Optical_Fiber_Communication_-_Solution_Manual

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1、ProblemSolutionsforChapter288E=100cos(2p10t+30°)ex+20cos(2p10t-50°)ey2-1.8+40cos(2p10t+210°)ez2-2.Thegeneralformis:y=(amplitude)cos(wt-kz)=Acos[2p(nt-z/l)].Therefore(a)amplitude=8mm(b)wavelength:1/l=0.8mm-1sothatl=1.25mm(c)w=2pn=2p(2)=4p(d)Att=0andz=4mmwe

2、havey=8cos[2p(-0.8mm-1)(4mm)]=8cos[2p(-3.2)]=2.4721.2402-3.ForEinelectronvoltsandlinmmwehaveE=l(a)At0.82mm,E=1.240/0.82=1.512eVAt1.32mm,E=1.240/1.32=0.939eVAt1.55mm,E=1.240/1.55=0.800eV(b)At0.82mm,k=2p/l=7.662mm-1At1.32mm,k=2p/l=4.760mm-1At1.55mm,k=2p/l=4

3、.054mm-12-4.x1=a1cos(wt-d1)andx2=a2cos(wt-d2)Addingx1andx2yieldsx1+x2=a1[coswtcosd1+sinwtsind1]+a2[coswtcosd2+sinwtsind2]=[a1cosd1+a2cosd2]coswt+[a1sind1+a2sind2]sinwtSincethea'sandthed'sareconstants,wecanseta1cosd1+a2cosd2=Acosf(1)1a1sind1+a2sind2=Asinf(

4、2)providedthatconstantvaluesofAandfexistwhichsatisfytheseequations.Toverifythis,firstsquarebothsidesandadd:222A2(sin2f+cos2f)=a1(sind1+cosd1)222+a2(sind2+cosd2)+2a1a2(sind1sind2+cosd1cosd2)or22A2=a+a+2a1a2cos(d1-d2)12Dividing(2)by(1)givesasind+asind1122ta

5、nf=acosd+acosd1122Thuswecanwritex=x1+x2=Acosfcoswt+Asinfsinwt=Acos(wt-f)2-5.FirstexpandEq.(2-3)asEy=cos(wt-kz)cosd-sin(wt-kz)sind(2.5-1)E0ySubtractfromthistheexpressionExcosd=cos(wt-kz)cosdE0xtoyieldEEyx-cosd=-sin(wt-kz)sind(2.5-2)EE0y0xUsingtherelationco

6、s2a+sin2a=1,weuseEq.(2-2)towrite22éæEöùsin2(wt-kz)=[1-cos2(wt-kz)]=1-çx÷(2.5-3)êúèEøë0xûSquaringbothsidesofEq.(2.5-2)andsubstitutingitintoEq.(2.5-3)yields22éEyEùéæExöù-xcosd=1-ç÷sin2dêëEEúûêèE0xøú0y0xëûExpandingtheleft-handsideandrearrangingtermsyields22æ

7、çExö÷æçEyöæçExö÷æçEyö+÷-2÷cosd=sin2dèE0xøèE0yøèE0xøèE0yø2-6.PlotofEq.(2-7).2-7.Linearlypolarizedwave.2-8.Air:n=1.033°33°Glass90°(a)ApplySnell'slawn1cosq1=n2cosq2wheren1=1,q1=33°,andq2=90°-33°=57°cos33°2==1.540cos57°(b)Thecriticalangleisfoundfromnglasssi

8、nfglass=nairsinfair3withfair=90°andnair=1.011fcritical=arcsin=arcsin=40.5°n1.540glass2-9AirrWaterq12cmFindqcfromSnell'slawn1sinq1=n2sinqc=1Whenn2=1.33,thenqc=48.75°rFindrfromtanqc=,whichyieldsr=13.7cm.12cm2-10.45°U