Summary of Lecture 20 TE0m mode TM0m mode Cutoff condition.

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1 Summary of Lecture 20 TE0m mode TM0m mode Cutoff condition

2 Summary of Lecture 20 EH modes HE modes (no HE11)

3 §12.3 Linearly Polarized Modes
Consider a fiber whose core refractive index is only slightly higher than that of the cladding medium, i.e., Such that H and E tangential component at the interface become identical. We may use Cartesian coordinate system to solve the wave equation with tremendous simplification. Assume: We now start solve the wave equation for the transverse filed components. The first case

4 §12.3 Linearly Polarized Modes
Coordinate Relation Bessel Function Relation and

5 §12.3 Linearly Polarized Modes
Solutions Core Cladding

6 §12.3 Linearly Polarized Modes
are the dominant field components Continuity condition requires is determined by the normalization condition The second case

7 §12.3 Linearly Polarized Modes
Solutions Core Cladding

8 §12.3 Linearly Polarized Modes
are the dominant field components So for both cases, the modes are nearly transverse and linearly polarized along the x or y direction. And two types guided modes whose transverse fields are polarized orthogonally to each other. Continuous conditions: Case I

9 §12.3 Linearly Polarized Modes
gets the same results. For case II, we also have the same results, which means two transversely orthogonal modes are degenerate in the propagation constant. Moreover the above equation are equivalent. Compare to the eq. (3.3-11), which has two solution, this indicates above solution is twofold degenerate. More detail comparison shows that the linearly polarized modes are actually a superposition of HEl+1,m and EHl-1,m modes. The mode cutoff condition is given by q=0

10 §12.3 Linearly Polarized Modes
The 1st zero No cutoff for The 2nd zero The 1st zero

11 §12.3 Linearly Polarized Modes
Two orthogonal HE

12 §12.4 Pulse Propagation and Pulse Spreading in Fibers
Pulse Broadening Group velocity dispersion limits the pulse width reduction. Group velocity Pulse spreading constant Field envelope Pulse duration Initial pulse width Pulse width after L For larger L

13 §12.4 Pulse Propagation and Pulse Spreading in Fibers
Group velocity dispersion Pulse width after L Group velocity dispersion is due to two mechanisms: (1) Meterial dispersion: the index of refraction depends on (2) Waveguide dispersion: the propagation constant depends on (a) Modal Dispersion: different modes have different group velocity Such as multimode waveguides (b) Group velocity dispersion Such as singlemode waveguides

14 §12.4 Pulse Propagation and Pulse Spreading in Fibers
Material dispersion Waveguide dispersion Assume

15 §12.4 Pulse Propagation and Pulse Spreading in Fibers
Frequency Chirp

16 §12.5 Compensation For Group Velocity Dispersion
(1) Compensation with opposite dispersion (2) Compensation by phase conjugation

17 §12.6 Attenuation in Silica Fibers
本征吸收、本征色散和OH-吸收 本征吸收：光子激发光纤中的电子到高能态时引起的损耗，比如紫外吸收。此外光子与本征晶格相互作用也会产生损耗，表现为红外吸收。 本征色散：包括瑞利散色、米氏散色、受激布里渊散色、受激拉曼散色等。其中比波长小的粒子引起瑞利散色；与波长相比拟的粒子引起米氏散色。瑞利散色为主要的本征散色，散色光强度与波长四次方成反比，因此光纤通信波长多为长波。 OH-吸收：主要由OH-离子振动的吸收产生。这些吸收峰将光纤通信波长选为三个波长窗口： 0.85um、1.31um和1.55um。

18 §12.7 Several Kinds of Fibers
石英光纤 石英多模光纤 应用与数据链、局域网等短距离通信，以及光纤传感技术和激光医学等领域 阶跃型多模光纤 梯度型多模光纤

19 §12.7 Several Kinds of Fibers
石英单模光纤 纤芯直径小，纤芯-包层折射率小，是一种理想的光通信传输媒质。 非色散位移石英单模光纤 （G.652A/B/C） 色散位移石英单模光纤 （G.653） 截止波长位移石英单模光纤 （G.654） 非零色散位移石英单模光纤 （G.655A/B）

20 §12.7 Several Kinds of Fibers
色散补偿石英单模光纤 色散平坦石英单模光纤

21 §12.7 Several Kinds of Fibers
石英保偏单模光纤 同时传播两个偏振正交基膜，并没有双折射现象 鞍槽型光纤：绝对单偏光纤，但归一化频率很窄，缺乏实用性。 熊猫型光纤 椭圆型光纤 蝴蝶结型光纤

22 §12.7 Several Kinds of Fibers
塑料光纤 PMMA，PS，PC 具有电磁兼容性、电绝缘、防窃听、材料轻、传输信息容量大等优点

23 §12.7 Several Kinds of Fibers
光纤光栅

24 §12.7 Several Kinds of Fibers
光子晶体光纤 空气孔纤芯 导光机制为布拉格衍射 石英孔纤芯 导光机制为全内反射 蜂窝状空气纤芯 光子带隙效应