1、Chapter 2 Dielectric Waveguides and Optical Fiberv 2.1 Symmetric planar dielectric Slab waveguidev 2.2 dispersion in the planar waveguide v 2.3 Step index fiberv 2.4 Numerical aperturev 2.5 Dispersion in single mode fibersv 2.6 Dispersion, electrical, and optical bandwidthv 2.7 The graded index opti
2、cal fiberv 2.8 Light absorption and scatteringv 2.9 Attenuation in optical fibersv 2.10 Fiber manufacture “The introduction of optical fiber systems will revolutionize the communications network. The low-transmission loss and the large bandwidth capability of the fiber systems allow signals to be tr
3、ansmitted for establishing communications contacts over large distance with few or no provisions of intermediate amplification.” Charles K.Kao光纤系统的引入将使通信网络产生革命。光纤系统的低传光纤系统的引入将使通信网络产生革命。光纤系统的低传输损耗和巨大的带宽能力允许信号在很少经过或者不经过输损耗和巨大的带宽能力允许信号在很少经过或者不经过中间放大的情况下实现超远距离的传输，建立通信联中间放大的情况下实现超远距离的传输，建立通信联系。系。 查尔斯查尔斯
4、高锟高锟TerminologyWaveguide :波导波导Further Phase Change of ：附加相位：附加相位；Optical Path Length（OPL）：光程；）：光程；Constructive Interference：相长干涉，相干加强；：相长干涉，相干加强；Destructive Interference：相消干涉，相干减弱；：相消干涉，相干减弱；Phase Difference (PD)：相位差；：相位差；Optical Path Difference (OPD):光程差；光程差；Polarization State of Light Wave ：光波偏振态：
5、光波偏振态State of Polarization （SOP）:偏振态偏振态Field Pattern：场图：场图Resultant Wave：合成波；：合成波；Standing Wave ：驻波；：驻波；TerminologyWavevector ：波矢：波矢Single Mode Waveguide (SM waveguide):单模波导单模波导Multimode Waveguide (MM waveguide):多模波导多模波导Normalized Thickness :归一化膜厚归一化膜厚Normalized Frequency: 归一化化频率归一化化频率V-number: V 数数
6、Cut-off Wavelength:截至波长截至波长Transverse Electric field mode:横电场模式横电场模式Transverse Magnetic field mode:横磁场模式横磁场模式Mode Field Width (MFW): 模场宽度模场宽度Mode Field Diameter (MFW): 模场宽度模场宽度Constant phase wavefront：等相位面：等相位面 To understand the general nature of light wave propagation in optical waveguides, we firs
7、t consider the planer dielectric slab waveguide shown in Figure 2.1, which is the simplest waveguide in terms of tractable analysis. A slab of dielectric of thickness 2a and refractive index n1 is sandwiched between two semi-infinite regions both of refractive index n2(n2 l1l1 lcw2 w1w1 vg1Thus, a g
8、reater portion of the light energy is carried by the cladding in which the phase velocity is higher. Longer wavelength propagate faster, even though by the same mode. This is called waveguide dispersion inasmuch as it results from the guiding properties of the dielectric structure and it has nothing
9、 to do with the frequency (or wavelength) dependence of the refractive of the guide, the disper-sion can also be state as due to the wavelength dependence of the V-number. The higher the wavelength (lower the frequency), the greater the penetration of the field into the cladding, as depicted in Figu
10、re .bmwSlope = c/n2Slope = c/n1TE0wcut-offTE1TE2The refractive index of the guide material will also depend on the wavelength and thus modify the -m behavior in Figure. The change in the group velocity of a given mode due to the n- dependence also gives rise to the broadening of a propagating light
11、pulse. This is called material dispersion. Thus both waveguide and material dispersion act together to broaden a light pulse propagating within a given mode. Combined dispersion is called intramode dispersion.Questions and Problems2.7 Dielectric slab waveguide (p.100)3.2 光纤的色散特性光纤的色散特性3.2.1 色散的概念色散的
12、概念 当日光通过棱镜或水雾时会呈现按红橙黄绿青蓝紫顺序排列的彩色光谱。这是由于棱镜材料（玻璃）或水对不同波长（对应于不同的颜色）的光呈现的折射率n不同，从而使光的传播速度不同和折射角度不同，最终使不同颜色的光在空间上散开。自然光的色散 光脉冲中的不同频率或模式在光纤中的群速度不同，这些频率成分和模式到达光纤终端有先有后，使得光脉冲发生展宽，这就是光纤的色散，如图所示。色散一般用时延差来表示，所谓时延差，是指不同频率的信号成分传输同样的距离所需要的时间之差。色散引起的脉冲展宽示意图模式色散：不同模式不同传输速度（模式色散：不同模式不同传输速度（仅多模光纤有仅多模光纤有）材料色散：不同频率不同折射
13、率材料色散：不同频率不同折射率波导色散：不同频率不同模场分布波导色散：不同频率不同模场分布偏振模色散：不同偏振态不同传输速度偏振模色散：不同偏振态不同传输速度色散分类色散分类t1t2t3t4脉冲展宽导致接收端无法将相邻的脉冲分开，从而导致误码。因此，射散特性限制了光纤的传输容量。色散描述方式色散描述方式1212lblwbcvgwbddLvLTg信号分量的群速率是频率/波长的函数：即不同的频率分量间存在群时延差。信号在传输了距离L，频率分量w经历的延时为：假设输入脉冲的谱宽Dw不太宽，那么脉冲展宽脉冲展宽的多少可以由下式决定：wbwwbwwwwDDDDD222LddLvLddddTTg222wb
14、bdd群速度色散群速度色散(GVD)（ps2/km)llwlwDD222cc llwbDDDDLLT2 通常光源的谱宽用Dl来表示。根据w和l之间的关系代入DT中，那么可以得到：其中D(l)称为 ps/(kmnm)222)(bllcD3.2.2 模式色散 多模光纤中不同模式的光束有不同的群速度，在传输过程中，不同模式的光束的时间延迟不同而产生的色散，称模式色散。 所谓模式色散，用光的射线理论来说，就是由于轨迹不同的各光线沿轴向的平均速度不同所造成的时延差。1. 阶跃型光纤中的模式色散在阶跃型光纤中，传播最快的和最慢的两条光线分别是沿轴线方向传播的光线和以临界角c入射的光线，如图3.6所示。因此
15、，在阶跃型光纤中最大色散是光线和光线到达终端的时延差。LnncLcnTcDD221111sin1DL为两种模式的光程差。2. 渐变型光纤中的模式色散 在渐变型光纤中合理地设计光纤折射率分布，使光线在光纤中传播时速度得到补偿，从而模式色散引起的光脉冲展宽将很小。cnLT8/21DD3.2.3 材料色散 由于光源的不同频率（或波长）成分具有不同的群速度，在传输过程中，不同频率的光束的时间延迟不同。由于材料折射率随光信号频率的变化而不同，光信号不同频率成分所对应的群速度不同，由此引起的色散称为材料色散。 一般情况下，材料色散往往是用材料色散系数这个物理量来衡量，材料色散系数定义为单位波长间隔内各频率
16、成份通过单位长度光纤所产生的色散。 光纤的折射率是波长的函数n(l)，则不同的波长的传播函数b不同： 可以得到传播了L后波长l所经历的群延时(材料色散)为： 式中：为光源的谱线宽度，即光功率下降到峰值光功率一半时所对应的波长范围；L是光纤的传播长度。Dm为材料色散系数。22)(llldndcDmlllblllbddnncLcLvLTng2)(22)(22lllllllmmDLdndcLddTTDDDD减小材料色散方法：选择谱宽窄的光源，采用较长的工作波长。3.2.4 波导色散 单模光纤只有约80%的光功率在纤芯中传播，20%在包层中传播的光功率其速率要更大一些。这种由于光纤波导结构引起的色散称
17、为波导色散。) 1(2DbknbDdVVbdnncLdkdcTw)(122b 假设纤芯和包层的折射率与波长无关，而且折射率差D = (n1-n2)/n1非常小，传播函数b近似等于：可以得到传播了L后波长l所经历的群延时为：其中V为归一化频率。进一步可以得到波导色散导致的脉冲展宽：)()(222llllllwwwDLdVVbdVcnLddTTDDDDDD222)()(dVVbdVcnDwll其中为光源的谱线宽度，即光功率下降到峰值光功率一半时所对应的波长范围；L是光纤的传播长度。 Dw()为波导色散系数波导色散系数一般为负值例：令n2 = 1.48，D = 0.2%，从左图可以看出当V = 2.
18、4时，有：因此可以算出在1320 nm处，波导色散为：26. 0)(22dVVbdV9 . 1)()(222DdVVbdVcnDwll2.422)(dVVbdV随 V变化的曲线标准单模光纤总的模内色散1320wmDDD一般来说材料色散的影响大于波导色散： |Dm| |Dw|波导色散特性波导色散特性取决于光纤的特性，如：芯径a，相对折射率差以及折射率分布等，因此可以通过改变光纤特性来改变其色散特性。色散的改变主要集中在零色散波长的位移和色散平坦两方面。3.2.5 偏振模色散（极化色散）偏振模色散（PMD）也称为极化色散。由于光信号的两个正交偏振态在光纤中有不同的传播速度而引起的色散称偏振模色散。
19、偏振模色散本征光纤双折射随机的偏振模耦合双折射的光通信器件 偏振模色散产生的原因偏振模色散 (PMD)PMD 受环境(如振动、温度、应力等)影响非常显著，跟模内色散相比具有不稳定性和突发性。因此，PMD补偿的难度比较大，关于补偿的方法目前尚无定论。PMD 对传输的影响PMD特点一般采用两偏振模的群时延差(Differential Group Delay)来表示偏振模色散的大小 n 两偏振模之间的模式耦合随波长和时间随机变化，所以偏振模色散是一个统计量，并随时间而变化n 当光纤很长时，PMD呈现为麦克斯韦分布。这个分布可以是一组相同的光纤在同一波长处测量的结果，也可以是一根光纤在同一波长处但不同
20、时间的测量结果，或者是同一光纤在不同波长处的测量结果111bbbtDDLLvLvLyxgxgxPMD表征方式tDLpsL/tD2tDtDPMD对光通信系统的影响 按照国际标准技术规范小组的观点：为保证PMD导致的系统功率代价在1dB以下，偏振模色散的群时延差的平均值必须小于一比特周期的十分之一(10ps for a 10Gb/s system) 。 当大于这一规定值时，需对系统偏振模色散进行补偿！比特率(Gb/s)允许的DGD平均值(ps)Mean DGD 系数 为0.1ps/km光纤的传输距离（km)2.540160000101010000402.56253.2.6光纤总色散光纤的总色散为：
21、光纤的总色散为： M模式色散，m材料色散，W波导色散。 单模光纤一般只给出色散系数D，其中包含了材料色散和波导色散的共同影响。多模光纤）（ 31. 3 )(22wmMtttt单模光纤）（ 32. 3 wmttt三种光纤的总色散三种光纤的总色散:1300nm最优化光纤色散平坦光纤色散位移光纤Chapter 2 Dielectric Waveguides and Optical Fiberv 2.1 Symmetric planar dielectric Slab waveguidev 2.2 dispersion in the planar waveguide v 2.3 Step index
22、fiberv 2.4 Numerical aperturev 2.5 Dispersion in single mode fibersv 2.6 Dispersion, electrical, and optical bandwidthv 2.7 The graded index optical fiberv 2.8 Light absorption and scatteringv 2.9 Attenuation in optical fibersv 2.10 Fiber manufacture Step Index FiberStep-index Fiber: Fiber that has
23、a uniform index of refraction throughout the core that is a step below the index of refraction in the cladding. Figure 2.12Step Index Fiber We recall that the planar waveguide is bounded only in one dimension so that reflections occur only in the y-direction. The requirement of constructive interfer
24、ence of waves then leads to the existence of distinct modes each labeled by m. The cylindrical guide in Figure 2.12 is bounded in two dimensions and the reflections occur from all the surfaces, i.e. from a surface encountered along any radial direction r ; along a radial direction at any angle to th
25、e y-axis in Figure 2.12. Since any radial direction can be represented in terms of x and y, reflection in both x and y directions are involved in constructive interference of waves and we therefore need two integers, l and m, to label all the possible traveling waves or guided modes that can exist i
26、n the guide .阶跃折射率光纤阶跃折射率光纤 让我们回忆一下, 平面波导的截面只在一维受到限制，因此反射只发生在y方向。因此，相干加强的光波引起的不同的导模，用m表示。 如图2.12 所示的柱形波导，镜面在二维都受到限制，而反射发生在所有的表面，也就是说，沿着任何半径r的方向的任何光线相遇的表面；图2.12中所示的沿着半径r与y轴成任意角度的方向。由于任何半径方向能够用坐标x和y表示，在x和y方向上光波的反射同样要求相干加强的条件，因此我们需要两个整数l和m标记波导中存在所有可能的传输波或者导模。Step Index Fiber In a step index fiber both
27、meridional and skew rays give rise to guided modes (propagating waves) along the fiber, each with a propagation constant along z. Guide modes resulting from meridional ray TE or TM type as in the case of the planar waveguide. Skew rays, on the other hand, give rise to modes that have both Ez and Bz
28、(or Hz) components and are therefore not TE or TM waves. They are called HE or EH modes as both electric and magnetic field can have components along z. They are called hybrid modes. It is apparent that guided modes in a step index fiber cannot be as easily described as those in the planar guide. 阶跃
29、折射率光纤阶跃折射率光纤 在阶越折射率光纤中，沿着光纤的方向子午光线和斜光线引起导模，他们沿z方向的传输常数为 。与平面波导的情况相同，子午光线的导模是TE或者TM波。另一方面，斜光线导致的模式具有Ez和Bz(Hz)的分量，因此不是TE或者TM波。他们称为HE或者EH模，因为沿着z具有电场和磁场的分量。他们被称为混合模式。在阶越折射率光纤中导模不象平面波导中描述的那样简单。Step Index Fiber Guided modes in a step index fiber with 1 (called weakly guiding fibers) are generally visualiz
30、ed by traveling waves that are almost plane polarized. They have transverse electric and magnetic fields (E and B are perpendicular to each other and also to z), analogous to field directions in a plane wave but the field magnitudes are not constant in the plane. Theses waves are called linearly pol
31、arized (LP) and have transverse electric and magnetic field characteristics. A guided LP mode along the fiber can be represented by the propagation of an electric field distribution E(r, ) along z. This field distribution, or pattern, is in the plane normal to the fiber axis and hence depends on r a
32、nd but not on z. Further, because of the presence of two boundaries, it is characterized by two integers, l and m. The propagating field distribution in an LP mode is therefore given by Elm (r,) and we represent the mode as LPlm。Thus, an LPlm mode can be described by a traveling wave along z of the
33、form,阶跃折射率光纤阶跃折射率光纤 在nbnc . Consider two close rays 1 and 2 launched from O at the same time but with slightly different launching angles. Ray 1 just suffers total internal reflection. Ray 2 becomes refracted at B and reflected at B.(a) A ray in thinly stratified medium becomes refracted as it passe
34、s from one layer to the next upper layer with lower n and eventually its angle satisfies TIR.(b) In a medium where n decreases continuously the path of the ray bends continuously. n decreases step by step from one layer to next upper layer; very thin layers.TIR(a)nContinuous decrease n in gives a ra
35、ypath changing continuously.TIR(b)Chapter 2 Dielectric Waveguides and Optical Fiberv 2.1 Symmetric planar dielectric Slab waveguidev 2.2 dispersion in the planar waveguide v 2.3 Step index fiberv 2.4 Numerical aperturev 2.5 Dispersion in single mode fibersv 2.6 Dispersion, electrical, and optical ba
36、ndwidthv 2.7 The graded index optical fiberv 2.8 Light absorption and scatteringv 2.9 Attenuation in optical fibersv 2.10 Fiber manufacture Optical Time Domain ReflectometerAn opto-electronic instrument used to characterize an optical fiber. Reyleigh scattering in optic fiberOptical Time Domain Refl
37、ectometer8 mW (9 dBm). Optical Time Domain ReflectometerChapter 2 Dielectric Waveguides and Optical Fiberv 2.1 Symmetric planar dielectric Slab waveguidev 2.2 dispersion in the planar waveguide v 2.3 Step index fiberv 2.4 Numerical aperturev 2.5 Dispersion in single mode fibersv 2.6 Dispersion, elec
38、trical, and optical bandwidthv 2.7 The graded index optical fiberv 2.8 Light absorption and scatteringv 2.9 Attenuation in optical fibersv 2.10 Fiber manufacture Si-O9mGe-O11mH-O 2.7mChapter 2 Dielectric Waveguides and Optical Fiberv 2.1 Symmetric planar dielectric Slab waveguidev 2.2 dispersion in
39、the planar waveguide v 2.3 Step index fiberv 2.4 Numerical aperturev 2.5 Dispersion in single mode fibersv 2.6 Dispersion, electrical, and optical bandwidthv 2.7 The graded index optical fiberv 2.8 Light absorption and scatteringv 2.9 Attenuation in optical fibersv 2.10 Fiber manufacture Vapors: SiC
40、l4 + GeCl4 + O2Rotate mandrel(a)Deposited sootBurnerFuel: H2Target rodDeposited Ge doped SiO2(b)FurnacePorous sootpreform with holeClear solidglass preformDrying gases(c)FurnaceDrawn fiberPreformSchematic illustration of OVD and the preform preparation for fiber drawing. (a) Reaction of gases in the
41、 burner flame produces glass soot that deposits on to the outside surface of the mandrel. (b) The mandrel is removed and the hollow porous soot preform is consolidated; the soot particles are sintered, fused, together to form a clear glass rod.(c) The consolidated glass rod is used as a preform in f
42、iber drawing.Fiber Manufacture OVDFiber Manufacture OVDFiber Manufacture MCVDPreform feedFurnace2000Thicknessmonitoring gaugeTake-up drumPolymer coaterUltraviolet light or furnacefor curingCapstanFiber Manufacture Fiber DrawingQuestions and Problems2.8 A multimode fiber2.9 A single mode fiber2.10 A single mode fiber design2.12 Waveguide dispersion2.17 Optical fibers2.18 Microbending loss
