光子晶體光纖分為兩種不同種類。第一種為介質導波(index-guiding)光子晶體光纖，藉由二氧化矽的核心區域和由空氣孔洞組成的包覆層所產生的全反射機制導光。另外一種是藉由完美週期性結構所存在的能隙效應使光傳導到折射係數的核心區域。
本論文中使用由時域有限差分法衍生的compact 2D-FDTD來分析介質導波光子晶體光纖和光子能隙光纖。我們研究介質導波光子晶體光纖基模模態傳播的特性、有效折射係數、模場直徑和顏色色散。藉由調整介質導波光子晶體光纖各圈的空氣孔洞直徑和整體空氣孔洞間距，我們可以在一個很寬的波長範圍同時控制色散和色散斜率。我們也同時研究光子能隙光纖的基模模態傳播特性和能隙效應。

Photonic crystal fibers (PCFs) are divided into two different kinds of fibers. The first one, index-guiding PCF, guides light by total internal reflection between a solid core and a cladding region with multiple air-holes. On the other hand, the second one uses a perfectly periodic structure exhibiting a photonic band-gap (PBG) effect at the operating wavelength to guide light in a low index core-region.
A compact 2D-FDTD method based on finite-difference time-domain method is formulated and is effectively applied to analysis PCFs and PBGFs. We study the propagation features of fundamental mode and the fundamental characteristics such as effective index, modal-field diameter and chromatic dispersion in index-guiding PCFs. By optimizing the air-hole diameters and the hole-to-hole spacing of index-guiding PCFs, both the dispersion and the dispersion slope can be controlled in a wide wavelength range. We also investigate the propagation features of fundamental mode and band-gap effect of PBGFs.

第一章 序論1.1 研究背景與目的
1.2 論文大綱

第二章 時域有限差分法
2.1 3D-FDTD演算法
2.2 Compact 2D-FDTD演算法
2.2.1 Compact 2D-FDTD理論推演
2.2.2 Compact 2D-FDTD穩定準則
2.2.3 Compact 2D-FDTD吸收邊界
2.2.4 Compact 2D-FDTD數值程序
2.3 Compact 2D-FDTD 計算二維光子晶體能隙

第三章 光子晶體光纖的模擬與特性分析
3.1 概論
3.2 傳播模態分析
3.2.1 基模模態場型分佈和極化分析
3.2.2 有效折射係數與波長關係
3.2.3 正規化頻率
3.2.4 模場直徑
3.2.5 接合損耗
3.3 顏色色散分析
3.3.1 材料色散
3.3.2 波導色散
3.3.3 顏色色散
3.3.4 顏色色散的設計

第四章 光子能隙光纖的模擬與特性分析
4.1 概論
4.2 二維光子晶體能隙
4.3 傳導模態分析

第五章 結論
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