光电学部分答案-刘旭版PPT课件

-,1,光电子学作业参考答案,-,2,作业1,FundamentalsofPhotonics（括号内为中文教材上题目的位置）：1.4-11.4-43.1-2(P41-2)3.1-3(P41-3)3.2-1(P41-4),-,3,作业1,1.4-1Ray-TransferMatrixofaLensSystem.Determinetheray-transfermatrixforanopticalsystemmadeofathinconvexlensoffocallengthfandathinconcavelensoffocallength-fseparatedbyadistancef.Discusstheimagingpropertiesofthiscompositelens.,f,-f,f,-,4,作业1,注意矩阵相乘的顺序,-,5,作业1,1.4-44X4Ray-TransferMatrixforSkewedRays.Matrixmethodsmaybegeneralizedtodescribeskewedparaxialraysincircularlysymmetricsystems,andtoastigmatic(non-circularlysymmetric)systems.Araycrossingtheplanez=0isgenerallycharacterizedbyfourvariables-thecoordinates(x,y)ofitspositionintheplane,andtheangles()thatitsprojectionsinthex-zandy-zplanesmakewiththezaxis.Theemergingrayisalsocharacterizedbyfourvariableslinearlyrelatedtotheinitialfourvariables.Theopticalsystemmaythenbecharacterizedcompletely,withintheparaxialapproximation,bya4X4matrix.(a)Determinethe4X4ray-transfermatrixofadistancedinfreespace.(b)Determinethe4X4ray-transfermatrixofathincylindricallenswithfocallengthforientedintheydirection(Fig.P1.4-4).Thecylindricallenshasfocallengthfforraysinthey-zplane,andnofocusingpowerforraysinthex-zplane.可列式求解：,-,6,作业1,(a)过长度为d的自由空间，光线角度不变，位置改变(近轴光线),-,7,作业1,(b)薄透镜厚度d0,y-z面上为焦距为f的薄透镜,-,8,作业1,3.1-2BeamIdentificationbyTwoWidths.AGaussianbeamofwavelength=10.6pm(emittedbyaCO2laser)haswidthsW1=1.699mmandW2=3.38mmattwopointsseparatedbyadistanced=10cm.Determinethelocationofthewaistandthewaistradius.借助公式：可求解，计算较麻烦,-,9,作业1,由方程组可得（舍去）由(2)得:解得：所以或者,-,10,作业1,3.1-3TheEllipticGaussianBeam.TheparaxialHelmholtzequationadmitsaGaussianbeamwithintensityinthez=0plane,withbeamwaistradiiW0 xandW0yinthexandy-directionsrespectively.Thecontoursofconstantintensityarethereforeellipsesinsteadofcircles.Writeexpressionsforthebeamdepthoffocus,angulardivergence,andradiiofcurvatureinthexandydirections,asfunctionsofW0 xW0y,andthewavelength.IfW0 x=2W0ysketchtheshapeofthebeamspotinthez=0planeandinthefarfield(zmuchgreaterthanthedepthsoffocusinbothtransversedirections).X和Y两方向独立求解,-,11,作业1,(a)(1)扩散角：(2)焦深：(3)曲率半径：,-,12,作业1,(b)当W0 x=2W0y时:(1)z=0(2)z=Mz0,-,13,作业1,3.2-1BeamFocusing.Anargon-ionlaserproducesaGaussianbeamofwavelength=488nmandwaistradiusW0=0.5mm.Designasingle-lensopticalsystemforfocusingthelighttoaspotofdiameter100um.Whatistheshortestfocal-lengthlensthatmaybeused?,-,14,作业1,由(3.2-5)及(3.2-9)得：求导得：,-,15,作业1,故z=0.1z0即f=161.75mm时候，f取得最小值,-,16,作业2,FundamentalsofPhotonics（括号内为中文教材上题目的位置）：1.3.1-1(P41-1)2.3.2-2(P41-5)3.3.2-3(P41-6)4.9.1-1(P42-10)5.9.1-2(P43-11),-,17,作业2,3.1-1BeamParameters.ThelightfromaNd:YAGlaseratwavelength1.06umisaGaussianbeamof1-Wopticalpowerandbeamdivergence2=1mrad.Determinethebeamwaistradius,thedepthoffocus,themaximumintensity,andtheintensityonthebeamaxisatadistancez=100cmfromthebeamwaist.本题求解激光（高斯）光束的束腰半径，焦深，最大光强和在光轴上z=100cm处的光强,-,18,作业2,由发散角公式得由得：,-,19,作业2,由光功率公式：得：由光轴上的光强分布公式得：,-,20,作业2,3.2-2SpotSize.AGaussianbeamofRayleighrangez0=50cmandwavelength=488nmisconvertedintoaGaussianbeamofwaistradiususingalensoffocallengthf=5cmatadistancezfromitswaist,asillustratedinFig.3.2-2.WriteacomputerprogramtoplotWdasafunctionofz.Verifythatinthelimitz-fz0(3.2-10)and(3.2-12)hold;andinthelimitzz0时该近似在z400后与原图像差别不大,-,24,作业2,(2)当zz0时该近似在zelectrons,-,39,作业3,11.1-5LevitationbyLightPressure.Consideranisolatedhydrogenatomofmass1.66x10-27kg.(a)Findthegravitationalforceonthishydrogenatomnearthesurfaceoftheearth(assumethatatsealevelthegravitationalaccelerationconstantg=9.8m/s2).(b)Letanupwardlydirectedlaserbeamemitting1-eVphotonsbefocusedinsuchawaythatthefullmomentumofeachofitsphotonsistransferredtotheatom.Findtheaverageupwardforceontheatomprovidedbyonephotonstrikingiteachsecond.(c)Findthenumberofphotonsthatmuststriketheatompersecondandthecorrespondingopticalpowerforitnottofallundertheeffectofgravity,givenidealizedconditionsinvacuum.(d)Howmanyphotonspersecondwouldberequiredtokeeptheatomfromfallingifitwereperfectlyreflecting?光子动量表达式和动量守恒,-,40,作业3,(a)氢原子重力：G=mg=1.66*10-27kg*9.8m/s2=1.63*10-26N(b)光子动量变化每秒有一个光子撞击氢原子时产生的平均作用力(c)理想情况下(d)当发生完全弹性碰撞时：,-,41,作业4,FundamentalsofPhotonics（括号内为中文教材上题目的位置）：12.2-1(P152-22)12.3-1(P153-24)12.3-2(P153-25),-,42,作业4,12.2-1ComparisonofStimulatedandSpontaneousEmission.Anatomwithtwoenergylevelscorrespondingtothetransition(=0.7um,tsp=3ms,=50GHz,Lorentzianlineshape)isplacedinaresonatorofvolumeV=100cm3andrefractiveindexn=1.Tworadiationmodes(oneatthecenterfrequencyandtheotherat)areexcitedwith1000photonseach.Determinetheprobabilitydensityforstimulatedemission(orabsorption).IfN2suchatomsareexcitedtoenergylevel2,determinethetimeconstantforthedecayofN2duetostimulatedandspontaneousemission.Howmanyphotons(ratherthan1000)shouldbepresentsothatthedecayrateduetostimulatedemissionequalsthatduetospontaneousemission?,-,43,作业4,(a)离散的模式，受激辐射（吸收）的概率密度(1)根据题意该光有两个辐射模式,-,44,作业4,(2)发射截面值(3)结果Pst=2.98*10-7s-1,-,45,作业4,(b)类似于故总时间常数为(c)由第二步，得：所需要的光子数为：,-,46,作业4,12.3-1RateEquationsforBroadbandRadiation.Aresonatorofunitvolumecontainsatomshavingtwoenergylevels,labeled1and2,correspondingtoatransitionofresonancefrequencyv0andlinewidth.ThereareN1andN2atomsinthelowerandupperlevels,1and2,respectively,andatotalofphotonsineachofthemodeswithinabroadbandsurroundingv0.Photonsarelostfromtheresonatoratarateasaresultofimperfectreflectionatthecavitywalls.Assumingthattherearenononradiativetransitionsbetweenlevels2and1,writerateequationsforN2and.,-,47,作业4,（1）对于上能级粒子数N2N2上粒子自发辐射损耗：N2上粒子受激辐射损耗：N1上粒子受激吸收使得N2增加:为光子数损耗因子，与N2无关若为洛伦兹线形有,-,48,作业4,忽略其他无辐射跃迁，则N2减少量等于光子增加量光子数损耗因子，三维态密度故若为洛伦兹线形：,-,49,作业4,12.3-2InhibitedSpontaneousEmission.Considerahypotheticaltwo-dimensionalblack-bodyradiator(e.g.,asquareplateofareaA)inthermalequilibriumattemperatureT.(a)DeterminethedensityofmodesM(v)andthespectralenergydensity(i.e.,theenergyinthefrequencyrangebetweenvandv+dvperunitarea)oftheemittedradiation(seeSec.9.1C).(b)FindtheprobabilitydensityofspontaneousemissionPspforanatomlocatedinacavitythatpermitsradiationonlyintwodimensions.,-,50,作业4,(a)设二维正方形腔边长为d，则A=d2在Z,Y方向上，模式间隔为,所以：故在倒易空间中，一个模式面积为假设在v时有N个态，则,-,51,作业4,一种模式两种偏振：,-,52,作业4,（b）由：,-,53,作业5,FundamentalsofPhotonics（括号内为中文教材上题目的位置）：13.1-2(P212-15)13.1-3(P212-16)13.2-1(P212-17),-,54,作业5,13.1-2LaserAmplifierGainandPopulationDifference.AH-cm-longrodofNd3+:glassusedasalaseramplifierhasatotalsmall-signalgainof10atA,=1.06pm.UsethedatainTable13.2-1onpage480todeterminethepopulationdifferenceNrequiredtoachievethisgain(Nd3+ionspercm3).由表得:,-,55,作业5,固体加宽线形比较复杂，不是洛伦兹线形,-,56,作业5,13.1-3AmplificationofaBroadbandSignal.ThetransitionbetweentwoenergylevelsexhibitsaLorentzianlineshapeofcentralfrequencywithalinewidth.Thepopulationisinvertedsothatthemaximumgaincoefficient=0.1cm-1.Themediumhasanadditionallosscoefficient=0.05cm-1,whichisindependentofv.Approximatelyhowmuchlossorgainisencounteredbyalightwavein1cmifithasauniformpowerspectra1densitycenteredaboutwithabandwidth?,-,57,作业5,总增益为泰勒展开，取一阶所以,-,58,作业5,13.2-1TheTwo-LevelPumpingSystem.Writetherateequationsforatwo-levelsystem,showingthatasteady-statepopulationinversioncannotbeachievedbyusingdirectopticalpumpingbetweenlevels1and2.图13.2-3：外加泵浦下能级粒子的跃迁示意图,-,59,作业5,对于2能级系统如上图，R1=R2=R令R=(N1-N2)W，光泵浦对受激吸收和发射的作用相同,-,60,作业5,平衡时所以不可能有稳定的粒子数反转,-,61,作业6,FundamentalsofPhotonics（括号内为中文教材上题目的位置）：14.2-1(P209-1)14.2-2(P209-2)13.3-1(P209-19)13.3-2(P209-20),-,62,作业6,14.2-1NumberofLongitudinalModes.AnAr+-ionlaserhasaresonatoroflength100cm.Therefractiveindexn=1.(a)DeterminethefrequencyspacingvFbetweentheresonatormodes.(b)DeterminethenumberoflongitudinalmodesthatthelasercansustainiftheFWHMDoppler-broadenedlinewidthis,=3.5GHzandthelosscoefficientishalfthepeaksmall-signalgaincoefficient.(c)Whatwouldtheresonatorlengthdhavetobetoachievoperationonasinglelongitudinalmode?WhatwouldthatlengthbeforaCO,laserthathasamuchsmallerDopplerlinewidth,vD=60MHzunderthesameconditions?,-,63,作业6,(a)vF=c/2dn=3*108/(2*1*1)=1.5*108Hz(b)题中B=Mb=B/vF=23(c)AsBvF=c/(2d)对于Ar+激光器B=3.5GHz0dc/2B=0.043m=4.3cm;对于CO2激光器B=60MHz0dc/2B=2.5m;,-,64,作业6,14.2-2FrequencyDriftoftheLaserModes.AHe-Nelaserhasthefollowingcharacteristics:(1)Aresonatorwith97%and100%mirrorreflectancesandnegligibleinternallosses;(2)aDoppler-broadenedatomictransitionwithDopplerlinewidth=1.5GHz;and(3)asmall-signalpeakgaincoefficient=2.5*10-3cm-1.Whilethelaserisrunning,thefrequenciesofitslongitudinalmodesdriftwithtimeasaresultofsmallthermallyinducedchangesinthelengthoftheresonator.Findtheallowablerangeofresonatorlengthssuchthatthelaserwillalwaysoscillateinoneortwo(butnotmore)longitudinalmodes.Therefractiveindexn=1.,-,65,作业6,忽略其他内部损耗，仅有境内反射损耗多普勒加宽为高斯线形令，得,-,66,作业6,只允许1到2个纵模振荡时带入已知条件则令t=2d；则解超越方程得:,-,67,作业6,13.3-1SignificanceoftheSaturationPhoton-FluxDensity.Inthegeneraltwo-levelatomicsystemofFig.13.2-3,representsthelifetimeoflevel2intheabsenceofstimulatedemission.In