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1、UltrashortLaserPulsesIDescriptionofpulsesIntensityandphaseTheinstantaneousfrequencyandgroupdelayZerothandfirst-orderphaseThelinearlychirpedGaussianpulseProf.RickTrebinoGeorgiaTechwww.frog.gatech.eduAnultrashortlaserpulsehasanintensityandphasevs.time.Neglectingthespatialdependencefornow,the
2、pulseelectricfieldisgivenby:IntensityPhaseCarrierfrequencyAsharplypeakedfunctionfortheintensityyieldsanultrashortpulse.Thephasetellsusthecolorevolutionofthepulseintime.ElectricfieldE(t)Time[fs]TherealandcomplexpulseamplitudesRemovingthe1/2,thec.c.,andtheexponentialfactorwiththecarrierfrequ
3、encyyieldsthecomplexamplitude,E(t),ofthepulse:Thisremovestherapidlyvaryingpartofthepulseelectricfieldandyieldsacomplexquantity,whichisactuallyeasiertocalculatewith.isoftencalledtherealamplitude,A(t),ofthepulse.ElectricfieldE(t)Time[fs]TheGaussianpulsewheretHW1/eisthefieldhalf-width-half-ma
4、ximum,andtFWHMistheintensityfull-width-half-maximum.Theintensityis:Foralmostallcalculations,agoodfirstapproximationforanyultrashortpulseistheGaussianpulse(withzerophase).Intensityvs.amplitudeTheintensityofaGaussianpulseis√2shorterthanitsrealamplitude.Thisfactorvariesfrompulseshapetopulsesh
5、ape.Thephaseofthispulseisconstant,(t)=0,andisnotplotted.It’seasytogobackandforthbetweentheelectricfieldandtheintensityandphase:Theintensity:Calculatingtheintensityandthephasef(t)=-Im{ln[E(t)]}Thephase:Equivalently,-f(ti)ReImE(ti)√I(ti)I(t)=
6、E(t)
7、2Also,we’llstopwriting“proportionalto”inthe
8、seexpressionsandtakeE,E,I,andStobethefield,intensity,andspectrumdimensionlessshapesvs.time.TheFourierTransformTothinkaboutultrashortlaserpulses,theFourierTransformisessential.WealwaysperformFouriertransformsontherealorcomplexpulseelectricfield,andnottheintensity,unlessotherwisespecified.Th
9、efrequency-domainelectricfieldThefrequency-domainequivalentsoftheintensityandphasearethespectrumandspectralphase.Fourier-transformingthepulseelectricfield:yields:Thefrequency-domainelectricfieldhaspositive-andnegative-frequencycomponents.Notethatfandjarediffer
