Q177625","display_name":"Electromagnetic field","level":2,"score":0.517820417881012},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4974541962146759},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44644638895988464},{"id":"https://openalex.org/C126753812","wikidata":"https://www.wikidata.org/wiki/Q653294","display_name":"Diffraction grating","level":3,"score":0.4202459156513214},{"id":"https://openalex.org/C120241303","wikidata":"https://www.wikidata.org/wiki/Q3503302","display_name":"Periodic sequence","level":2,"score":0.4172462224960327},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3052384555339813},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2847162187099457},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.2638634741306305},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24766656756401062},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0740087628364563}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0002-9947-2011-05334-1","doi":"https://doi.org/10.1090/s0002-9947-2011-05334-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-2011-05334-1","pdf_url":"https://www.ams.org/tran/2011-363-09/S0002-9947-2011-05334-1/S0002-9947-2011-05334-1.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-72175","doi":null,"is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-72175","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Article"},{"id":"pmh:oai:repository.ust.hk:1783.1-72175","doi":null,"is_oa":false,"landing_page_url":"http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=LinksAMR&SrcApp=PARTNER_APP&DestLinkType=FullRecord&DestApp=WOS&KeyUT=000293715700002","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1090/s0002-9947-2011-05334-1","doi":"https://doi.org/10.1090/s0002-9947-2011-05334-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-2011-05334-1","pdf_url":"https://www.ams.org/tran/2011-363-09/S0002-9947-2011-05334-1/S0002-9947-2011-05334-1.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G248631173","display_name":"FRG:  Collaborative Research:  Modeling, Computation, and Analysis of Optical Responses of Nano Structures","funder_award_id":"0968360","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2917864174","display_name":"Collaborative Research:    CMG --Quantifying Tectonic and Geomorphic Interpretations of Thermochronometer Data with Inverse Problem Theory","funder_award_id":"0724527","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4185194039","display_name":"Modeling, Analysis, and Computation of Diffractive and Nano Optics","funder_award_id":"0908325","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7385976626","display_name":"Direct and Inverse Modeling of Diffractive Optics and Near-Field Optics","funder_award_id":"0604790","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8147697595","display_name":"Gaussian Beam Methods for Large-Scale Computational Electromagnetics and Applications","funder_award_id":"0830161","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320324116","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2004308494.pdf","grobid_xml":"https://content.openalex.org/works/W2004308494.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1502426115","https://openalex.org/W1513869700","https://openalex.org/W1517670975","https://openalex.org/W1523113578","https://openalex.org/W1659382607","https://openalex.org/W1802820270","https://openalex.org/W1884845041","https://openalex.org/W1967181753","https://openalex.org/W1995254409","https://openalex.org/W1999354924","https://openalex.org/W2001288210","https://openalex.org/W2014293656","https://openalex.org/W2037113093","https://openalex.org/W2047851587","https://openalex.org/W2049692977","https://openalex.org/W2054682323","https://openalex.org/W2089343106","https://openalex.org/W2092645615","https://openalex.org/W2092705619","https://openalex.org/W2106714821","https://openalex.org/W2141545885","https://openalex.org/W2504091120","https://openalex.org/W2795407492","https://openalex.org/W2994782354","https://openalex.org/W4213260229","https://openalex.org/W4245054374","https://openalex.org/W4245515027","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2371210267","https://openalex.org/W2904350067","https://openalex.org/W2765848447","https://openalex.org/W1552218349","https://openalex.org/W4281806199","https://openalex.org/W332600388","https://openalex.org/W2243515400","https://openalex.org/W2261340125","https://openalex.org/W1551974663","https://openalex.org/W2532347373"],"abstract_inverted_index":{"This":[0],"work":[1],"is":[2,29,42,51,63],"concerned":[3],"with":[4],"the":[5,24,40,55,60,108,112,120],"unique":[6,121],"determination":[7,122],"of":[8,64,107,115,123],"a":[9,124],"periodic":[10,61,88,125],"diffraction":[11],"grating":[12],"profile":[13],"in":[14],"three":[15,82,109],"dimensions":[16],"by":[17,95],"some":[18],"scattered":[19],"electromagnetic":[20],"fields":[21],"measured":[22],"above":[23],"grating.":[25],"In":[26],"general,":[27],"it":[28,103],"well":[30],"known":[31],"that":[32,86],"global":[33,56],"uniqueness":[34,57],"may":[35],"not":[36],"be":[37,92,129],"true":[38],"when":[39,59],"measurement":[41],"only":[43,101],"taken":[44],"for":[45,119],"one":[46,96],"incident":[47,70,97,116],"field.":[48],"Our":[49],"goal":[50],"to":[52,68,76,105],"completely":[53],"characterize":[54],"properties":[58],"structure":[62,90,127],"polyhedral":[65,89,126],"type.":[66],"Corresponding":[67],"each":[69],"plane":[71],"wave,":[72],"we":[73],"are":[74],"able":[75],"classify":[77],"all":[78],"unidentifiable":[79],"structures":[80],"into":[81],"classes":[83],"and":[84,100],"show":[85],"any":[87],"can":[91,128],"uniquely":[93],"determined":[94],"field":[98],"if":[99,102],"belongs":[104],"none":[106],"classes.":[110],"Consequently,":[111],"minimum":[113],"number":[114],"waves":[117],"required":[118],"easily":[130],"read.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}
