{"id":"https://openalex.org/W7213497658","doi":"https://doi.org/10.48550/arxiv.2609.18837","title":"From Multimode Near-Field Coupling to Friis","display_name":"From Multimode Near-Field Coupling to Friis","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213497658","doi":"https://doi.org/10.48550/arxiv.2609.18837"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.18837","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18837","pdf_url":"https://arxiv.org/pdf/2609.18837","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.18837","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105336920","display_name":"Mats Gustafsson","orcid":"https://orcid.org/0000-0003-4362-5716","observed_orcids":["https://orcid.org/0000-0003-4362-5716"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gustafsson, Mats","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5105336920"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10936","display_name":"Millimeter-Wave Propagation and Modeling","score":0.76419997215271,"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/T10936","display_name":"Millimeter-Wave Propagation and Modeling","score":0.76419997215271,"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/T10851","display_name":"Optical Wireless Communication Technologies","score":0.06589999794960022,"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/T11851","display_name":"Electromagnetic Compatibility and Measurements","score":0.06319999694824219,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/near-field-propagation","display_name":"near-field propagation","score":0.9620000123977661},{"id":"https://openalex.org/keywords/far-field-propagation","display_name":"far-field propagation","score":0.6830000281333923},{"id":"https://openalex.org/keywords/friis-transmission-formula","display_name":"Friis transmission formula","score":0.9070000052452087},{"id":"https://openalex.org/keywords/spatial-degrees-of-freedom","display_name":"spatial degrees of freedom","score":0.9179999828338623},{"id":"https://openalex.org/keywords/circular-aperture","display_name":"circular aperture","score":0.8629999756813049}],"concepts":[{"id":"https://openalex.org/C56034020","wikidata":"https://www.wikidata.org/wiki/Q1071734","display_name":"Paraxial approximation","level":3,"score":0.5637000203132629},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5321000218391418},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.5026000142097473},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.49939998984336853},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.47929999232292175},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.4546999931335449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45019999146461487},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.43470001220703125},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.41119998693466187},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.41040000319480896},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.3968000113964081},{"id":"https://openalex.org/C185254563","wikidata":"https://www.wikidata.org/wiki/Q6888105","display_name":"Mode coupling","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C78336883","wikidata":"https://www.wikidata.org/wiki/Q4779385","display_name":"Aperture (computer memory)","level":2,"score":0.36000001430511475},{"id":"https://openalex.org/C101645829","wikidata":"https://www.wikidata.org/wiki/Q1781857","display_name":"Multi-mode optical fiber","level":3,"score":0.3449000120162964},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2928999960422516},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C150060386","wikidata":"https://www.wikidata.org/wiki/Q7574054","display_name":"Spatial correlation","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.2547999918460846},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.18837","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18837","pdf_url":"https://arxiv.org/pdf/2609.18837","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2609.18837","doi":"https://doi.org/10.48550/arxiv.2609.18837","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.18837","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.18837","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18837","pdf_url":"https://arxiv.org/pdf/2609.18837","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213497658.pdf","grobid_xml":"https://content.openalex.org/works/W7213497658.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W7131654269","https://openalex.org/W7147189037","https://openalex.org/W7165365428"],"related_works":["https://openalex.org/W7139106585","https://openalex.org/W4414165603","https://openalex.org/W7213458902","https://openalex.org/W7131654269","https://openalex.org/W3194986986","https://openalex.org/W7130378464","https://openalex.org/W4408697706","https://openalex.org/W2769781136","https://openalex.org/W7166902045","https://openalex.org/W4405968041"],"abstract_inverted_index":{"Near-field":[0],"propagation":[1],"between":[2,29,38],"finite":[3],"apertures":[4,135],"can":[5],"support":[6],"multiple":[7],"spatial":[8,52,100],"channels,":[9],"while":[10,102],"far-field":[11],"transmission":[12,21,129],"is":[13],"effectively":[14,78],"single":[15],"mode":[16],"and":[17,41,144,150],"follows":[18],"the":[19,34,39,48,58,73,96,111,113,120,127,137,139,145,148,158,161],"Friis":[20,128],"formula.":[22,130],"This":[23],"letter":[24],"establishes":[25],"a":[26,63,69],"direct":[27],"connection":[28],"these":[30],"two":[31],"regimes":[32],"through":[33],"mutual":[35,45],"shadow":[36,46],"area":[37],"transmitting":[40],"receiving":[42],"apertures.":[43,152],"The":[44,81,153],"determines":[47],"asymptotic":[49],"number":[50,97],"of":[51,54,98],"degrees":[53],"freedom":[55],"and,":[56],"in":[57],"paraxial":[59,162],"regime,":[60],"leads":[61],"to":[62,77,119],"simple":[64],"beamforming":[65],"distance":[66],"that":[67],"provides":[68],"characteristic":[70],"scale":[71],"for":[72,133],"transition":[74],"from":[75],"multimode":[76],"single-mode":[79],"propagation.":[80],"channel":[82,115],"singular-value":[83],"sum":[84],"rule":[85],"further":[86],"shows":[87],"that,":[88],"below":[89],"this":[90],"distance,":[91],"increasing":[92],"separation":[93],"primarily":[94],"reduces":[95],"supported":[99],"channels":[101],"their":[103],"average":[104],"normalized":[105],"strength":[106,116],"remains":[107],"approximately":[108],"constant.":[109],"Beyond":[110],"transition,":[112,138],"remaining":[114],"decreases":[117],"according":[118],"conventional":[121],"free-space":[122],"quadratic":[123],"power":[124],"law,":[125],"recovering":[126],"Numerical":[131],"results":[132],"circular":[134],"demonstrate":[136],"scaling":[140],"with":[141],"aperture":[142],"size,":[143],"dependence":[146],"on":[147],"transmitter":[149],"receiver":[151],"mutual-shadow":[154],"formulation":[155],"also":[156],"extends":[157],"description":[159],"beyond":[160],"regime.":[163]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-18T00:00:00"}