激光的参数描述和光束质量

*吕百达1,2,季小玲1,罗时荣1,陶向阳1,2(1.四川大学激光物理与化学研究所,四川成都610064;2.江西师范大学物理与通信电子学院,江西南昌330027):激光光束质量是一个很有现实意义的论题对实际激光,一方面或多或少存在硬边光阑光学元件影响另一方面,人们常对远场激光束的可聚焦能力感兴趣对有光阑情况时光束传输因子(M2因子)的推广作了讨论对有代表性的3种方法,即广义截断二阶矩法渐近分析法和自收敛束宽法及其应用作了分析引入了桶中功率(PIB)和B参数用以描述远场光束质量然后,研究了实际应用对激光光束质量的一些要求和相关的评价参数最后,讨论了复杂的高功率激光系统的全程光束质量控制问题:激光光束质量;参数描述;硬边光阑;光束传输因子;桶中功率:TN24:A:1007-2276(2004)01-0014-04Parametriccharacterizationoflaserbeamsandbeamquality*L&UBa-ida1,2,JIXiao-ling1,LUOSh-irong1,TAOXiang-yang1,2(1.InstituteofLaserPhysics&Chemistry,SichuanUniversity,Chengdu610064,China;2.CollegeofPhysics&CommunicationElectronics,JiangxiNormalUniversity,Nanchang330027,China)Abstract:Thelaserbeamqualityisatopicofcurrentinterest.Forareallaser,thereexistshard-aper-tureopticsmoreorless.Ontheotherhand,thepeopleareoftenconcernedaboutthefocusabilityoflaserbeamsinthefarfield.Theextensionofthebeampropagationfactor(M2factor)totheaperturedcaseisdis-cussed.Threetypicalapproachestotruncatedbeams,i.e.thegeneralizedtruncatedsecond-momentsmethod,asymptoticanalysisandsel-fconvergen-tbeam-widthmethod,aswellastheirapplicationsareanalyzed.Thepowerinthebucket(PIB)andB-parameterareusedtocharacterizethebeamqualityinthefarfield.Then,somepracticalrequirementsforthelaserbeamqualityandrelatedcharacteristicparametersarestudied.Fina-lly,abriefdiscussionaboutthebeamqualitycontrolofacomplicatedhigh-powerlasersystemasawholeismadeinthispaper.Keywords:Laserbeamquality;Parametriccharacterization;Hard-edgedaperture;Beampropagationfactor;Powerinthebucket:2003-08-20;:2003-10-17*:(A823070);(0212021):(1943-),,,,,,,300第33卷第1期红外与激光工程2004年2月Vol.33No.1InfraredandLaserEngineeringFeb.200402080,,,,M2,1Siegman(M2)[1],ABCD,M2,,,M2/0,,M2\1M2,,[2],M2/0,,M2,,,M2,M2(1)Martine-zHerrero[3]:,x2u2xu():x2=1I0Qa-ax2E(x)2dx(1)u2=1k2I0Qa-aEc(x)2dx+4k2I0a[E(a)2+E(-a)2](2)xu=12ikI0Qa-a{x[Ec(x)]*E(x)-xEc(x)E*(x)}dx(3)a;k;/c0x;*;I0,:I0=Qa-a|E(x)|2dx(4)M2,M2,[4](1)~(3)[5](2)Pare,f((6)),(),M2[5]:R2x=Qxc-xcx2|E(x,0)|2dxQxc-xc|E(x,0)|2dx(5)E(x,0)(z=0)xc:Qxc-xc|E(x,0)|2dx=fQa-a|E(x,0)|2dx(6)f:R2s=Qsc-scs2|E(s,0)|2dsQsc-sc|E(s,0)|2ds(7),Qsc-sc|E(s,0)|2ds=fQa-a|E(x,0)|2dx(8),M2:M2Q=4PR2xR2s(9)M2Q,f=100%,M2Qf,15第1期吕百达等:激光的参数描述和光束质量,M2Qf95%~99%,[5][6]M2Q,(3)Amarande[7],:R2x(z)=1pQxlim-xlimx2|E(x,z)|2dx(10)p=Qxlim-xlim|E(x,z)|2dxxlimR2xw(Fs):w(Fs)=2R2x(z)(11)xlim:xlim=Fsw(Fs)(12)Fs;w(Fs),[7]Fs,M2,,M2:w2(z)=w20+KM2sPw02(z-z0)2(13)w0,z0;K,,,M2,(fFs)[8],M212B,(PIB)[9]/0,:PIB=Qb-b|E(x,z)|2dxQ]-]|E(x,z)|2dx(14)E(x,z)(fz=f,z=zmax);b0[PIB[1,PIB,B,B:B=AmA0(15)Am,A0PIB=63%[10],BPIB,,,,B,M2,PIBB,,PIBBBPIB=63%(),M2,,B1[11]3M2(B),:(1)(),,()()B(2),GmPs(T|Gm|2)GmPs[12,13]:Gm=1P]Q]-]E(x)[E(x-D)exp(-ik8x)]*dx(16)Ps=1TQT0|Gm(t)|2dt(17)16红外与激光工程第33卷E(x),E(x-D)exp(-ik8x);D,8,P]=Q]-]|E(x)|2dx(3),,1)()G=Imax-Imin/Imax+Imin(18)Imax,IminG,2)F=€I/Imax(19)€IF,(4)$tK,:S=Kmin(t)Kmax(t)$t(20)Kmin(t),Kmax(t)$tS,(5),[14],4,,/0,,(),,(),(),,,,:[1]SiegmanAE.Newdevelopmentsinlaserresonators[A].SPIE[C].1990,1224.2-14.[2]WeberH.Somehistoricalandtechnicalaspectsofbeamquality[J].Opt&QuantElectron,1992,24(9):861-864.[3]Martinez-HerreroR,MejiasPM,AriasM.Parametriccharacterizationofcoherent,lowes-torderGaussianbeamspropagatingthroughhard-edgedapertures[J].OptLett,1995,20(2):124-126.[4]L™B,LuoS.GeneralizedM2factorofhigh-edgeddiffractedflattenedGaussianbeams[J].JOptSocAm(A),2001,18(9):2098-2101.[5]PareC,BelangerPA.Propagationlawandquas-iinvariancepropertiesofthetruncatedsecond-ordermomentofadiffractedbeam[J].OptCommun,1996,123.679-693.[6]L™B,LuoS.Asymptoticapproachtothetruncatedcosh-Gaussianbeams[J].Opt&QuantElectron,2001,33(2):107-113.[7]AmarandeS,GiesenA,H™gelH.Propagationanalysisofsel-fconver-gentbeamwidthandcharacterizationofhard-edgeddiffractedbeams[J].ApplOpt,2000,39(22):3914-3924.[8]L™B,QingY.Sel-fconvergentbeamwidthapproachtotruncatedHer-mite\|cosh-Gaussianbeamsandacomparisonwiththeasymptoticana-lysis[J].OptCommun,2001,199(1):25-31.[9]SiegmanAE.Howto(maybe)measurelaserbeamquality[A].OSATrendsinOpticsandPhotonicsSeries[C].1998,17.184-199.[10]GarayA.Continuouswavedeuteriumfluoridelaserbeamdiagnosticsystem[A].SPIE[C].1998,888.17-22.[11]L™B,JiX,LuoS.Thebeamqualityofannularlasersandrelatedproblems[J].JModOpt,2001,48(7):1171-1178.[12]MorinM,BernardP,GalarneauP.Momentdefinitionofthepointingstabilityofalaserbeam[J].OptLett,1994,19(18):1379-1381.[13]L™B,LuoS.ThepointingstabilityofflattenedGaussianbeams[J].JModOpt,2002,49(7):1089-1094.[14].[M].:,1999.17第1期吕百达等:激光的参数描述和光束质量