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1、1Fundamentals1.1.CHARACTERISTICSOFFEMTOSECONDLIGHTPULSESFemtosecond(fs)lightpulsesareelectromagneticwavepacketsandassucharefullydescribedbythetimeandspacedependentelectricfield.Intheframeofasemiclassicaltreatmentthepropagationofsuchfieldsandtheintera
2、ctionwithmatteraregovernedbyMaxwell'sequationswiththematerialresponsegivenbyamacroscopicpolarization.Inthisfirstchapterwewillsummarizetheessentialnotationsanddefinitionsusedthroughoutthebook.Thepulseischaracterizedbymeasurablequantitiesthatcanbedirec
3、tlyrelatedtotheelectricfield.Acomplexrepresentationofthefieldamplitudeisparticularlyconvenientindealingwithpropagationproblemsofelectromagneticpulses.Thenextsectionexpandsonthechoiceoffieldrepresentation.1.1.1.ComplexRepresentationoftheElectricFieldL
4、etusconsiderfirstthetemporaldependenceoftheelectricfieldneglectingitsspatialandpolarizationdependence,i.e.,E(jc,>',z,0=^(0-Acompletedescriptioncanbegiveneitherinthetimeorthefrequencydomain.Eventhoughthemeasuredquantitiesarereal,itisgenerallymoreconve
5、nienttousecomplexrepresentation.Forthisreason,startingwiththerealE(t),onedefinesthecomplex2FundamentalsspectrumofthefieldstrengthE(Q),throughthecomplexFouriertransform(T):E(Q)=J='[£(!)]=[E(t)e-'^'dt=E{^)W^^^^(1.1)Inthedefinition(1.1),
6、£'(^)
7、denotest
8、hespectralamplitude,andO(^)isthespectralphase.Hereandinwhatfollows,complexquantitiesrelatedtothefieldaretypicallywrittenwithatilde.BecauseE{t)isarealfunction,E(Q)=E*{-Q)holds.GivenEiQ),thetimedependentelectricfieldisobtainedthroughtheinverseFouriertr
9、ansform(T~^):E(t)=T-^{£(^)}=—/*E{Q.)e'^'dO..(1.2)Forpracticalreasonsitmaynotbeconvenienttousefunctionsthatarenonzerofornegativefrequencies,asneededintheevaluationofEq.(1.2).Frequendyacomplexrepresentationoftheelectricfieldinthetimedomainisalsodesired
10、.Bothaspectscanbesatisfiedbyintroducingacomplexelectricfieldas£+(r)=—{E{Q,)e'^'dQ.(1.3)27rJoandacorrespondingspectralfieldstrengththatcontainsonlypositivefrequencies:/cD(Q)IE{Q.)for^>0£n^)=
11、£(^)
12、.--={-"'-^-^(1.4)E^(t)andE^{Q.)arerelatedtoeachotherthr
