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1、2026OPTICSLETTERS/Vol.18,No.23/December1,1993Effectofbeamellipticityonself-modelockinginlasersRobertE.Bridges,RobertW.Boyd,andGovindP.AgrawalTheInstituteofOptics,UniversityofRochester,RiverCampus,WilmotBuilding,Rochester,NewYork14627ReceivedJune24,1993Inthecavityofaself-mode-locked
2、(Kerr-lensmode-locked)laser,anoncircularbeamexperiencesanonlinearcouplingbetweenbeamparametersinthexandyplanes.ThiscouplingproducesasignificantchangeinbeamradiithroughoutthecavityandmayresultinmorethanoneTEMOOcavitymode.ThedramaticnatureofthiseffectisdemonstratedwiththeTi:sapphirel
3、aserasanexample.Self-mode-lockingisacommonwayofgeneratingveryshortlaserpulses.12ItoccurswhenabeamAn=-n2=In22Pexp(-2--2Y8self-focusesandnarrowsasitpassesthroughanon-IT~w(22,TWX2wx2linearintracavitymaterial,thusexpandingorcon-tractingatotherlocationsofthelasercavity.3Since2P(b22y2AX
4、ln22X_(1)self-focusingisanintensity-dependentprocess,at7TW,Wyaxw,2ayWY2anypointinthecavityanintense(mode-locked)laserbeamhasadifferentsizefromaweak(cw)laserwhereI(x,y)isthebeamintensityandbeam.Ifcavityelementsarearrangedcorrectly,theP=ffI(x,y)dxdyisthebeampower.Ifwehigh-intensitybe
5、ammayexperiencelowerdiffractionsety=0inEq.(1),wefindthattheindexoflosses,e.g.,throughslitsoraroundprisms,thantherefractionatapointinthex-zplaneisdependentlow-intensitybeam.Thehigh-intensitybeammayonnotonlythebeamradiusinthexdirection(w,)alsoexperiencehighergainintheactivemediumbuta
6、lsoonthebeamradiusintheydirection(wy).throughbettermodematchingwiththepumpbeam.Thisistheoriginofthenonlinearx-ycoupling.TheseconditionstendtofavormodelockingovercwInrelation(1),theparametersa.,ay,andbareoperation.Inpractice,self-mode-lockingisusuallyfoundbyminimizationofthemean-squ
7、areerror.6initiatedbyamechanicalperturbation.Wefindthemean-squareerrorbysquaringthediffer-Intheliterature,researchershavepresentedvari-encebetweentheGaussianandquadraticfunctions,ousmethodsforcalculatingtheintensity-dependentweightingtheresultbytheGaussianfunction,andbeamradiiinala
8、sercavity,4-6butnoneofthes
