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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 趙聖德 | |
dc.contributor.author | Jyun-Jie Wang | en |
dc.contributor.author | 王俊傑 | zh_TW |
dc.date.accessioned | 2021-06-15T04:52:21Z | - |
dc.date.available | 2013-08-12 | |
dc.date.copyright | 2010-08-12 | |
dc.date.issued | 2010 | |
dc.date.submitted | 2010-07-30 | |
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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/46049 | - |
dc.description.abstract | 為了快速尋找最大完全帶隙,我們希望可以正確判斷尋找的方向。所以本論文主要使用平面波展開法的理論模擬方法來研究不同的介電質材料圓柱經過週期排列後而形成不同結構的二維光子晶體。對由低到極高的材料參數與幾何參數做進一步分析,探討其最大完全帶隙與各參數間的關係。我們將完全帶隙、TM模態與TE模態帶隙頻率對各可變參數做分析後,發現TM與TE帶隙邊緣頻率值相同時會有最大完全帶隙,亦即最佳結構會出現在TM與TE模態帶隙邊緣頻率相同的情況。且根據最大完全帶隙與TE、TM帶隙的關係,我們可發現完全帶隙是由TE模態來決定。
觀察由低到極高的材料參數以及幾何參數之頻帶圖,可發現幾何填充率與材料參數增加則帶隙邊緣頻率會有紅移現象,所有頻帶的紅藍移有一致性,且帶隙大小是取決於頻帶的紅藍移速度。而最大完全帶隙都落在高頻帶區域,且在高頻帶區的特性與之前研究低頻帶的帶隙特性有很大不同。另外,完全帶隙附近的頻帶隨著參數改變有很明顯的重光子現象,我們發現重光子現象在高介電質材料時會趨於飽和,而幾何結構造成的重光子現象則取決於完全帶隙的大小。 | zh_TW |
dc.description.abstract | In this paper, we employ a plane wave expansion method to calculate the band structures of two-dimensional photonic crystals. For the types of photonic crystal, we have studied square lattice, triangular lattice, honeycomb lattice of circular columns, each connected to its nearest neighbors by rectangular rods.
We explore the relation of the radius r/a and the dielectric constant ε of rods, the width d/a of connecting rods to determine full band gaps. The dispersion curves for the TM and TE modes of the propagating electromagnetic waves have been analyzed separately. We found some characteristics of full band gaps : (1)When TM and TE mode band gaps have approaching the same band edges, maximum full band gaps occur. (2) Unlike the fundamental band gap which usually opens larger in low-lying bands, we obtain the maximum full band gap to open with high-lying bands. When changing the parameter, the dispersion curves around the full band gap are dense and flat. Material and geometry parameters can affect heavy photon state, but material parameter affect more than geometry parameters. The band structure exhibits a red shift phenomenon in frequency as the geometrical fill factor and material parameter increase. The width of band gaps have depends on the velocity of frequency shift. (4)For honeycomb lattice, we added the connecting rods and obtain the full band gaps which are smaller than the full band gaps of no connecting rods. (5) Band gaps of TE mode is very much more variation than band gaps of TM mode. | en |
dc.description.provenance | Made available in DSpace on 2021-06-15T04:52:21Z (GMT). No. of bitstreams: 1 ntu-99-R97543069-1.pdf: 5218235 bytes, checksum: 06c3eb5ea75271ef4dee0d67278e70fa (MD5) Previous issue date: 2010 | en |
dc.description.tableofcontents | 口試委員會審定書 #
誌謝 i 中文摘要 ii ABSTRACT iii 總目錄 v 圖目錄 viii 表目錄 xi Chapter 1 簡介 1 1.1 緒論 1 1.1.1 研究動機 1 1.1.2 光子晶體介紹 2 1.2 重要文獻回顧 7 1.3 論文導覽 10 Chapter 2 基本理論與數值方法 11 2.1 馬克士威爾方程式 12 2.2 週期介電質分佈與布洛赫定理 14 2.2.1 週期介電質分佈 14 2.2.2 布洛赫定理 15 2.3 比例定律 18 2.4 光子晶體能帶結構 19 Chapter 3 光子晶體的帶隙分析 25 3.1 二維正方晶格光子晶體 26 3.2 二維三角晶格光子晶體 30 3.2.1 三角晶格-介電質圓柱 31 3.2.2 三角晶格-空氣圓柱 34 3.3 二維六角晶格光子晶體 37 3.4 最大完全帶隙特性分析 40 3.4.1 最大完全帶隙對圓柱半徑分析 42 3.4.2 最大完全帶隙對介電質分析 45 3.4.3 最大完全帶隙對連接柱寬度分析 48 3.4.4 頻帶圖分析 51 3.4.5 討論 61 Chapter 4 光子晶體電磁場應用-與淺水波的比較 64 4.1 統御方程式 64 4.1.1 動量方程式 64 4.1.2 TE模態電磁波方程式 65 4.1.3 流場與磁場關係式 66 4.2 電磁場分析 66 Chapter 5 結論與未來展望 72 5.1 結論 72 5.2 未來展望 73 參考文獻 74 附錄一 78 附錄二 81 | |
dc.language.iso | zh-TW | |
dc.title | 計算分析高介電質材料光子晶體的最大完全帶隙特性及應用 | zh_TW |
dc.title | Calculation of the high dielectric contrast photonic crystals with maximal full band gaps | en |
dc.type | Thesis | |
dc.date.schoolyear | 98-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 張家歐,吳政忠,欒丕綱 | |
dc.subject.keyword | 光子晶體,高介電質,完全帶隙,米氏共振,重光子態, | zh_TW |
dc.subject.keyword | Photonic crystals,full band gap,high dielectric,Mie resonance,heavy photon state, | en |
dc.relation.page | 83 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2010-08-02 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 應用力學研究所 | zh_TW |
顯示於系所單位: | 應用力學研究所 |
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