使用長週期光纖光柵作為光放大器增益平坦化濾波器的元件，就各種結構的長週期光纖光柵的頻譜探討，歸納出其頻譜特性作為設計時的參考依據。針對於不同增益平坦化濾波器的目標頻譜特性使用不同的光柵結構，其中光柵參數的使用基因演算法決定，最後提出了利用長週期光纖柵設計濾波器的流程，且歸納出設計長週期光纖光柵濾波器的心得。於本論文中，使用長週期光纖光柵對摻鉻釔鋁石榴石晶體光放大器(Cr:YAG optical amplifier)，EDFA 光纖放大器(Erbium-
doped optical amplifier)，的增益頻譜作增益平坦化;一者達成接近300nm 的頻寬，一者達成接近40nm 的頻寬。

Using Long-Period Fiber Gratings as component of Gain-Flattening filter ofOptical Amplifier, and discuss spectrum of different struture of Long-Period Fiber Gratings. To investigate the spectra characteristics of Long-Period fiber Gratings for designing reference resources. Aiming at different Gain-Flattening filter uses different struture of fiber grating, and the decision of parameter of fiber grating using Genetic Algorithm. Finally delcaring the dataflow of designing filter using Long-Period Fiber
Grating and conclusion.In this paper , gain flatttening Cr:YAG optical amplifier spectrum and Erbium-doped optical amplifier spectrum,one achieve 300nm bandwidth and
another achieve 40nm.

第一章序論．．．．．．．．．．．．．．．．．．．．．．． １
1.1 研究背景與動機．．．．．．．．．．．．．．．．．．． １
1.2 長週期光纖光柵作為增益平坦化濾波器．．．．．．．．． １
1.3 光纖光柵的各種方法．．．．．．．．．．．．．．．．． １
1.4 論文大綱．．．．．．．．．．．．．．．．．．．．．．２
第二章光纖光柵的簡介及數學分析工具．．．．．．．．．．． 6
2.1 光纖光柵的歷史簡介．．．．．．．．．．．．．．．．． 6
2.2 光纖光柵的原理簡介．．．．．．．．．．．．．．．．． 8
2.3 長週期光纖光柵的製作方式．．．．．．．．．．．．．． 9
2.4 光柵的應用．．．．．．．．．．．．．．．．．．．．．10
2.5 Coupled Mode Theory．．．．．．．．．．．．．．．．12
第三章長週期光纖光柵的模擬與討論．．．．．．．．．．．．19
3.1 前言．．．．．．．．．．．．．．．．．．．．．．．．19
3.2 長週期光纖光柵的數學模型．．．．．．．．．．．．．．19
3.3 推導長週期光纖光柵的close form solution．．．．．．23
3.4 均勻長週期光纖光柵模擬結果與討論．．．．．．．．．．25
(A) dc n 和頻譜響應的關係
(B) ac n 和頻譜的關係
(C)光柵週期長度和頻譜的關係
(D)固定中心波長，改變耦合模態
(E)單一均勻光纖光柵長度和頻譜的關係
(F)cladding 的半徑大小和頻譜的觀係
3.5 Phase-shift long period fiber grating．．．．．．．．33
3.6 Phase-Shift Long-Period Fiber Grating 的模擬結果及討論．．．．35
3.7 結論．．．．．．．．．．．．．．．．．．．．．．．37
第四章基因演算法．．．．．．．．．．．．．．．．．．．39
4.1 基因演算法簡介．．．．．．．．．．．．．．．．．．39
4.2 基因演算法於數值的描述方式．．．．．．．．．．．．39
4.3 基因演算法．．．．．．．．．．．．．．．．．．．．39
4.4 基因演算法的資料結構．．．．．．．．．．．．．．．43
4.5 驗證基因演算法．．．．．．．．．．．．．．．．．．45
4.6 結論．．．．．．．．．．．．．．．．．．．．．．．47
第五章光放大器的增益平坦化設計．．．．．．．．．．．．49
5.1 前言．．．．．．．．．．．．．．．．．．．．．．．49
5.2 增益平坦化濾波器的設計流程．．．．．．．．．．．．49
5.3 Cr:YAG 光放大器的架構．．．．．．．．．．．．．．50
5.4 Cr-coped 光放大器的增益平坦化．．．．．．．．．．51
5.5 EDFA 光纖放大器(Erbium-doped fiber amplifier)的簡介．．．．．．．62
5.6 EDFA 增益平坦化CASE 1．．．．．．．．．．．．．．63
5.7 EDFA 增益平坦化CASE 2．．．．．．．．．．．．．．68
第六章結論與未來工作．．．．．．．．．．．．．．．．73

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