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1、1612J.Opt.Soc.Am.A/Vol.18,No.7/July2001FrancoGoriPolarizationbasisforvortexbeamsFrancoGoriDipartimentodiFisica,UniversitaÁdegliStudiRomaTre,andIstitutoNazionaleperlaFisicadellaMateria,ViadellaVascaNavale84,I-00146Rome,ItalyReceivedSeptember6,2000;revised
2、manuscriptreceivedJanuary31,2001;acceptedFebruary1,2001AttentioniscalledtoapolarizationbasisformedbyfourJonesvectorsthatisreducibletotwobasicstructures.Inthesestatesthe®eldislinearlypolarizedatanypoint,butthepolarizationdirectionchangeswiththean-gularcoo
3、rdinate.Verysimpleequationsholdforthe®eldlinesofthesebasisvectors.Theadoptionofthisbasisisofinterestforbeamspossessingasinglevortexofanyorder,say,m,aswellasforbeamswithtwovorticesofoppositecharges,mand2m.Asanexample,theapplicationtovectorialBessel±Gaussb
4、eamsisbrie¯ydiscussed.©2001OpticalSocietyofAmericaOCIScodes:260.5430,350.5500.1.INTRODUCTIONisthatthecorrespondingpolarizationpatternsarequitesimpleandelegant.Theequationsofthe®eldlinescanThevectorialpropertiesofnonuniformlypolarizedbeamseasilybederiveda
5、ndspecifycurvesthatarewellknownintheparaxialregimehaverevealedsigni®cantfeaturesfromgeometry.sincetheadventoflasers.Inrecenttimes,interestinAsfortheintensitydistribution,thefourbasisstatesthissubjecthasbeengrowing,andseveralvectorialtreat-arecircularlysy
6、mmetric.Thecaseofm51deservesmentshavebeenpresentedinboththecoherent(see,forspecialmention.Itincludesasparticularcasestheazi-example,Refs.1±6)andthepartiallycoherent(see,formuthalandtheradialpolarizationswithacontinuousexample,Refs.7±12)cases.passagefromo
7、netotheotherthroughintermediateThesimplestapproachtostudyingarbitrarilypolarizedstatesofpolarizationinwhichthe®eldlineshavethebeamsistodecomposetherepresentative®eldvector(ei-formofspirals.Itfurtherisseenthat,exceptformtherelectricormagnetic)atanypointof
8、asectionintoor-51,twoofthebasisstatesaresimplyrotatedversionsofthogonallinearlypolarizedparts.Free-propagationtheothertwo.problemscanthenbetreatedasapairofscalarproblems.Foranyofthefourbasispolarizationstates,and,in-Thesam
