光纤通信课件第二章

1、光纤通光纤通FiberOpticIntroduction:Introduction:Theory and ApplicationsLensesImagingNumerical ApertureDiffraction TheorySummary and Discussion2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage2Ray Theory and ApplicationsRefractive index (折射率)Ray Theory and Applicationsc = 3 x 108 m/s, velocity of light

2、 in free space v = velocity of light in the mediumMaterialIndexnCO2MaterialIndexnCO21Water1.33Glass1.5Silicon3.5GaAs3.35更多材料的折射率见P32表2.12012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage3REFLECTIONReflection ataBoundary(媒质分界面的反射)n1n2ReflectedRayRayriIncident tBoundary Normal两种媒质分界面上入射光线、反射光线和折射光线

3、2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage4REFLECTIONIf any power crosses the tis given terms of law: titn n2n 1n2(2.3)sini2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage5REFLECTIONFrom Snells law（斯奈尔定律）If n1 n2 , then sin(t) sin(i) and t n2 , then sin(t) sin(i) and t i.The transmit

4、ted ray is bent away from the normal.n1nn1n2itBoundary2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage72).全反射定律根据Snell定律右图的折射满足：入射光线反射光线n1sin1 n2 sin2折射角 arcsinsin1 若n ,则在n1c212n则色光线2nn1 sin190n2n90n2时，折射角2 ，当n1 sin1n2时发生了全反射。光在两种介质界面上的反射和全反射sin1n2=1时的入射角1为全反射时的临界角，记为c,有c 2012年2月27419分Chapter 2

5、OpticReviewBy QianSheng,HDUPage8Lenses Consider a thinIndex of RefractionIndex of RefractionP (Focal Point)DnFiberfFocal Length一束平行光（准直光束）通过薄透镜可以聚焦到一点2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage9R若R1 R2 表示透镜的曲率半径.R111 (nf (2.4)f透镜的f数DIf f (focal length) is large, then R1 and R2 must be larg

6、e making the lens a fairly flat surface.If f (focal length) is small, then R1 and R2 must be small. Thislimits the lens size, since Dmax =2R.透镜主要用于将光源产生的光耦合进光纤，有时也用于将一根光纤射出的光耦合进另一根光纤.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage10RAY TRACING 21flens axis4f3planeRays traveling through the cen

7、ter of the lensarenot deviated.Incident rays traveling parallel to the lens axis pass through the focal point after emerging fromthe lens.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPageRAY TRACING RULESAn incident ray traveling parallel to acentral ray intersects that ray in the focal plane af

8、ter transmission through thelens.An incident ray passing through the focalpoint travels parallel to the lens axis after it emerges from thelens.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage12CYLINDRICAL LENSFocal Line焦线(Line Source)lens axiscollimated beamfCylindricallensescollimate（校准）rays

9、fromaline source.Collimated means that all rays from the line source emerge from the lens parallel to the lensaxis.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage13侧视图CYLINDRICAL LENSff俯视图俯视图2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage14rGRADED INDEX ROD LENS (GRIN ROD LENS)rThe refra

10、ctive index is a function of radialposition n=n(r).Ray paths aresinusoidal.lens axisPSinusoidal raypathsP:The pitch is the length of onecycle2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage15GRADED INDEX ROD LENSa quarter pitch length(1/4节距）P: Pitch准直点光源发出的射线聚焦准直光束raysP/42012年2月27419分Chapter 2O

11、pticReviewBy QianSheng,HDUPage162012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage17光束在2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage18GRADED INDEX ROD LENSGRIN-rod lenses are used in many fiber devices.The main purposes for which GRIN-rod lenses are used are:collimate light beams coming f

12、rom a fiberfocus light beams onto a fiberThe GRIN-rod lens can have a small focal length.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage19ImagingImagingfocal pointfocal pointdoIdiThe distance from the object O to the lens is do，the distance from the image I to the lens is di .The distance from

13、 the object O to the lens is do The distance from the image I to the lens is di .2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage20IMAGINGThe position of the object and focused imagerelated by the thin lensequation.(2.5)dodifProof:Using the diagram on the previous slide, we findthe following.20

14、12年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage21证明:IMAGING通过前面薄透镜成像的简图，我们可以证明成像公式.tan tan O I , M I didodiOdo(2.6)Where M is the magnification factor.Alsotan O fFrom(2.6)Idi I MO O didodiO diO doOfdi fdi dofdi f1 i1 did f d f f diidodo 1 1 1fdido1 1 1fdodi2012年2月27419分Chapter 2OpticReviewBy Qia

15、nSheng,HDUPage22RELATIONSHIP BETWEEN OBJECT DISTANCE AND MAGNIFICATION111(2.5)fdodithendo1 do 11/ M 1/ M do 1fdifsoM 1do 1f(2.7)上式说明了放大倍数和物距之间的关系.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage23RELATIONSHIP BETWEEN OBJECT DISTANCE AND MAGNIFICATIONMagnification1 do 2MagnificationfM 1do 1fd /f

16、o2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage24RELATIONSHIP BETWEEN OBJECT DISTANCE AND MAGNIFICATIONExamples: Using equations (2.5),(2.6),and (2.7).1)若M=1，试计算物距和像距：M1do 1fdo 2M1ddfiosoo111 o 2 fdodofdi 2 f2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage25ANGULAR SPREAD（张角）Fibers accep

17、t light over a limited range of angles.Point SourcePoint SourceoxFiberiidodio = angular spread at the sourcei = angular spread at the image2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage26preiosfSPREADtno x,tni x2d2doso (2.9)tani 2 do1tno xdiM2doM is the linear magnificationi 1 oM(2.10)i o MFo

18、rForsmall angles,tan (validwhen 5 ).Under this condition上述结果显示通过透镜可以减小光源出射光束的张角2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage27ANGULAR SPREADLinear magnification will resultinangulardemagnification.This setup is useful in coupling light from a divergentsource intoafiber(which has a limited ra

19、y acceptanceangle).3232yc1lc 123x纤芯n1Lo1包层n22012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage28NumericalNumerical ApertureConsider an opticalreceiver: IncomingraysPhotodetectorfddfd光检测器表面区域直径为 d.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage29NUMERICAL APERTUREdf入射线如果大于接受的角度 入射线如果大于接受的角度

20、将不会投射到光检测器上.tand2 f(2.11)The numerical aperture is defined as：NA no sinno is the index of refraction for the surrounding media. is the acceptancecone half-angle2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage30NUMERICAL APERTUREExample:某接收机中透镜的焦距为10cm，光检测器的直径为1cm，透镜和检测器之间为空气，计算接收机的NA。f 10cm, d

21、1Computethe NANA no sinsintanNA d10.05NA 2f200.05 sin10.05 0.05rad 2.872012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage31NUMERICAL APERTURE APPLICATIONS TO FIBERSFibers have limited acceptance angles and thusa small NA.Light SourceRays outside 2 are not reflected2FiberRays inside 2 reflected典型的

22、光纤数值孔径（典型的光纤数值孔径（NA）范围为 0.1 to 0.5.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage32NUMERICAL APERTURENA and the corresponding acceptance angles :NA 0.10.20.317.50.423.60.530.02012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage33Diffraction Theory（衍射）Some experiments do not exactly follow ra

23、y theory. Diffraction is the deviation from the predictions of ray theory.As an example of the difference between ray theory and diffraction, consider focusing by a lens of a uniform beam of light.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage34DIFFRACTION THEORY下图展示了一束准直的均匀光束为透镜所聚焦的情形.衍射理论和较

24、仔细的实验表明光束不是汇聚到一点，而是汇聚到一个中心光斑和环绕它一系列强度递减的环形带上。DUniformDUniformbeam of lightfCentral spot with surrounding rings of lightdd is the diameter of the central spot.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage35DIFFRACTION THEORYThe diameter of the central spot is found from:d fD(2.14)Example:Iff2

25、D,1then2.44106 2Dd D4.88 2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage36GAUSSIAN BEAM0.135r (m)w = 10 0.135r (m)w = 10 mI/Io = exp(-2r2/w2)I/Io =exp(-2r2/w2)2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage37GAUSSIAN BEAM2r22I Ioe w2(2.15)where w = spot size （光斑尺寸）and r = radial distance

26、 from thecenter of the beam pattern.Example:atr0IIo e0 1atrwIIoe2or 13.5%ofpeak高斯强度分布是非常重要的一种模型，因为大多数激光器发出高斯强度分布是非常重要的一种模型，因为大多数激光器发出的光都是接近高斯分布，同时也是单模光纤内的场分布的模型2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage38GAUSSIAN BEAM2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage39GAUSSIAN BEAMThe

27、Guassian intensity distribution is useful because most lasers emit in this pattern and it is the field pattern inside a single-mode fiber.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage40FOCUSING A GAUSSIANBEAMGaussian input beam2w2wCentral spot2wofis given I I2r2owo2ois given (2.16)TheThepeak

28、 intensitywill be more intense, becausethebeam is compressed.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage41COLLIMATING A GAUSSIAN BEAMPoint sourcePoint source2wofz在透镜附近光线被准直得非常好，远离透镜则光束趋向相互分离.2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage42A GAUSSIANBEAMFar from the lens the beam div

29、erges according to:2r2I Ie wowhere 2oo2Thedivergenceangleisfoundfromsoz2 zwz(2.17)2012年2月27419分Chapter 2OpticReviewBy QianSheng,HDUPage43COLLIMATING A GAUSSIAN BEAMExample: Spot size w = 1 mm at the lens and = 0.82m.Find and wo at z = 10 m, 1km,and 10 km.20.82106103 0.522103rad 0.02992012年2月27420分Chapter 2OpticReviewBy QianSheng,HDUPage44At z = 10 m, 1 km, and 10 km respecti