考前复习参考0711

Chapter1lightwavesphotonsmodes&statescoherencetemporalcoherencespatialcoherencecoherenceareacoherencevolumetemporalcoherencelengthtransversecoherencelengththermalradiationPlanck’sLawabsorptioninducedemissionspontaneousemission.transitionprobabilitytheEinsteincoefficientbasicelementsofalaserpopulationinversionthresholdcondition…Thenumberofmodes1.Inthevisiblepartofthespectrum(=500nm;=6x1014s-1),thenumberofmodesperunitvolumewithintheDopplerwidthofaspectralline(=109s-1)is.2.Inthemicrowaveregion(=1cm;=3x1010s-1),thenumberofmodesperunitvolumewithinthetypicalDopplerwidth=105s-1is.3.IntheX-rayregion(=1nm;=3x1017s-1),thenumberofmodesperunitvolumewithinthetypicalDopplerwidth=1011s-1ofanX-raytransitionis.LightSourcesa)ExamplesofrealradiationsourceswithspectralenergydistributionsclosetothePlanckdistributionarethesun,thebrighttungstenwireofalightbulb,flashlamps,andhigh-pressuredischargelamps.b)Spectrallampswhichemitdiscretespectraareexamplesofnonthermalradiationsources.Inthesegas-dischargelamps,thelight-emittingatomsormoleculesmaybeinthermalequilibriumwithrespecttotheirtranslationalenergy,whichmeansthattheirvelocitydistributionisMaxwellian.However,thepopulationofthedifferentexcitedatomiclevelsmaynotnecessarilyfollowaBoltzmanndistributionandthereisgenerallyalsonothermalequilibriumbetweentheatomsandtheradiationfield.Theradiationmayneverthelessbeisotropic.c)Lasersareexamplesofnonthermalandanisotropicradiationsources.Theradiationfieldisconcentratedinafewmodes,andmostoftheradiationenergyisemittedintoasmallsolidangle.Thismeansthatthelaserrepresentsanextremeanisotropicradiationsource.InducedEmissiona)Inthethermalradiationfieldofa100wlightbulb,10cmawayfromthetungstenwire,thenumberofphotonspermodeat=500nmisabout10-8.Ifamolecularprobeisplacedinthisfield,theinducedemissionisthereforecompletelynegligible.b)Inthecenterspotofahigh-currentmercurydischargelampwithveryhighpressurethenumberofphotonspermodeisabout10-2atthecenterfrequencyofthestrongestemissionlineat=253.6mm.Thisshowsthateveninthisverybrightlightsourcetheinducedemissiononlyplaysaminorrole.c)InsidethecavityofaHe-Nelaser(outputpower1mwwithmirrortransmittanceT=1%)whichoscillatesinasinglemode,thenumberofphotonsinthismodeisabout107.Inthisexamplethespontaneousemissionintothismodeiscompletelynegligible.Note,however,thatthetotalspontaneousemissionpowerat=632.8nm,whichisemittedintoalldirections,ismuchlargerthantheinducedemission.Thisspontaneousemissionismoreorlessuniformlydistributedamongallmodes.Assumingavolumeof1cm3forthegasdischarge,thenumberofmodeswithintheDopplerwidthoftheneontransitionisabout108,whichmeansthatthetotalspontaneousrateisabout10timestheinducedrate.TemporalCoherenceWhatisthetemporalcoherencelengthLcof(1)amercuryvaporlampemittinginthegreenportionofthespectrumatawavelengthof546.1nmwithanemissionbandwidthof=6x108Hz,and(2)ahelium-neonlaseroperatingatawavelengthof632.8nmwithanemissionwidthof=106Hz?SpatialCoherenceAlaser-producedplasmaconsistingofa100mdiameterballradiatesverystronglyatawavelengthof10nm.Atadistanceof0.5mfromsource,whatisthespatialcoherenceresultingfromlightemittedfromoppositesidesoftheplasma?JE=hc/heVE(J)/1.602110-19nm=c/cm-11/cmc(cm/s)Hz=c/1.00m?????1.00GHz?????cm-1表示单位长度（厘米）中的波数。e=1.602110-19C，即1eV=1.602110-19J，h=6.625610-34J.s。思考题：1.1*设一光子的波长=5×10-1m，单色性=10-7，试求光子位置的不确定量x。若光子的波长变为5×10-4m（x射线）和5×10-8m(射线),则相应的x又是多少？1.2*假定工作物质的折射率试问为多大时，J·S/m3，这是什么光范围？1.3*如果工作物质的某一跃迁波长为100nm的远紫外光，自发跃迁几率A10等于106S-1，试问：[1]该跃迁的受激辐射爱因斯坦系数B10是多少？[2]为使受激跃迁几率比自发跃迁几率大三倍，腔内的单色能量密度ρ应为多少？1.4*如果受激辐射爱因斯坦系数B10=1019m3s-3w-1，试计算在[1]λ=6m(红外光)；[2]λ=600nm(可见光)；⑶λ=60nm(远紫外光)；⑷λ=0.60nm(X射线时)，自发辐射跃迁几率A10和自发辐射寿命。又如果光强I=10W/mm2，试求受激跃迁几率W10。有一支输出波长为，线宽为z,输出功率为1mW的氦氖激光器，发散角为1mrad。问：⑴每秒发出的光子数目是多少？⑵如果输出光束的直径是1毫米，那么对于一个黑体来说，要求它从相等的面积上以及整个相同的频率间隔内，发射出与激光器发射相同数目的光子，所需温度应多高？AnswertotheQuestionsofChapter1/Lc610–1051019s–1(10m);n21/tP/hP/hc2.51018s–1(500nm);51023s–1(3000MHz).3.(a)n2/n1e–4.8x10–41;(b)n2/n1e–480;(c)T–h/[kln(n2/n1)]–hc/[kln(n2/n1)]6.26103k4.三能级系统，在理想情况下有N/2的粒子产生激光694.3nmEmaxhN/2(/8)d2lnhc/16.9JPEmax/1.69109W1.69GW6.(a)41/(A41+A42+A43)(1/9)10–7s；(b)稳态时各能级上的粒子数保持不变，忽略受激辐射以及E3和E2能级的自发辐射对其他能级布居数的影响,则有：n3/3n4A43n3/n4A4330.5n2/2n4A42n2/n4A4220.06n2/2n4A42n1/n4A411158.(1)e-z1/e=36.8%(2)egz2,g=(ln2)/z=0.693m-1ExampleNd3+ionsaredopedintoYAGata1%atomicconcentration,whichcorrespondstoadensityofNdatomsof1.38x1026percubicmeterinthelaserrod.Ifalloftheseatomswereinstantlypumpedtotheupperlaserlevelandthenbegantoradiate,whatwouldbetheradiatedenergypercubicmeterandtheaveragepowerpercubicmeterradiatedfromthismaterialattheemissionwavelengthof1.06m?Ifthepowerradiatedfromonecubiccentimetercouldbeconcentratedintoaspot1mmindiameter,whatwouldbetheintensity(power/m2)?Eachphotonradiatedat1.06mwouldhaveanenergyofE=h=hc/=1.87x10-19J=1.17ev.Thus,thetotalenergyradiatedpercub