由於光通訊的快速成長，高光學品質的光纖元件變成技術研發的重點。而由週期性空氣孔洞所組成的光子晶體光纖，因為其獨特的特性，如全光子能隙、零色散、無截止單模態、雙折射等，近年來也越來越受到重視。

所以本論文著重於探討光子晶體光纖的結構，對於其光子能帶結構與傳播特性的影響。此外，我們也提出另一創新概念，三維光子晶體光纖。並且首度利用LHPG生長方法生長光子晶體光纖，再進行光學量測。

在本論文中，我們利用RSoft模擬軟體研究二維、三維光子晶體光纖的光學特性。由模擬的結果可知，對於以Pyrex為材料，具有均勻空氣孔洞的二維光子晶體光纖而言，以0.7

Because of the fast growing in communications, the quality of signal transmission in optical fiber becomes very important. Concurrently, photonic crystal fiber (PCF) consisting of a central defect region surrounded by multiple air holes is attracting much attention in recent years because of its unique properties, such as full photonic bandgaps, wideband, dispersion, endlessly single mode and birefringence, etc.

This thesis is mainly focused on the development of the photonic band structures and propagation properties of PCF. And we propose a novel ideal about 3-D PCF, which can be fabricated using the laser heated pedestal growth (LHPG) method.

In the thesis, we study the optical properties of 2-D and 3-D PCFs made by Pyrex using the software RSoft. From the result of simulation, the 2-D out-of-plane bandgaps for a hexagonal close packed structure appear between the air filling fraction range from 0.30 to 0.88 for the incident light of wavelength range from 0.7 to 1

中文摘要 i
英文摘要 ii
目錄 iii
圖目錄 v
表目錄 x

第一章 緒論 1
1.1 簡介 1
1.2 研究動機 2
1.3 論文架構 3
第二章 光子晶體光纖之原理及應用 5
第三章 數值計算方法理論 12
3.1 前言 12
3.2 平面波展開法 12
3.3 有限差分時域法 16
3.4 有限元素法 22
第四章 光子晶體光纖結構設計及其模擬結果與分析 29
4.1 二維光子晶體光纖之結構設計 31
4.2 二維光子晶體光纖之模擬結果與分析 31
4.2.1 均勻空氣孔洞的二維光子晶體光纖之入平面
光子晶體模擬 32
4.2.2 均勻空氣孔洞的二維光子晶體光纖之出平面
光子晶體模擬 38
4.2.3 非均勻空氣孔洞的二維光子晶體光纖之出平
面光子晶體模擬 45
4.3 三維光子晶體光纖之結構設計 46
4.4 三維光子晶體光纖之模擬結果與分析 48
第五章 實驗量測結果與討論 53
5.1 LHPG生長法生長光子晶體光纖 53
5.2 光子晶體光纖之光學量測 64
第六章 結論 67

參考文獻 70
中英對照表 74

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