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1、JOURNALOFMODERNOPTICS,1996,VOL.43,NO.6,1155-1166GeneralizedBessel-GaussbeamsV.BAGINIT,F.FREZZAS,M.SANTARSIEROt,G.SCHETTINIS,andG.SCHIRRIPASPAGNOLO8tDipartimentodiFisica,Universiti‘LaSapienza’,PiazzaleAldoMoro,5-00185Roma,Italy$DipartimentodiIngegneriaElettronica,Universiti‘LaS
2、apienza’,ViaEudossiana,18-00184Roma,ItalyDownloaded8UniversitidiL’Aquila.DipartimentodiEnergetica,LocalitiMontelucodiRoio,67040RoioPoggio,L’Aquila,Italy(Received23May1995;revisionreceived16October1995)By:[Abstract.InthispaperwedescribeasuperpositionmodelforBessel-GaussUniversi
3、tbeams,inwhichhigherordersareincluded.Ananalogousmodelleadstoadifferentclassofbeams,namelythemodifiedBessel-Gaussbeams.Thenageneralizedsetofbeams,containingthepreviousbeamsasparticularcases,isa'introduced.Thebehaviourofthesebeamsuponpropagationisinvestigated,deglibothanalytica
4、llyandnumerically.StudiRoma1.IntroductionBessel-Gaussbeamswereintroduced[13toovercomethedifficultiesofphysicalTre]realizationofdiffraction-freebeamsorBesselbeams[2-91,inwhichthedisturbanceAinatransverseplanevariedlikeaBesselfunctionofzeroorder.AGaussiant:11:modulationhadbeenad
5、dedsothatthesefieldsdonotcarryaninfiniteamountof11energy.Opticalmethodshavebeensuggested[lo,113togeneratepracticallya19Bessel-Gaussbeamofzeroorder.JanuaryWereviewinsection2howtheBessel-GaussbeamofzeroordermaybeviewedasacoherentsuperpositionofordinaryGaussianbeamshavingacommonw
6、aistplane,whoseaxesareuniformlydistributedonacone.Thiswaspointedoutin2007[l,103.Bessel-Gaussbeamsofhigherorderareobtainedwhenthesuperimposedbeamshaveamplitudesvaryingwiththeazimuthalangle.Insection3weconsideradifferentsetoffields,whichmaybegeneratedbysuperimposingordinaryGauss
7、ianbeamswhoseaxesareonacylinder.SinceinthiscasetheamplitudeoftheresultingdisturbanceinvolvesthemodifiedBesselfunctionsofthevariousorders,wecallthesefieldsmodifiedBessel-Gaussbeams.WeremarkthatthemodifiedBessel-Gaussbeamofzeroorderhasbeenrecentlyintroducedin[12].Insection4wesho
8、wthatallthepreviouscasesarecontainedinageneralizedsetoffields
