光纖為目前發展最為迅速的產業，且應用不只在通信上，在其他產業也廣泛被利用，對未來的科技的發展值得研究探討。本論文內容主要的工作是介紹光纖模態的理論，進而討論光纖的各種特徵及其被使用範圍，使的光纖能夠被準確的工作在任一位置上。第一章為緒論。第二章我們介紹了光纖的原理，對光纖有基本的認識。第三章介紹最簡單的平行波導，利用馬克斯威爾方程式去推導波導管的各種特性，進而了解TE模態及TM模態。第四、五、六章則推導基本的光纖總類，了解其模態場解、截止條件等，最後討論光纖的色散情況及原因。

Fiber is the fastest growing industries, and applications not only in communication but also has been widely used in other industries .For the future development of science and technology research worth exploring. The major work of this thesis is the introduction is optical mode of fiber, and then discuss the various features of the fiber and its scope is used to make the fiber can be accurately work in any position. The first chapter is an introduction. The second chapter we introduced the principle of optical fiber. The third chapter describes the most simple parallel waveguides using Maxwell's equations to derive various properties of the waveguide, and then understand TE mode and TM mode. The fourth, fifth and sixth chapters derive the basic fibers, understand their mode field solution, cut off conditions, and finally discuss fiber dispersion.

目錄
中文摘要............................I
英文摘要............................II
目錄................................III
圖表錄...............................V
第一章 緒論..........................1
第二章 光纖基本介紹..................3
    2-1歷史沿革......................3
    2-2優點..........................4
    2-3光纖結構......................4
    2-4光纖傳播原理..................5
    2-5光纖總類......................6
第三章 平行光波導....................9
    3-1馬克斯威爾方程式..............9
    3-2 TE模態.......................12
    3-3 TM模態.......................14
第四章 步階式折射率光纖..............16
    4-1模態場解......................16
    4-2截止條件......................20
第五章 弱波導光纖....................23
    5-1模態場解......................23
    5-2截止條件......................25
    5-3模態數目......................27
    5-4模態功率......................28
    5-5步階式單模光纖................30
 第六章 漸變式折射率光纖.............32
    6-1模態場解......................32
    6-2截止條件......................34
第七章 光纖的色散....................36
    7-1單模光纖色散..................37
    7-2多模光纖色散..................38
第八章 積體光學......................40
第九章 Bessel函數....................42
第十章 結論..........................49
參考文獻.............................50 

圖表目錄
圖2-1光纖結構示意圖......................4
圖2-2 光在光纖內全反射...................5
圖2-3光在介質間傳播......................5
圖2-4單模光纖............................7
圖2-5步階式折射率光纖....................8
圖2-6漸變式折射率光纖....................8
圖3-1電磁波示意圖.......................10
圖3-2TE模態電磁場方向...................12
圖3-3介質波導中TE模態的瞬時電力線與磁力線分佈....13
圖3-4TM模態電磁場方向...................15
圖3-5對稱平板波導的橫向模態圖...........15
圖3-6非對稱平板波導模態圖...............15
圖4-1 步階式折射率光纖圓柱座標..........16
圖4-2步階式光纖模態圖...................21
表4-1 光纖模態對應的規一化截止頻率......22
圖4-3 傳播模態數與V的關係...............23
圖5-1 光纖的橫切面......................23
圖5-2 模態空間圖........................28
圖5-3 不同模態在V值變化下所占能量比.....30
表5-1G.652單模光纖特性..................31
表6-1光纖特性資料.......................31
圖7-1光纖傳輸損耗理論與實際量測值.......38
圖7-2 步階式光纖示意圖..................38
圖7-3 色散關係圖........................39
圖9-1第一類Bessel 函數..................45
圖9-2第一類Bessel 函數..................45
圖9-3 第一類Modified Bessel’s函數......47
圖9-4 第二類Modified Bessel’s函數......48

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