臺灣博碩士論文加值系統

本論文之研究是一階與二階布拉格光纖光柵模擬，我們使用Floquet-Bloch理論去分析布拉格光纖光柵，以Floquet-Bloch的形式能夠嚴格的求解出光纖光柵的傳播常數和場分布，然後考慮光柵區與無光柵區之間的不連續邊界，我們使用Mahmoud-Beal’s方法計算出傳輸效率與反射效率，再取n=-1 的諧波去計算輻射效率，綜合上述方法便可以得到布拉格光纖光柵的頻譜，在一階布拉格的部分，我們比較了FBT與CMT差異，在二階布拉格的部分，我們有兩組實驗結果並且嘗試由模擬去符合實驗的結果，而我們使用矩形光柵並且改變duty cycle來模擬出與實驗相近的結果。

This study is modeling of first and second order Fiber Bragg Gratings in this paper, we use the Floquet-Bloch Theory to analyze Fiber Bragg Gratings, the Floquet-Bloch formalism can rigorously solve to propagation constant and field distribution, and then consider the discontinuous interface between the grating region and non-grating region, we use the Mahmoud-Beal’s method to calculate transmission efficiency and reflection efficiency, and take the n=-1 harmonic to calculate the radiation efficiency, sum above method can obtain the Fiber Bragg Gratings spectrum, in first Bragg part, we compare difference of FBT and CMT, in second Bragg part, we have two experiment results and try to match experiment results with simulation, and we use rectangular grating and change the duty cycle to simulate experiment results.

中文摘要 I
英文摘要 II
目錄 III
圖目錄 V
表目錄 VIII
第一章 緒論 1
1.1 前言 1
1.2 研究背景與動機 2
1.3 研究方法 4
1.4 論文架構 5
第二章 場理論分析 6
2.1 Floquet-Bloch理論 6
2.2 光柵區外電磁場 7
2.2.1 第二層之電磁場分佈 11
2.3 光柵層傅立葉級數展開 15
2.3.1 矩形光柵 15
2.3.2 弦波光柵 18
2.4 光柵區的電磁場 23
2.4.1 無光柵之光纖電磁場23
2.4.2 有光柵之光纖電磁場 27
2.4.3 有光柵之光纖電磁場空間諧波表示式 29
2.4.3.1 Ez對r微分的表示式 29
2.4.3.2 Hz對r微分的表示式 32
2.4.3.3 Ephi對r微分的表示式 34
2.4.3.4 Hphi對r微分的表示式 36
2.4.4 以Runge-Kutta Method求解電磁場解 39
2.5 邊界條件與特徵方程式 48
2.6 橫向波數的分支選擇 49
第三章 傳輸、反射與輻射理論 52
3.1 有限長度光柵的電磁場 53
3.2 傳輸效率和反射效率 56
3.3 輻射效率 62
第四章 一階布拉格光纖光柵 64
4.1 空間諧波數 64
4.2 Dispersion relationship 72
4.3 Spectrum of Transmission and Reflection 82
4.4 與CMT的頻譜比較 91
第五章 二階布拉格光纖光柵 93
5.1 空間諧波數 93
5.2 Dispersion relationship 99
5.3 Spectrum of Transmission, Reflection and Radiation 110
5.4 不同r值的輻射 116
5.5 改變duty cycle的影響 117
5.6 理論模擬與實驗比較 122
第六章 結論 129
參考文獻 131

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