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研究生:劉得銓
研究生(外文):De Chung Liu
論文名稱:光子晶體能帶研究與最佳化結構設計
論文名稱(外文):Photonic band gap research and optimum structure design of photonic crystal
指導教授:張宗文張宗文引用關係
指導教授(外文):Zong Wen Zhang
學位類別:碩士
校院名稱:長庚大學
系所名稱:光電工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:89
中文關鍵詞:光子晶體平面波展開法有限時域差分法
外文關鍵詞:Photonic crystal、PWD、FDTD
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今日,光子晶體的研究已成為全世界注目的焦點課題。光子晶體是一種新型的光學材料,他是將不同介電常數的材料在一維、二維或三維空間內組成具有光波長等級的週期性結構,其根本的物理特性即是光子禁帶。另外,它還有其他獨特的物理特性如週期性結構、光子局域、偏振特性等。
本論文首先運用平面波展開法針對各種情形下的光子禁帶進行分析與計算,結果發現不同影響因子對光子禁帶都會產生影響。然後依據上述分析的結果找出光子禁帶的最佳化結構,並利用此結構模擬光子晶體的缺陷態。
光子晶體中的缺陷給人們提供了局域電磁波和引導電磁波的可能。隨著現代光通信、積體光學的發展,光子晶體越來越廣泛的應用在光通信與積體光學的眾多領域當中,光波導作為積體光學的主要組成的部份,其表現直接決定了積體光學整個元件的性能。因此,研究光子晶體對積體光學來說是一項非常重要的課題。
The research on photonic crystals has become a hotspot of discussion in the world nowadays. Photonic crystals are new type of optical materials. It was composed by permittivity with periodic structure which has the same order with wavelength of light in one、two and three dimension. The essential physical characteristic of photonic crystal is that the material has photonic band gap (PBG). The material has many other unique properties such as periodic structure, photonic localization, polarization etc.
First of all, we use plane wave expansion method (PWE) to analyze and calculate the PBG of different structure, and PBG rules are found by different factors. Then, we can found the optimum structure according to the results we have analyzed above, and use the optimum structure to simulate the defect state of photonic crystals.
The defect of photonic crystal can localize and guide electromagnetic. With the development of the optic communication and integrated optics, photonic crystal has been applied in various areas. Waveguide is the main configuration of the integrated optics and the performance of the integrated optics will be determined by waveguide. So it’s a very important assignment to study photonic crystal.
第一章 緒論……………………………………………………… ..- 1 -
1.1光子晶體的基本概念……………………………………...- 1 -
1.2光子晶體的製造…………………………………………...- 3 -
1.2.1 一維光子晶體……………………………………….- 3 -
1.2.2 二維光子晶體……………………………………….- 4 -
1.2.3 三維光子晶體……………………………………….- 6 -第二章 光子晶體的特性與應用………………………………….- 10 -
2.1光子晶體的物理特性…………………………………….- 10 -
2.1.1 光子晶體具有週期性結構………………………...- 10 -
2.1.2 光子晶體具有光子禁帶…………………………...- 11 -
2.1.3 抑制自發性輻射(Purcell效應) …………….……..- 12 -
2.1.4 光子局域…………………………………….……..- 13 -
2.1.5 偏振特性…………………………………….……..- 14 -
2.2光子晶體的應用………………………………………….- 14 -
2.2.1 光子晶體全反射鏡………………………………...- 15 -
2.2.2 微波天線…………………………………………...- 16 -
2.2.3 光子晶體LED和光子晶體雷射………………….- 16 -
2.2.4 寬帶及極窄帶選頻濾波器………………………...- 17 -
2.2.5 光子晶體波導和光子晶體光纖…………………...- 18 -
2.2.6 光子晶體偏振器…………………………………...- 19 -
第三章 光子晶體的研究方法……………………………………..- 21 -
3.1 平面波展開法(PWE) …………………………………....- 22 -
3.2 時域有限差分法(FDTD) ………………………………..- 30 -
3.2.1 FDTD的起源與回顧……………………………….- 30 -
3.2.2 Maxwell方程式和Yee晶格…………………….....- 34 -
3.2.3 三維直角座標中的FDTD………………………....- 37 -
3.2.4 二維直角座標中的FDTD………………………....- 41 -
3.3 解的穩定條件…………………………………………....- 45 -
3.4吸收邊界值條件………………………………………….- 47 -
第四章 二維光子禁帶因素影響分析與缺陷模態分析………….- 56 -
4.1 二維光子晶體製程方式對光子禁帶的影響…………....- 56 -
4.2 二維光子晶體晶格架構對光子禁帶的影響……….…...- 60 -
4.3 二維光子晶體材料折射率對光子禁帶的影響….……...- 66 -
4.4 二維光子晶體填充比對光子禁帶的影響………………- 71 -
4.5 二維光子晶體柱體形狀對光子禁帶的影響……………- 75 -
4.6 二維光子晶體缺陷模態分析……………………………- 80 -
4.6.1 點缺陷……………………………………………...- 80 -
4.6.2 線缺陷……………………………………………...- 82 -
4.6.3 分光器……………………………………………...- 83 -
第五章 結果討論與未來展望…………………………………….- 85 -
參考文獻…………………………………………………………...- 87 -
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