干涉自相关曲线

InterferometricAutocorrelationSimulatetheIntensityautocorrelation&interferogramofthePulseMeasurementintheTimeDomainTheE-homeworkforNovel-laser&ApplicationWangYing2.10131.101301.10132.101300.5116.2731014−×Ixt()0.521013−×2−1013−×tProblem：InputLaserPulse:UnchirpedGaussianPulse∆τp=50x10-15SimulatetheIntensityautocorrelation&interferogramintheMichelsonInterferometerusedforthePulseMeasurement()22ln2expFWHMptIxt⎡⎤⎛⎞⎢⎥=−⎜⎟⎜⎟∆τ⎢⎥⎝⎠⎣⎦Reference1.D.J.BRADLEYandGEOFFREYH.C.NEW,ProceedingsoftheIEEE,VoL.62,No.3,March19742.钟伟彬等，飞秒脉冲激光的测量与诊断，中山大学学报，Vol.40，No.5,20013.逯美红等，简易自相关仪对飞秒激光脉冲宽度的测量，大学物理，Vol.27，No.4,2008….函数相关自相关函数物理含义:两个信号之间的交迭程度(相关程度):两信号完全不交迭时积分为零；完全交迭时积分值最大；部分交迭时积分值介于零与最大值之间。*()()()Rststdtττ∞−∞=+∫Deviceprofile:DevelopedbyJ-CDiels2(2)2()[()()]∞−∞≡+−∫IAEtEtdtττ2(2)22()()()2()()∞−∞≡+−+−∫IAEtEtEtEtdtτττUsualAutocor-relationtermNewtermsAlsocalledthe“Fringe-ResolvedAutocorrelation”FilterSlowdetectorSHGcrystal()()+−EtEtτ2[()()]+−EtEtτLensBeam-splitterInputpulseDelayMirrorMirrorE(t)E(t–t)MichelsonInterferometerDielsandRudolph,UltrashortLaserPulsePhenomena,AcademicPress,1996.TheinputlightoftheinterferenceTheoutput:ThereceivedSHG:)]()([)]([)()()()(τϕτωϕωττ−+−+−=−=ttittietAtEetAtE22(,)()()(,)*[()()]EtEtEtEtdEtEtωωττττ=+−=+−SHG22()(,)*(,)2TTDIEtEtdtTωωτττ−=⋅∫Ifτismuchfastthentheresponseofthereceiver.Soallthecosineitemequal0244222222(){()()4()()24()()[()()]cos[()()]2()()cos2[()()]}TTDIdAtAtAtAtTAtAtAtAtttAtAtttdtτττττωτϕϕττωτϕϕτ−=+−+−+−+−+−−+−+−−∫44220(){()()4()()}−=+−+−∫TTIaAtAtAtAtdtτττ2044220404002(){()()4()()}0,(0)6(),()2()(0):()3:1TTTTTTDdaTIaAtAtAtAtdtIaAtdttITaAtdtIITτττττ−−−==+−+−====∫∫∫NodelayNocorrelationIntensitycorrelationfunctionSo,receivercangettheIntensitycorrelationcurvewiththecontrastof3:1GaussianPulseand3:1Intensitycorrelation(0):()3:1=IIT2.10131.101301.10132.10130.330.530.730.9310.331I1t()I10()0.521013−×2−1013−×tDoityourself244222222(){()()4()()24()()[()()]cos[()()]2()()cos2[()()]}TTDIdAtAtAtAtTAtAtAtAtttAtAtttdtτττττωτϕϕττωτϕϕτ−=+−+−+−+−+−−+−+−−∫Iftheresponseofthereceiverisfast.Sothecosineitemnotequalto024004000,(0)16()2,()2()(0):()8:1TTTTDdaIaAtdtTtITaAtdtIITττ−−=====∫∫(1)pnckλτ−=Iftheresponseofthereceiverisfast.Wecangetthecorrelationcurveof8:1,whichincludethephaseandprofileinformationofthepulse.2.10131.101301.10132.10131.9765.10172.10134.10136.10137.2741013−×0I2t()I1t()3.6371013−⋅21013−×2−1013−×tDoityourselfOutclasspracticerequirements1、小组合作；2、提交电子作业（以报告形式）；3、准备ppt宣讲；4、12月10日前完成；5、12月17日课堂宣讲