我們可以利用改變光子晶體光纖的孔洞大小以及週期間距來得到許多獨特的光學特性，但是製作好的光子晶體光纖，其結構參數已經固定，因此其光學特性難以改變。如果在光子晶體光纖的空氣孔洞內填入可調控的液體材料，便可使光子晶體光纖元件擁有可調變的特性。
本論文中，我們模擬在光子晶體光纖中填入可調控材料，藉由改變可調控材料之折射率並與實驗結果相比較，以得知液體填充光子晶體光纖的傳輸特性以及液晶等效折射率對於外在照光、電場、溫度變化的關聯性。首先我們使用三維光束傳播法模擬液體填充光子晶體的傳輸頻譜，以確認此模擬方法的可行性。接著模擬不同液晶等效折射率的傳輸頻譜，發現當外加電場上升到90V時，由於此區間的電壓太小無法驅使液晶轉動，因此液晶等效折射率差只有小幅度地上升0.025。當外加電場由90V加到200V時，由於此區間的電場足夠拉動液晶排列，導致液晶等效折射率差上升0.063。而當操作溫度由40oC升溫到59oC時，由於此時溫度靠近相變點，造成液晶no急遽地上升，導致液晶等效折射率差大幅增加了0.064。
最後模擬不同等效折射率下的光控液晶光子晶體光纖之傳輸頻譜，我們觀察摻雜不同4MAB濃度的光控液晶混合物發現，當照射藍光時間5秒時，液晶等效折射率差上升趨勢相似，但由於20wt%4MAB濃度之光控液晶混合物其大部分trans態已轉換成cis態，因此在照射藍光時間5到25秒區間，液晶等效折射率差只平緩增加了0.002，而25wt%以及30wt%4MAB濃度的液晶混合物，則在同樣照射時間區間下，其液晶等效折射率差分別增加了0.0062以及0.008。

The unique optical properties of photonic crystal fibers (PCFs) are mainly determined by the size and distribution of the air holes in the fiber cladding region. However, it is difficult to modulate the optical properties of fabricated PCFs due to the fixed geometries. By filling index-tunable materials into the air holes of PCFs, we can realize tunable PCFs.
In this thesis, we simulate the optical properties of PCFs filled with index-tunable materials. The relationships between the effective index of the liquid crystal (LCs) and the external environment (illumination, electric field, temperature) are determined. We first use a 3-D beam propagation method (BPM) to simulate the transmission spectra of the photonic liquid crystal fibers (PLCFs). The results show that as the applied voltage is from 0V to 90V, the effective index of LCs raises only 0.025. As the applied voltage is from 90V to 200V, the effective index of LCs increases by 0.063. Next, we demonstrate tunable of the effective index of the LCs by changing the temperature. The effective index of LCs increases rapidly as the operation temperature is from 40oC to 59oC.
We also simulate the transmission spectra of the light-controllable PLCFs with variant 4MAB concentrations. The results show that as the blue-laser irradiation time is 5 seconds, the effective indices of LCs doped with variant concentrations of 4MAB are the same. However, as the blue-laser irradiation time is from 5 to 25 seconds, the effective index of LCs doped with 20wt% 4MAB only increases 0.002. On the contrary, the effective indices of LCs doped with 25wt% and 30wt% 4MAB increase by 0.0062 and 0.008, respectively.

誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
第一章 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1-1 光子晶體. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1-2 光子晶體光纖介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
1-3 液體光子晶體光纖 . . . . . . . . . . . . . . . . . . . . . . . . . . .5
1-4 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
第二章 波束傳播法及其在光纖元件上的模擬應用. . . . . . . . . . . . . .14
2-1 波束傳播法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
2-2 光纖干涉儀. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
2-3 中空光纖干涉儀. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
2-3.1 光子晶體光纖的錯位結構. . . . . . . . . . . . . . . . . . . .25
第三章 液體填充光子晶體光纖元件之特性分析. . . . . . . . . . . . . . . .28
3-1 液體填充光子晶體光纖元件之特性模擬. . . . . . . . . . . . . . . . . . .28
3-2 液體填充光子晶體光纖元件之溫度調變特性模擬. . . . . . . . . . .31
3-3 選擇性液體填充光子晶體光纖元件之特性模擬. . . . . . . . . . . . . .32
3-3.1 選擇性液體填充光子晶體光纖濾波器之折射率調變
特性模擬. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
第四章 液晶光子晶體光纖元件之特性分析 . . . . . . . . . . . . . . . .38
4-1 液晶簡介. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
4-1.1 液晶光子晶體光纖之外加電場調控特性模擬. . . . . . . .39
4-2 液晶光子晶體光纖之溫度調控特性模擬. . . . . . . . . . . . . . . .43
4-3 不同照射時間下之光控液晶光子晶體光纖之特性模擬. . . . . . . .47
4-4 光控液晶光子晶體光纖之溫度調控特性模擬. . . . . . . . . . . . .57
第五章 結論與未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68

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