{"id":"https://openalex.org/W1977726596","doi":"https://doi.org/10.1155/1998/81752","title":"Theory and Modeling of Lasing Modes in Vertical Cavity Surface Emitting Lasers","display_name":"Theory and Modeling of Lasing Modes in Vertical Cavity Surface Emitting Lasers","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1977726596","doi":"https://doi.org/10.1155/1998/81752","mag":"1977726596"},"language":"en","primary_location":{"id":"doi:10.1155/1998/81752","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1998/81752","pdf_url":"https://downloads.hindawi.com/archive/1998/081752.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/archive/1998/081752.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063432335","display_name":"Benjamin Klein","orcid":"https://orcid.org/0000-0002-8583-2716"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Benjamin Klein","raw_affiliation_strings":["Beckma Institute and Coordinated Science Laboratory, University of lllinois at Urbana-Champaign, Urbana, Illinois 6180, USA"],"affiliations":[{"raw_affiliation_string":"Beckma Institute and Coordinated Science Laboratory, University of lllinois at Urbana-Champaign, Urbana, Illinois 6180, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064689433","display_name":"Leonard F. Register","orcid":"https://orcid.org/0000-0001-5023-0953"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leonard F. Register","raw_affiliation_strings":["Beckma Institute and Coordinated Science Laboratory, University of lllinois at Urbana-Champaign, Urbana, Illinois 6180, USA"],"affiliations":[{"raw_affiliation_string":"Beckma Institute and Coordinated Science Laboratory, University of lllinois at Urbana-Champaign, Urbana, Illinois 6180, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035982092","display_name":"K. Hess","orcid":"https://orcid.org/0000-0002-7145-8735"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Karl Hess","raw_affiliation_strings":["Beckma Institute and Coordinated Science Laboratory, University of lllinois at Urbana-Champaign, Urbana, Illinois 6180, USA"],"affiliations":[{"raw_affiliation_string":"Beckma Institute and Coordinated Science Laboratory, University of lllinois at Urbana-Champaign, Urbana, Illinois 6180, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072739006","display_name":"D.G. Deppe","orcid":null},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dennis Deppe","raw_affiliation_strings":["Microelectronics Center, Department of Eledtrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78712-1084, USA"],"affiliations":[{"raw_affiliation_string":"Microelectronics Center, Department of Eledtrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78712-1084, USA","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063432335"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.5695,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.80636336,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"1-4","first_page":"87","last_page":"91"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11429","display_name":"Semiconductor Lasers and Optical Devices","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11429","display_name":"Semiconductor Lasers and Optical Devices","score":0.9998999834060669,"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/T10299","display_name":"Photonic and Optical Devices","score":0.9976999759674072,"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/T10666","display_name":"Photonic Crystals and Applications","score":0.9945999979972839,"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/lasing-threshold","display_name":"Lasing threshold","score":0.9632478952407837},{"id":"https://openalex.org/keywords/laser","display_name":"Laser","score":0.6968622207641602},{"id":"https://openalex.org/keywords/gain-switching","display_name":"Gain-switching","score":0.6261272430419922},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6195515394210815},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.49258071184158325},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.48568519949913025},{"id":"https://openalex.org/keywords/optoelectronics","display_name":"Optoelectronics","score":0.43903839588165283},{"id":"https://openalex.org/keywords/semiconductor-laser-theory","display_name":"Semiconductor laser theory","score":0.43807607889175415},{"id":"https://openalex.org/keywords/vertical-cavity-surface-emitting-laser","display_name":"Vertical-cavity surface-emitting laser","score":0.4254492521286011},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.42166927456855774},{"id":"https://openalex.org/keywords/gain","display_name":"Gain","score":0.4212111830711365},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.41041862964630127},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3904651999473572},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.37803250551223755},{"id":"https://openalex.org/keywords/active-laser-medium","display_name":"Active laser medium","score":0.3111884593963623},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.257533997297287},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1971263587474823},{"id":"https://openalex.org/keywords/laser-power-scaling","display_name":"Laser power scaling","score":0.12796124815940857},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07903754711151123}],"concepts":[{"id":"https://openalex.org/C40637687","wikidata":"https://www.wikidata.org/wiki/Q676237","display_name":"Lasing threshold","level":3,"score":0.9632478952407837},{"id":"https://openalex.org/C520434653","wikidata":"https://www.wikidata.org/wiki/Q38867","display_name":"Laser","level":2,"score":0.6968622207641602},{"id":"https://openalex.org/C170931432","wikidata":"https://www.wikidata.org/wiki/Q5517204","display_name":"Gain-switching","level":4,"score":0.6261272430419922},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6195515394210815},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.49258071184158325},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.48568519949913025},{"id":"https://openalex.org/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","level":1,"score":0.43903839588165283},{"id":"https://openalex.org/C121477167","wikidata":"https://www.wikidata.org/wiki/Q17154002","display_name":"Semiconductor laser theory","level":3,"score":0.43807607889175415},{"id":"https://openalex.org/C106246969","wikidata":"https://www.wikidata.org/wiki/Q2009618","display_name":"Vertical-cavity surface-emitting laser","level":3,"score":0.4254492521286011},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.42166927456855774},{"id":"https://openalex.org/C166566249","wikidata":"https://www.wikidata.org/wiki/Q5517209","display_name":"Gain","level":5,"score":0.4212111830711365},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.41041862964630127},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3904651999473572},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.37803250551223755},{"id":"https://openalex.org/C28745240","wikidata":"https://www.wikidata.org/wiki/Q1806565","display_name":"Active laser medium","level":4,"score":0.3111884593963623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.257533997297287},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1971263587474823},{"id":"https://openalex.org/C200649887","wikidata":"https://www.wikidata.org/wiki/Q17154544","display_name":"Laser power scaling","level":3,"score":0.12796124815940857},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07903754711151123}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1155/1998/81752","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1998/81752","pdf_url":"https://downloads.hindawi.com/archive/1998/081752.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1155/1998/81752","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1998/81752","pdf_url":"https://downloads.hindawi.com/archive/1998/081752.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"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/W1977726596.pdf","grobid_xml":"https://content.openalex.org/works/W1977726596.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1524573041","https://openalex.org/W1552845478"],"related_works":["https://openalex.org/W1562910892","https://openalex.org/W2549058413","https://openalex.org/W2121894807","https://openalex.org/W2062939752","https://openalex.org/W1566491118","https://openalex.org/W2154440099","https://openalex.org/W2266141150","https://openalex.org/W2062303493","https://openalex.org/W2122130792","https://openalex.org/W4321520950"],"abstract_inverted_index":{"The":[0,43,55],"problem":[1,24],"of":[2],"obtaining":[3],"the":[4,62,71,75,84,88],"lasing":[5,57],"modes":[6,60],"and":[7,29,34,59,81],"corresponding":[8,30],"threshold":[9],"conditions":[10,52],"for":[11,53,74],"vertical":[12],"cavity":[13],"surface":[14],"emitting":[15],"lasers":[16],"(VCSELs)":[17],"is":[18],"formulated":[19],"as":[20],"a":[21],"frequency-dependent":[22],"eigenvalue":[23],"in":[25,78],"required":[26],"gain":[27,35,45,72,85],"amplitudes":[28],"fields.":[31],"Both":[32],"index":[33],"guiding":[36],"are":[37,66,93],"treated":[38],"on":[39],"an":[40],"equal":[41],"footing.":[42],"complex":[44],"eigenvalues":[46],"define":[47],"necessary":[48,73],"but":[49],"not":[50],"sufficient":[51],"lasing.":[54],"actual":[56],"frequencies":[58],"that":[61],"VCSEL":[63],"can":[64],"support":[65],"then":[67],"determined":[68],"by":[69],"matching":[70],"optical":[76],"system":[77],"both":[79],"magnitude":[80],"phase":[82],"to":[83],"available":[86],"from":[87],"laser\u2032s":[89],"electronic":[90],"system.":[91],"Examples":[92],"provided.":[94]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
