{"id":"https://openalex.org/W1978360373","doi":"https://doi.org/10.1615/telecomradeng.v63.i9.30","title":"Band Structure Analysis of 1D and 2D Photonic Crystals by Coupled Wave Method","display_name":"Band Structure Analysis of 1D and 2D Photonic Crystals by Coupled Wave Method","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1978360373","doi":"https://doi.org/10.1615/telecomradeng.v63.i9.30","mag":"1978360373"},"language":"en","primary_location":{"id":"doi:10.1615/telecomradeng.v63.i9.30","doi":"https://doi.org/10.1615/telecomradeng.v63.i9.30","is_oa":false,"landing_page_url":"https://doi.org/10.1615/telecomradeng.v63.i9.30","pdf_url":null,"source":{"id":"https://openalex.org/S58266129","display_name":"Telecommunications and Radio Engineering","issn_l":"0040-2508","issn":["0040-2508","1943-6009"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310315730","host_organization_name":"Begell House","host_organization_lineage":["https://openalex.org/P4310315730"],"host_organization_lineage_names":["Begell House"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Telecommunications and Radio Engineering","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"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/A5086650566","display_name":"V. M. Fityo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"V. M. Fityo","raw_affiliation_strings":["Lviv Polytechnic National University 12 Stepan Bandera Str, Lviv, 79013, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lviv Polytechnic National University 12 Stepan Bandera Str, Lviv, 79013, Ukraine","institution_ids":["https://openalex.org/I98435010"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077203246","display_name":"Ya. V. Bobytskiy","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]},{"id":"https://openalex.org/I98559091","display_name":"University of Rzesz\u00f3w","ror":"https://ror.org/03pfsnq21","country_code":"PL","type":"education","lineage":["https://openalex.org/I98559091"]}],"countries":["PL","UA"],"is_corresponding":false,"raw_author_name":"Ya. V. Bobytskiy","raw_affiliation_strings":["Lviv Polytechnic National University,  Ukraine; and Institute of Technology, University of Rzeszow, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lviv Polytechnic National University,  Ukraine; and Institute of Technology, University of Rzeszow, Poland","institution_ids":["https://openalex.org/I98435010","https://openalex.org/I98559091"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022695853","display_name":"H. P. Laba","orcid":"https://orcid.org/0000-0002-8549-9036","observed_orcids":["https://orcid.org/0000-0002-8549-9036"]},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"H. P. Laba","raw_affiliation_strings":["Lviv Polytechnic National University, 12 St. Bandera Str., Lviv, 79013, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lviv Polytechnic National University, 12 St. Bandera Str., Lviv, 79013, Ukraine","institution_ids":["https://openalex.org/I98435010"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"9","first_page":"795","last_page":"813"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10666","display_name":"Photonic Crystals and Applications","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/T10666","display_name":"Photonic Crystals and Applications","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/T10245","display_name":"Metamaterials and Metasurfaces Applications","score":0.000699999975040555,"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"}},{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":9.999999747378752e-05,"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/photonic-crystals","display_name":"photonic crystals","score":0.9490000009536743},{"id":"https://openalex.org/keywords/band-structure","display_name":"electronic band structure","score":0.8069999814033508},{"id":"https://openalex.org/keywords/coupled-wave-method","display_name":"coupled-wave method","score":0.984000027179718},{"id":"https://openalex.org/keywords/one-dimensional-photonic-crystals","display_name":"one-dimensional photonic crystals","score":0.8610000014305115},{"id":"https://openalex.org/keywords/two-dimensional-photonic-crystals","display_name":"two-dimensional photonic crystals","score":1.0},{"id":"https://openalex.org/keywords/t-algorithm","display_name":"T-algorithm","score":0.7459999918937683},{"id":"https://openalex.org/keywords/eigenvalue-problem","display_name":"eigenvalue problem","score":0.8889999985694885},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"periodic boundary conditions","score":0.8140000104904175},{"id":"https://openalex.org/keywords/plane-wave-decomposition","display_name":"plane wave decomposition","score":0.6179999709129333}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7876091003417969},{"id":"https://openalex.org/C75302062","wikidata":"https://www.wikidata.org/wiki/Q900150","display_name":"Photonic crystal","level":2,"score":0.7246800661087036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5621170997619629},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.49951767921447754},{"id":"https://openalex.org/C40308292","wikidata":"https://www.wikidata.org/wiki/Q122518","display_name":"Plane wave","level":2,"score":0.4913462698459625},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47771191596984863},{"id":"https://openalex.org/C115827552","wikidata":"https://www.wikidata.org/wiki/Q3333626","display_name":"Plane wave expansion method","level":3,"score":0.4713275730609894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46030381321907043},{"id":"https://openalex.org/C16291881","wikidata":"https://www.wikidata.org/wiki/Q917246","display_name":"Brillouin zone","level":2,"score":0.4278002977371216},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40989744663238525},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.3026537001132965},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1862524151802063},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.07816165685653687},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1615/telecomradeng.v63.i9.30","doi":"https://doi.org/10.1615/telecomradeng.v63.i9.30","is_oa":false,"landing_page_url":"https://doi.org/10.1615/telecomradeng.v63.i9.30","pdf_url":null,"source":{"id":"https://openalex.org/S58266129","display_name":"Telecommunications and Radio Engineering","issn_l":"0040-2508","issn":["0040-2508","1943-6009"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310315730","host_organization_name":"Begell House","host_organization_lineage":["https://openalex.org/P4310315730"],"host_organization_lineage_names":["Begell House"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Telecommunications and Radio Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1973061124","https://openalex.org/W2047633079","https://openalex.org/W1053412870","https://openalex.org/W2118954834","https://openalex.org/W1980199369","https://openalex.org/W2358793845","https://openalex.org/W2028130441","https://openalex.org/W2042462545","https://openalex.org/W2139161129","https://openalex.org/W1980260827"],"abstract_inverted_index":{"The":[0,26,95,159,170,194,233,283,323,340],"electromagnetic":[1],"field":[2],"of":[3,19,21,28,30,47,51,65,73,86,93,98,100,116,140,152,162,173,180,183,201,213,225,236,238,247,253,267,279,289,305,312,314,319,325,328,334,342,348],"wave":[4,36,109,226],"that":[5,89],"propagates":[6],"in":[7,15,38,132,293],"the":[8,16,31,39,52,60,66,83,101,107,113,134,137,146,149,181,184,198,207,210,245,268,276,290,294,300,306,310,335,346,349],"crystal":[9,23,333],"is":[10,43,79,104,122,155,166,188,216,258,264,281,297,321],"decomposed":[11],"into":[12,75],"plane":[13,76],"waves":[14,77,351],"classic":[17,307],"method":[18,97,110,121,296,308],"computation":[20],"photonic":[22,127,192,230,332],"band":[24,326],"structure.":[25],"problem":[27,139,172,200,235],"finding":[29,46,64,133],"allowed":[32,67,102],"frequencies":[33,103],"for":[34,59,63,125,190,228],"a":[35,178,265],"vector":[37,227],"first":[40],"Brillouin":[41],"zone":[42],"reduced":[44],"to":[45,70,81,136,157,197,244,299,356],"eigenvalues":[48],"and":[49,129,145,206,222,256,330],"eigenvectors":[50],"corresponding":[53,114],"dimensional":[54,160,284],"representation":[55,161,252,285],"matrix,":[56],"which":[57,187],"provides":[58],"required":[61],"precision":[62],"frequencies.":[68],"Due":[69],"slow":[71],"convergence":[72],"decomposition":[74],"it":[78,130],"necessary":[80],"solve":[82],"matrix":[84,164,291],"equation":[85,292],"large":[87],"dimension":[88,301],"requires":[90],"considerable":[91],"time":[92],"calculation.":[94],"suggested":[96,295],"determination":[99],"based":[105],"on":[106],"coupled":[108,269,350],"(CWM)":[111],"at":[112,218],"setting":[115],"periodic":[117],"boundary":[118],"conditions.":[119],"This":[120],"especially":[123],"simple":[124],"1D":[126,191,329],"crystals":[128],"consists":[131],"solution":[135,195],"eigenvalue":[138,153,171,199,214,234,280],"TX":[141,202,239],"=":[142,203,240],"\u03c1X":[143],"type":[144,175,205,237],"check-up":[147,208],"whether":[148,209],"absolute":[150,211,277],"value":[151,212,278],"p":[154],"equal":[156],"one.":[158,282],"quadratic":[163],"T":[165,255],"2":[167],"\u00d7":[168,260,287,303],"2.":[169],"this":[174],"appears":[176],"as":[177],"result":[179],"application":[182,246],"so-called":[185],"T-algorithm,":[186],"stable":[189,248],"crystal.":[193],"leads":[196],"\u03c1RX":[204,241],"\u03c1":[215],"one":[217],"given":[219],"frequency":[220],"v":[221],"component":[223],"kx":[224],"2D":[229,331],"crystals,":[231],"too.":[232],"arises":[242],"due":[243],"numerical":[249],"S-algorithm.":[250],"Dimensional":[251],"matrices":[254],"R":[257],"2N":[259,286,288],"2N,":[261],"where":[262],"N":[263],"number":[266,347],"waves.":[270],"Frequency":[271],"will":[272],"be":[273],"allowed,":[274],"if":[275],"equivalent":[298],"N2":[302,304],"from":[309,354],"point":[311],"view":[313],"calculation":[315,320,343],"accuracy.":[316],"Stable":[317],"S-algorithm":[318],"developed.":[322],"calculations":[324],"structure":[327],"simplest":[336],"form":[337],"are":[338,358],"performed.":[339],"dependencies":[341],"accuracy":[344],"upon":[345],"(N":[352],"varies":[353],"1":[355],"29)":[357],"obtained.":[359]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
