基础光学(赵凯华版)课件Chap3_Interference.ppt

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1、1第3章光的干涉§3.1波的叠加和干涉(book3.1)我们将会学到平面波的表示波的叠加原理干涉公式2ESolution:Ex,tE0coskxtBx,tB0coskxtAeitx,t一维平面波EtE0B0BtB00平面波(PlaneWave)是自由空间电磁波的一基元成分在标量波近似下(例如各向同性介质中的旁轴条件)，且取exp(-wt):x,tAcoskxtx,tAsinkxtkxphase:kxt

2、3r,tAeikrtkrkxxkyykzz3DPlanewaves:Cartesiancoordinatesikxxkyykzztx,y,z,tAeWaveeq-nsinCartesiancoordinates:x,y,z,tAeikxyzt,,-directioncosinesofkkkx2ky2kz22221Importanceofplanewaves:•easytogenerateusinganyharmonicgenerator•any3Dwavecanbeex

3、pressedassuperpositionofplanewaves4xAsinkxtHarmonicwave:PhaseCanusecos():x,tAsinkxtx,tAcoskxt2equivalentequationsxSpecialcase:==180ophaseshiftx,tAsinkxtx,tAsintkxx,tAcostkx/2Note:sin(kx-t)andsin(t-kx)bothdescribewavemovingright,butphase-

4、shiftedby180degrees().56Thesuperpositionprinciple波的叠加原理：在两列或多列波的交叠区域内，每点的振动等于各列波在该点振动的代数和。Superpositionprinciple:theresultingdisturbanceateachpointintheregionofoverlapoftwoormorewavesisthealgebraicsumoftheindividualconstituentwavesatthatlocation.Note:oncewavespasstheintersectingregiontheywil

5、lmoveawayunaffectedbyencounter(光的独立传播原理)7Thesuperpositionprinciple:exampleNote:theresultingwaveisstillaharmonicwave(thesamek)8Thesuperpositionprinciple:specialcasesTwowavesare‘in-phase’:(同相)1A1sinkxt2A2sinkxtA1A2sinkxtAmplitudeoftheresultingwaveincreases:constructiveinter

6、ference（相干相长）Twowavesare‘out-of-phase’:(反相，=180o=)1A1sinkxt2A2sinkxt2A2sinkxtA1A2sinkxtAmplitudeoftheresultingwavedecreases:destructiveinterference（相干相消）3Dplanewave:r,tAsinkrt'AcoskrtiAeConvention-usecos:r,tReAcoskrtik

7、rtUsuallyomit‘Re’:r,tAeir9ArganddiagramThecomplexrepresentationComplexnumbers:~zxiy,wherei1Inpolarcoordinates:xrcos,yrsin~zrcosisinEulerformula:eicosisinAnycomplexnumber:~zreicanusesinorcostodescribeaw