{"id":"https://openalex.org/W4287833489","doi":"https://doi.org/10.1007/s11082-022-03946-8","title":"Focusing properties and focal shift of vortex Hermite-cosh-Gaussian beams","display_name":"Focusing properties and focal shift of vortex Hermite-cosh-Gaussian beams","publication_year":2022,"publication_date":"2022-07-25","ids":{"openalex":"https://openalex.org/W4287833489","doi":"https://doi.org/10.1007/s11082-022-03946-8"},"language":"en","primary_location":{"id":"doi:10.1007/s11082-022-03946-8","doi":"https://doi.org/10.1007/s11082-022-03946-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11082-022-03946-8","pdf_url":null,"source":{"id":"https://openalex.org/S133811445","display_name":"Optical and Quantum Electronics","issn_l":"0306-8919","issn":["0306-8919","1572-817X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","poland-40","russia-white-list-2"],"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":"Optical and Quantum Electronics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.researchsquare.com/article/rs-423144/latest.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010256882","display_name":"Zoubir Hricha","orcid":"https://orcid.org/0000-0001-8029-3103","observed_orcids":["https://orcid.org/0000-0001-8029-3103"]},"institutions":[{"id":"https://openalex.org/I4210125507","display_name":"Chouaib Doukkali University","ror":"https://ror.org/036kgyt43","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210125507"]}],"countries":["MA"],"is_corresponding":true,"raw_author_name":"Z. Hricha","raw_affiliation_strings":["Laboratory LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Choua\u00efb Doukkali University, P. B 20, 24000, El Jadida, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Choua\u00efb Doukkali University, P. B 20, 24000, El Jadida, Morocco","institution_ids":["https://openalex.org/I4210125507"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007589638","display_name":"E. M. El Halba","orcid":"https://orcid.org/0000-0003-2272-6761","observed_orcids":["https://orcid.org/0000-0003-2272-6761"]},"institutions":[{"id":"https://openalex.org/I4210125507","display_name":"Chouaib Doukkali University","ror":"https://ror.org/036kgyt43","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210125507"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"E. M. El Halba","raw_affiliation_strings":["Laboratory LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Choua\u00efb Doukkali University, P. B 20, 24000, El Jadida, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Choua\u00efb Doukkali University, P. B 20, 24000, El Jadida, Morocco","institution_ids":["https://openalex.org/I4210125507"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034119119","display_name":"Abdelmajid Belafhal","orcid":"https://orcid.org/0000-0003-2735-3108","observed_orcids":["https://orcid.org/0000-0003-2735-3108"]},"institutions":[{"id":"https://openalex.org/I4210125507","display_name":"Chouaib Doukkali University","ror":"https://ror.org/036kgyt43","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210125507"]}],"countries":["MA"],"is_corresponding":true,"raw_author_name":"A. Belafhal","raw_affiliation_strings":["Laboratory LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Choua\u00efb Doukkali University, P. B 20, 24000, El Jadida, Morocco"],"raw_orcid":"https://orcid.org/0000-0003-2735-3108","affiliations":[{"raw_affiliation_string":"Laboratory LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Choua\u00efb Doukkali University, P. B 20, 24000, El Jadida, Morocco","institution_ids":["https://openalex.org/I4210125507"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010256882","https://openalex.org/A5034119119"],"corresponding_institution_ids":["https://openalex.org/I4210125507"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":null,"fwci":0.5843,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.54618879,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"54","issue":"9","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10490","display_name":"Orbital Angular Momentum in Optics","score":0.9994999766349792,"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/T10490","display_name":"Orbital Angular Momentum in Optics","score":0.9994999766349792,"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/T14158","display_name":"Optical Systems and Laser Technology","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11517","display_name":"Advanced optical system design","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/focal-shift","display_name":"focal shift","score":0.7350000143051147},{"id":"https://openalex.org/keywords/focusing-properties","display_name":"focusing properties","score":0.8009999990463257},{"id":"https://openalex.org/keywords/fresnel-number","display_name":"Fresnel number","score":0.828000009059906},{"id":"https://openalex.org/keywords/vortex-charge","display_name":"vortex charge","score":0.7630000114440918},{"id":"https://openalex.org/keywords/beam-spot-size","display_name":"beam spot size","score":0.7699999809265137},{"id":"https://openalex.org/keywords/huygens-fresnel-diffraction","display_name":"Huygens-Fresnel diffraction","score":0.8389999866485596},{"id":"https://openalex.org/keywords/beam-propagation","display_name":"beam propagation","score":0.6230000257492065},{"id":"https://openalex.org/keywords/beam-shaping","display_name":"beam shaping","score":0.7300000190734863},{"id":"https://openalex.org/keywords/optical-vortex","display_name":"optical vortices","score":0.5839999914169312}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7851319909095764},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.7055270671844482},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.6472035646438599},{"id":"https://openalex.org/C166453422","wikidata":"https://www.wikidata.org/wiki/Q1455717","display_name":"Fresnel number","level":3,"score":0.6391404271125793},{"id":"https://openalex.org/C207114421","wikidata":"https://www.wikidata.org/wiki/Q133900","display_name":"Diffraction","level":2,"score":0.6001068353652954},{"id":"https://openalex.org/C2778315978","wikidata":"https://www.wikidata.org/wiki/Q944873","display_name":"Gaussian beam","level":3,"score":0.5266470909118652},{"id":"https://openalex.org/C50282329","wikidata":"https://www.wikidata.org/wiki/Q2286895","display_name":"Fresnel diffraction","level":3,"score":0.49717476963996887},{"id":"https://openalex.org/C173781883","wikidata":"https://www.wikidata.org/wiki/Q850928","display_name":"M squared","level":5,"score":0.49151358008384705},{"id":"https://openalex.org/C119440689","wikidata":"https://www.wikidata.org/wiki/Q4876179","display_name":"Beam diameter","level":4,"score":0.4669561982154846},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4573819041252136},{"id":"https://openalex.org/C62172962","wikidata":"https://www.wikidata.org/wiki/Q1230543","display_name":"Beam divergence","level":5,"score":0.4411349892616272},{"id":"https://openalex.org/C82552819","wikidata":"https://www.wikidata.org/wiki/Q193540","display_name":"Focal length","level":3,"score":0.433838814496994},{"id":"https://openalex.org/C15336307","wikidata":"https://www.wikidata.org/wiki/Q1766051","display_name":"Lens (geology)","level":2,"score":0.34662920236587524},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17471861839294434},{"id":"https://openalex.org/C2984025587","wikidata":"https://www.wikidata.org/wiki/Q38867","display_name":"Laser beams","level":3,"score":0.11304619908332825},{"id":"https://openalex.org/C520434653","wikidata":"https://www.wikidata.org/wiki/Q38867","display_name":"Laser","level":2,"score":0.07618856430053711}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11082-022-03946-8","doi":"https://doi.org/10.1007/s11082-022-03946-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11082-022-03946-8","pdf_url":null,"source":{"id":"https://openalex.org/S133811445","display_name":"Optical and Quantum Electronics","issn_l":"0306-8919","issn":["0306-8919","1572-817X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","poland-40","russia-white-list-2"],"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":"Optical and Quantum Electronics","raw_type":"journal-article"},{"id":"doi:10.21203/rs.3.rs-423144/v1","doi":"https://doi.org/10.21203/rs.3.rs-423144/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-423144/v1","pdf_url":"https://www.researchsquare.com/article/rs-423144/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.21203/rs.3.rs-423144/v1","doi":"https://doi.org/10.21203/rs.3.rs-423144/v1","is_oa":true,"landing_page_url":"https://doi.org/10.21203/rs.3.rs-423144/v1","pdf_url":"https://www.researchsquare.com/article/rs-423144/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Square","raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4287833489.pdf","grobid_xml":"https://content.openalex.org/works/W4287833489.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1545182255","https://openalex.org/W1966566625","https://openalex.org/W1970512457","https://openalex.org/W1988421992","https://openalex.org/W1988694467","https://openalex.org/W2002581311","https://openalex.org/W2004373204","https://openalex.org/W2006759163","https://openalex.org/W2008610922","https://openalex.org/W2011425158","https://openalex.org/W2030113976","https://openalex.org/W2034135805","https://openalex.org/W2040068051","https://openalex.org/W2041868297","https://openalex.org/W2047045209","https://openalex.org/W2062802874","https://openalex.org/W2069911808","https://openalex.org/W2074703989","https://openalex.org/W2132491352","https://openalex.org/W2136049689","https://openalex.org/W2148318787","https://openalex.org/W2155469182","https://openalex.org/W2159501656","https://openalex.org/W2270509420","https://openalex.org/W2336309837","https://openalex.org/W2535305418","https://openalex.org/W2801213956","https://openalex.org/W2808159050","https://openalex.org/W3030225038","https://openalex.org/W3030734413","https://openalex.org/W3125518880","https://openalex.org/W3127897139","https://openalex.org/W3170311194","https://openalex.org/W3176186158","https://openalex.org/W3207094262","https://openalex.org/W4205234915","https://openalex.org/W4206992504","https://openalex.org/W4233886201","https://openalex.org/W4321264539"],"related_works":["https://openalex.org/W3170311194","https://openalex.org/W4283170980","https://openalex.org/W2155469182","https://openalex.org/W3125518880","https://openalex.org/W2358302203","https://openalex.org/W6991327687","https://openalex.org/W2041868297","https://openalex.org/W4311427265","https://openalex.org/W3173254094","https://openalex.org/W3030734413"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"work,":[3],"we":[4],"investigate":[5],"the":[6,28,40,45,48,51,57,61,64,69,74,84,91,101,104,107,116,124,134,140,144,156,175,178],"focusing":[7],"properties":[8],"of":[9,32,50,63,103,132,158,177],"a":[10,17,33,129],"vortex":[11,117,145],"Hermite-cosh-Gaussian":[12],"beam":[13,29,58,70,93,125,181,184],"(vHChGB)":[14],"passing":[15],"through":[16],"converging":[18],"lens":[19],"system.":[20],"The":[21,150,168],"analytical":[22],"propagation":[23],"equation":[24],"as":[25,27],"well":[26],"width":[30,95],"expression":[31],"focused":[34],"vHChGB":[35],"is":[36,81,88,97,112,137,148],"derived":[37],"based":[38],"on":[39,60],"Huygens-Fresnel":[41],"diffraction":[42],"principle.":[43],"From":[44],"obtained":[46,169],"formulae,":[47],"effects":[49],"Gaussian":[52],"Fresnel":[53,105,159],"number":[54,160],"NF":[55],"and":[56,68,110,120,183],"parameters":[59],"structure":[62],"light":[65],"intensity":[66],"distribution":[67],"spot":[71,94],"size":[72],"in":[73,180],"focal":[75,85,135,151],"region":[76],"are":[77],"analyzed":[78],"numerically.":[79],"It":[80],"shown":[82],"that":[83],"shift,":[86],"which":[87],"determined":[89],"from":[90],"minimum":[92],"criterion,":[96],"affected":[98],"strongly":[99],"by":[100,115],"change":[102],"number,":[106],"parameter":[108,141],"b,":[109],"it":[111,162],"slightly":[113],"altered":[114],"charge":[118,146],"M":[119,147],"nearly":[121],"insensitive":[122],"to":[123],"order":[126],"n.":[127],"For":[128],"fixed":[130],"value":[131],"NF,":[133],"shift":[136,152],"smaller":[138],"when":[139],"b":[142],"or":[143],"larger.":[149],"decreases":[153],"monotonously":[154],"with":[155],"increase":[157],"until":[161],"vanishes":[163],"asymptotically":[164],"for":[165,174],"large":[166],"NF.":[167],"results":[170],"may":[171],"be":[172],"useful":[173],"applications":[176],"vHChGBs":[179],"shaping":[182],"focusing.":[185]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2022-07-26T00:00:00"}