刀口法测量高斯光束光斑尺寸的重新认识-陆璇辉

32　3　　　　　　　　　　　　　　　Vol.32,No.3　20026　　　　　　　　　　　　　　LASER　&　INFRAREDJune,2002·光电技术·　　:1001-5078(2002)03-0186-02陆璇辉,陈许敏,张　蕾,薛大建(,,,310028)　:文中对刀口法测量高斯光束光斑直径时,通常多用能量比值86.5%所对应的位置作为光斑直径,但在一维测量情况下不能用这一数值,通过理论计算,导出了新的数值为95.4%。:高斯光束;刀口法;光斑半径:TN206　　　:ARe-cognitionofKnife-edgeMethodMeasuringtheSpotSizeofGaussianBeamLUXuan-hui,CHENXu-min,ZHANGLei,XUEDa-jian(StateKeyLab.ofModernOpticalInstrumentation,CentreforOptical&ElectromagneticResearchInstituteofOptics,ZhejiangUniversity,Hangzhou310028,China)Abstract:Inthepaper,theproportionoftheGaussianbeamspot'senergyinthewholebeamenergyisinvestigated.Theresultshowsthattheproportionis95.4%,not86.5%whenthespotsizeofGaussianbeamismeasuredbytheknife-edgemethod.Keywords:Gaussianbeam;knife-edgemethod;beamsize1　　,,。。M2,M2[1],,M2:M2=(1),,。,M2。M2:M2=πD0θ/4λ(2)(2)M2,D0θ。,、[2]CCD,,,;CCD,。,CCD,,。,。,。,,86.5%,。2　[3],:E(r,z)=Eoω0ωe-i[kz-Υ(z)]e-ikr2/q(3):I=E2=E20ω0ωe-2x2+y2ω2(x)=E20ω0ωe-2r2/ω2(x)(4):R(z)=z[1+kω202z2],　　:(1957-),,,,,70。:2002-01-22ω2(z)=ω20[1+2zkω202],ω0。ω=ωs,I=E20e-2r2/ω2s(5)ωs。1　,:f(r)=I=Ae-2r2/r20,A=E20,r0=ωsD0={(x,y)x∈R,y∈R}={(r,θ)0≤r≤+∞,0≤θ≤2π}D1={(x,y)x2+y2≤r20}={(r,θ)0≤r≤r0,0≤θ≤2π}D2={(x,y)r0≤r≤r0,y∈R},∫+∞0e-x2dx=π2S0=D0f(r)drdθ=∫2π0dθ∫+∞0Ae-2r2/r20rdr=πAr202(6),S1,S1=D1f(r)rdrdθ=πAr202(1-e-2)(7)I1=S1S0=1-e-2=86.466%,ωs86.466%。,。,y,x,r0※-r0,,1。1,:S2=D2f(x,y)dxdy=∫r0-r0dx∫+∞-∞Ae-2x2+y2r20dy=A∫r0-r0e-2xr2dx∫+∞-∞e-2yr02dy=Ar202∫r0-r0e-2xr02d2xr0∫+∞-∞e-2yr02d2yr0=Aπr20∫20e-x2dxx2=t2/2,x=t/2,:S2=Aπr20∫20e-t2/2dt/2=Aπr202×0.9544(8)I2=S2S0=95.44%.,95.44%,。,I=86.5%,r=ar0,a。S3=Ar202∫ar0-ar0e-2xr0d2xr0∫+∞-∞e-2yr02d2yr0=Aπr20∫02ae-x2dxx2=t2/2,x=t/2,:S3=Aπr20∫2a0e-t2/2dt/2=Aπ2r202π12π∫2a-∞e-t2/2dt-∫0-∞e-t2/2dt=Aπr2012π∫2a-∞e-t2/2dt-0.5I=S3S0=86.5%,(6)、(9):12π∫2a-∞e-t2/2dt=0.93252a=1.4946,a=0.7473,:r=0.7473r0=0.7473ωsI=86.5%,。3　　,86.5%,γ-γ0γ×100%=33.8%。,95.4%,86.5%。,,95.4%。86.5%。:[1]　AESiegman.DefiningandMeasuringLaserBeamQuali-ty,inSolid-stateLasers-NewDevelopmentsandApplica-tion[M].(M.InguscioandR.Wallensein,eds.)Plenum,NewYork,1993,13-28.[2]　HansRBilger,TaufiqHabib.Knife-edgescanningofanastigmaticGaussianbeam[J].appliedoptics,1985.24(5):686-690.[3]　HKogelnik,TLi.LaserBeamsandResonators[J].Ap-pl.Opt.1996.5:1550.1873