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1、JOURNALOFTHEOPTICALSOCIETYOFAMERICAVOLUME62,NUMBER10OCTOBER1972ElectromagneticFieldofaGaussianBeamwithanEllipticalCrossSectionWILLIAMH.CARTERNavalResearchLaboratory,Washington,D.C.20390(Received28April1972)Theelectromagneticfieldassociatedwithageneralizedbeamisanalyzedtheoreticall
2、y,wherethebeammaytakeonanirradiancecrosssectiondescribedbyagaussianfunctionwitharbitraryellipticalsymmetry.Forthisanalysis,thefieldisrepresentedbyanexpansionintoanangularspectrumofplanewaves.Ex-pressionsforthefieldcomponentsthroughoutamediumthatisfreeofsourcesarefoundbyuseofanasym
3、p-toticapproximationthatiscommoningaussian-beamanalysis.Inaddition,more-preciseexpressionsforthesecomponentsarefound,whicharevalidoutsidetheneighborhoodoffocus.Nearfocus,gaussianbeamsmayhaveonlyapproximatelygaussiancrosssections,andinthisregionthebehaviorofbeamswithoutcircularsymm
4、etryisgreatlycomplicated.Theeffectsofnoncircularsymmetryarediscussedinsomedetail,andamethodforcorrectingabeamtoproducecircularsymmetryisdescribed.INDEXHEADINGS:Laser;Radiation.Lasers,whenoscillatinginthegenerallypreferredcircularsymmetry.Thenearfieldaboutfocusisnotlowest-ordermode
5、,producebeamsofnearlymono-welldefinedexceptforcircularbeams.Underalimitingchromaticlightwhichexhibitanapproximatelycondition,thegaussianfieldevolvesintoamagnetic-gaussianirradiancedistributionoveranycrosssectiondipolefieldawayfromfocus.Amethodforcorrectingnormaltothedirectionofpro
6、pagation.Almostallanarbitraryellipticalcrosssectiontoproduceacon-lasersproducegaussianbeamswithcircularsymmetryventionalcirculargaussianbeamisdescribed.aboutthebeamaxis.Thisisnotaninherentpropertyofgaussianbeams,however,butresultsfromtheCOMPONENTSOFTHEELECTROMAGNETICcircularsymmet
7、ryoflasers.ThefieldsassociatedwithFIELDsuchcirculargaussianbeamshavebeenstudiedWeareconcernedherewiththeelectromagneticextensively.'fieldduetoamonochromaticbeamofradiationsimilarMorerecently,opticalsecond-harmonicgeneratorstothatproducedbyalaseroscillatinginitslowest-orderandparam
8、etricoscillatorshavebeendeveloped
