臺灣博碩士論文加值系統

本論文利用光纖結構的公式，發展出分析多層光纖結構的軟體，以用來分析光纖的特性。在論文中我們首先與過去發表過的論文比較數據，並且獲得相同的結果。我們繼而計算多種光纖結構的色散值，其中包含色散位移光纖與色散平坦光纖的色散值，並且探討光纖結構之參數對色散的影響。最後我們以phase-matching condition來分析Acoustics-Induced Fiber Bragg Grating反射器的物理特性，根據實驗量測的傳輸與反射頻譜之圖形，分析元件的反向與順向的耦合效應，同時討論光纖結構之參數的改變對反射器的影響。

In this thesis we developed numerical software to analyze the characteristics of the optical fiber. Our results are consistent with those of published papers. We also calculated dispersions of many optical fiber profiles including dispersion-shifted fiber and dispersion-flattened fiber. Furthermore, we discussed the relationship between parameters of fibers and dispersions. Finally, we analyzed the properties of the acoustics-induced fiber Bragg grating reflector by using the phase-matching conditions. Both the contra- and co- directional coupling mechanisms are applied to illustrate the transmission and reflection spectrum of the device. We also discussed the relationship between device parameters and the device.

中文摘要…………………………………………………………………………i
英文摘要…………………………………………………………………………ii
致謝………………………………………………………………………………iii
目錄………………………………………………………………………………iv
圖目錄…………………………………………………………………………... vi
表目錄……………………………………………………………………………viii
第一章 緒論…………………………………………………………………. 1
1.1 前言……………………………………………………………….. 1
1.2 研究動機………………………………………………………….. 1
1-3 論文架構………………………………………………………….. 5
第二章 理論推導…………………………………………………………….. 6
2.1 前言………………………………………………………………... 6
2.2 兩層步階型光纖結構……………………………………………… 6
2.2.1波動方程式…………………………………………………….. 6
2.2.2兩層結構的特徵方程式……………………………………….. 10
2.2.3模式判定……………………………………………………….. 12
2.2.3.1 TE與TM mode的判別方法…………………………… 12
2.2.3.2 EH與HE mode的判別方法…………………………… 13
2.2.4係數求法……………………………………………………….. 16
2.2.4.1 TE與TM 模式係數之求法…………………………. 16
2.2.4.2 EH與HE 模式係數之求法…………………………... 16
2.3 以Runge-Kutta方法求解漸變型光纖結構………………………. 17
2.3.1微分方程式………..…………………………………………….17
2.3.2 Runge-Kutta 方法 …………………………………………… 19
第三章 數值方式的比較………………………………………………………21
3.1 前言………………………………………………………………….21
3.2 數值方法比較……………………………………………………….21
3.2.1求解兩層步階型光纖的比較…………………………………...21
3.2.2求解兩層漸變型光纖…………………………………………...22.
3.3 數值結果…………………………………………………………….25
3.3.1 步階型結構的模擬分析………………………………………..25
3.3.2 漸變-步階型結構的模擬分析………………………………… 26
3.3.3 漸變型結構的模擬分析………………………………………..27
第四章 光纖色散模擬結果分析………………………………………………33
4.1 前言………………………………………………………………….33
4.2 色散的種類……………………………………………………….…33
4.3 色散的計算………………………………………………………….34
4.3.1材料色散計算方式…………………………………………… 35
4.3.2波導色散的算法……………………………………………… 36
4.3.3近似法求解波導色散………………………………………… 37
4.3.4數值微分求解色散…………………………………………… 38
4.4 色散計算結果………………………………………………………. 40
4.4.1色散位移光纖………………………………………………… 40
4.4.1.1步階型光纖的色散位移………………………………….41
4.4.1.2漸變型光纖的色散位移………………………………….43
4.4.1.3多層結構光纖的色散位移…………………………………. 43
4.4.2色散平坦光纖………………………………………………… 45
4.4.2.1第二層半徑變化對色散的影響……………….………... 46
4.4.2.2第二層折射率的變化對色散的影響…………………….47
4.5 總結…………………………………………………………………. 48
第五章 Acoustics-Induced Fiber Bragg Grating反射器分析………………… 60
5.1 實驗結構……………………………………………………………...60
5.2 實驗結果……………………………………………………..……… 60
5.3 數值結果…………………………………………………………… 61
5.4 結果討論…………………………………………………………… 67
5.4.1改變光纖的折射率的影響……………………………………… 67
5.4.2光纖半徑的影響………………………………………………… 68
5.4.3微彎週期的影響………………………………………………… 69
5.4.4光纖的披覆的影響………………………………………………. 70
第六章 結論…………………………………………………………………….79
參考文獻………………………………………………………………………… 81
圖目錄
圖2-1兩層步階型光纖………………………………………………………… 20
圖2-2兩層漸變型光纖………………………………………………………… 20
圖3-1 漸變型光纖切割為多層示意圖………………………………………... 29
圖3-2 三種不同折射率形式的光纖結構與半徑的關係圖…………………... 29
圖3-3a 步階結構的色散曲線…………………………………………………. 30
圖3-3b以推導的公式計算得到步階結構的色散曲線……………………….. 30
圖3-4a 漸變-步階結構的色散曲線…………………………………………… 31
圖3-4b以推導的公式計算得到漸變-步階結構的色散曲線…………………. 31
圖3-5a 漸變結構的色散曲線…………………………………………………. 32
圖3-5b以推導的公式計算得到漸變結構的色散曲線……………………….. 32
圖4-1 脈衝延展示意圖………………………………………………………... 49
圖4-2步階型光纖的材料色散、波導色散、總色散………………………… 49
圖4-3四種材料製成光纖的材料色散………………………………………… 50
圖4-4近似公式對於半徑不同所得到的波導色散與其材料色散…………… 50
圖4-5 數值微分法所得不同半徑的色散圖……………………………………51
圖4-6 數值微分法求得步階型光纖的色散總色散……………………………51
圖4-7半徑對於步階型光纖零色散點的關係圖……………………………….52
圖4-8 漸變型色散位移光纖折射率與半徑的關係圖…………………………52
圖4-9傳統步階型光纖,三角形結構,與多層結構的波導色散曲線…………. 53
圖4-10 W形光纖結構與其參數………………………………………………..53
圖4-11三角形漸變型光纖在包層一個環形………………………………….. 54
圖4-12三角形＋環形結構,改變第二層的半徑所得到的色散位移…………. 54
圖4-13 計算步階型光纖,三角形結構,與多層結構的波導色散曲線………... 55
圖4-14 W型色散平坦光纖結構,改變第二層厚度…………………………….55
圖4-15 W型光纖改變第二層厚度所得到的色散曲線………………………. 56
圖4-16改變W型光纖第二層厚度所得到的色散曲線……………………….56
圖4-17改變W型光纖第二層折射率示意圖………………………………….57
圖4-18 改變W型光纖第二層折射率所得到的色散曲線…………………... 57
圖4-19 改變W型光纖第二層折射率所得到的色散曲線…………………... 58
圖5-1實驗結構圖……………………………………………………………… 71
圖5-2實驗所量測到的傳輸頻譜圖…………………………………………… 71
圖5-3實驗所量測到的反射頻譜……………………………………………… 72
圖5-4光纖結構與前八個模式的等效折射率分佈圖形……………………… 72
圖5-5反向耦合示意圖………………………………………………………… 73
圖5-6a 纖芯模式(LP01)反向傳播與順向傳播模式…………………………… 73
圖5-6b 纖芯模式(LP01)反向傳播與順向傳播模式…………………………… 74
圖5-7同向耦合的示意圖……………………………………………………… 74
圖5-8 順向耦合長度為452μm時,LP01、LP11、LP21的色散曲線…………. 75
圖5-9 順向耦合長度為452μm時,LP01、LP31、LP41的色散曲線…………. 75
圖5-10a 改變包層半徑時,模式等效折射率的變化圖………………………. 76
圖5-10b LP01反向傳播模式與包層順向模式相交圖………………………… 76
圖5-11 在半徑為29μm,傳播常數與波長的關係圖…….…………………... 77
圖5-12 λB=1.5415μm時非同向耦合波長與包層半徑的關係圖………….. 77
圖5-13 微彎曲週期與圖5-12中耦合波長的關係圖………………………… 78
圖5-14 披覆層折射率對模式等效折射率的關係圖…………………………..78
表目錄
表3-1 兩層步階型光纖以兩種方法求解比較表……………………………..22
表3-2 兩層漸變型光纖以兩種方法求解比較表……………………………..24
表4-1 材料折射率的係數………………………………………………….….36
表5-1 各模式與耦合波長的關係……………………………………………..64
表5-2 以長週期光柵計算求得耦合模式波長與光柵週期…………………..65
表5-3 在第二階耦合時，耦合模式等效折射率與光柵週期………………..66
表5-4 以短週期光柵計算，耦合模式波長與光柵週期……………………..68
表5-5 順向包層模式與反向纖芯模式的耦合波長…………………………..69

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