超快光学-第05章-色散ppt课件.ppt

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1、Angulardispersionandgroup-velocitydispersionPhaseandgroupvelocitiesGroup-delaydispersionNegativegroup-delaydispersionPulsecompressionChirpedmirrorsDispersionandUltrashortPulsesDispersioninOpticsThedependenceoftherefractiveindexonwavelengthhastwoeffectsonapulse,oneinspaceandtheotherintim

2、e.GroupdelaydispersionorChirpd2n/dl2Angulardispersiondn/dlBothoftheseeffectsplaymajorrolesinultrafastoptics.Dispersionalsodispersesapulseintime:Dispersiondispersesapulseinspace(angle):vgr(blue)qout(red)Whentwofunctionsofdifferentfrequencyinterfere,theresultisbeats.ta

3、kingE0tobereal.Addingwavesoftwodifferentfrequenciesyieldstheproductofarapidlyvaryingcosine(wave)andaslowlyvaryingcosine(Dw).Let:Whentwowavesofdifferentfrequencyinterfere,theresultisbeats.Indiv-idualwavesSumEnvel-opeIrrad-iancetime2p/DwInphaseOutofphaseInphaseOutofphaseInphaseWhentwowav

4、esofdifferentfrequencyinterfere,theyalsoproducebeats.takingE0tobereal.Traveling-WaveBeatsIndiv-idualwavesSumEnvel-opeInten-sityInphaseOutofphaseInphaseOutofphaseInphaseztimeInphaseOutofphaseSeeingBeatsIt’susuallyverydifficulttoseeopticalbeatsbecausetheyoccuronatimescalethat’stoofasttod

5、etect.Thisiswhywesaythatbeamsofdifferentcolorsdon’tinterfere,andweonlyseetheaverageintensity.However,asumofmanyfrequencieswillyieldatrainofwell-separatedpulses:Indiv-idualwavesSumIrrad-iance2p/DwmaxPulseseparation:2p/DwminGroupVelocityvgºdw/dkLight-wavebeats(continued):Etot(z,t)=2E0cos(

6、kavez–wavet)Pulse(Dkz–Dwt)Thisisarapidlyoscillatingwave:[cos(kavez–wavet)]withaslowlyvaryingamplitude:[2E0Pulse(Dkz–Dwt)]Thephasevelocitycomesfromtherapidlyvaryingpart:v=wave/kaveWhatabouttheothervelocity—thevelocityofthepulseamplitude?Definethegroupvelocity:vgºDw/DkTakingthecontinuousl

7、imit,wedefinethegroupvelocityas:carrierwaveamplitudeGroupvelocityisnotequaltophasevelocityifthemediumisdispersive(i.e.,nvaries).Evaluatethegroupvelocityforthetwo-frequencycase:wherek1andk2arethek-vectormagnitudesinvacuum.PhaseandGroupVelocitiesUnrealisticUnrealisticInvacuumMos