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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 趙聖德(Sheng-Der Chao) | |
| dc.contributor.author | Ssu-Che Wang | en |
| dc.contributor.author | 王思哲 | zh_TW |
| dc.date.accessioned | 2021-06-17T00:24:01Z | - |
| dc.date.available | 2015-06-27 | |
| dc.date.copyright | 2012-06-27 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-05-17 | |
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Sheng, “Two-Dimensional Photonic Band Structures”, Optics Communications 80, pp. 199-204(1991). [29] M Plihal, A. Shambrook, A. A. Maradudin, “Photonic Band Structures of Two-Dimensional Systems: The Triangular Lattice”, Phys. Rev. B 44, pp. 8565-8571(1991). [30] R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a Photonic Band Gap in Two Dimensions”, Appl. Phys. Lett. 61, pp3 495-497 (1992). [31] J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic Crystals: putting a new twist on light”, Nature 386, 143-149 (1997). [32] J. D. Joannopoulos, R. D. Meade, J. N. Winn, “Photonic Crystals-Molding the Flowing of Light”, Princeton University Press (1995). [33] R. L. Chern, C. C. Chang, C. C. Chang, R. Hwang, “Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration”, Phys. Rev. E 68, 26, 704 (2003). [34] R. L. Chern, Chien-Chung Chang, Chien C. Chang, “Two Classes of Photonic Crystals with Simultaneous Band Gaps,” Japanese J. Appl. Phys. 43, 3484 (2004). [35] H. K. Fu, Y. F. Chern, R. L. Chern, C.Ｃ. Chang,”Connected hexagonal photonic crystals with largest full band gap”, Opt. Exp. 13, 7854 (2005). [36] R. L. Chern and S. D. Chao, “Optimal higher-lying band gaps for photonic crystals with large dielectric contrast,” Opt. Exp. 16, 16600 (2008) [37] J. D. Joannopoulos, P. R. Villenenve, S. Fan Nature386, 143-149(1997) [38] N. W. Ashcroft and N. D. Mermin, Solid State Physis (1976). [39] Dae Jung Yu and Kihong Kim, Waves in Random and Complex Media Vol. 18, No. 2, May 2008,325-341 [40] 欒丕綱 陳啟昌 ,光子晶體從蝴蝶翅膀到奈米光子學, 五南出版社(2006) [41] Y. F. Chau and F. L. Wu, ”Evolution of the complete photonic bandgap of two-dimensinoal pphotonic crystal,” Opt. Exp. vol.19 No.6 (2011) [42] S. D. Chao and N. Chan, “計算分析變化單位晶格角度下二維光子晶 體的最大 完全能隙,” 台灣大學(2011) | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/66161 | - |
| dc.description.abstract | 在以往光子晶體的研究中，許多晶格都已經廣泛被研究，其中包含：三角晶格（triangular lattice）、四角晶格（square lattice）、六角晶格（Hexagonal lattice）以及可果美晶格（Kagome lattice）。而其中可果美晶格相對來說被研究的範圍比較少，因此本篇的研究主要大部份針對可果美晶格的光子晶體來探討，另一方面以往對於２Ｄ光子晶體的研究主要著重在實心柱體，並改變上述晶格中的圓柱幾何半徑參數(radius/lattice constant=r/a)與介電材料強度參數（ε），以找尋擁有最大完全能隙（Full Band Gap）的光子結構，而本篇研究主要依照平面波展開法的理論循序漸進來研究可果美晶格的能帶情況，其中包含了不同的連橋方式、俗稱半月型的空心圓環圓柱體以及單位晶格內擁有不同幾何半徑參數與介電材料強度參數時，擁有最大完全能係的光子結構。
可果美單位晶格內有三根圓柱，分別擺在晶格原點與兩單位向量1/2的地方，週期性展開之後就是最原始的可果美晶格，本篇把三根圓柱的幾何參數與介電參數分開討論，藉由改變r1/a、r2/a、r3/a、ε1、ε2、ε3來找出擁有最大完全能隙的光子晶體結構，當幾何參數 r1/a = r2/a = r3/a，材料參數ε1 = ε2 = ε3 時，就是最原始的可果美晶格。研究的主要計算上是使用布洛赫理論(Bloch Theorem) 模擬電磁波在光子晶體結構內產生多重的穿透與反射之交互作用之結果。另一方面針對俗稱半月型的空心圓環圓柱體的光子晶體作探討，意思就是說將各種光子晶體晶格原本的的實心柱體改變成圓環柱體，我們在各種晶格原本柱體(r1/a)的位置再擺放了以空氣為材料的柱體(r2/a)，當 r1/a 大於 r2/a 的時候，就是一個半月型空心圓環圓柱體的光子晶體結構，這個動作將有機會幫助我們尋找到更大的完全能隙；當 r1/a 小於 r2/a 的時候，那整個平面就都是空氣了，當然不會有能係出現。我們主要發現在可果美晶格沒有加橋的情況下，kagome-r1r2r3擁有的最大的能隙0.077(ωa/(2πc))，材料參數ε=30，幾何參數r1/a=0.16，r2/a=0.17，r3/a=0.09；而kagome-ε1ε2ε3擁有的最大的能隙0.071(ωa/(2πc))，材料參數ε1=33，ε2=34，ε3=10，幾何參數r/a=0.15。而圓環柱體的部分，我們發現各種晶格呈現的結果並不一樣，可果美晶格加橋後的確實能找到更大的完全能隙，但沒加橋的可果美晶格卻反而沒更好；但對於六角晶格、四角晶格以及三角晶格都有不錯的效果。 最後我們發現，即使利用了多種的幾何參數與材料參數或是圓環柱體使kagome晶格的能隙變大，但還是都符合了本研究室先前研究的一些結論，當幾何參數(r/a)與材料參數(ε)逐漸增加時，使得幾何填充率(Geometry fill factor) 與能量填充率(Energy fill factor)增加，因此促使頻帶紅移。且各個參數都有最大完全能隙出現之前，下緣頻率紅移速率大於出現後的紅移速率的現象。此現象可以在將來用在混用多種參數時，經由比較完全能隙下緣頻率的斜率來快速的找到最大完全能隙的參數點。 | zh_TW |
| dc.description.abstract | In this paper, we use the plane wave expansion(PWE) method to calculate the band structures of two-dimensional high dielectric contrast photonic crystals, which are formed by kagome array of solid or hollow dielectric rods connected with dielectric rectangular rods. We scan the material parameter and geometric parameter to find the full band gaps. We found some characteristics In kagome crystals of full band gaps :
(1) The largest absolute full band gap in kagome crystals is 0.159 (ωa / (2πc)) appears when the crystals is hollow with simple connected by dielectric rectangular rods, the ε=55, r1/a=0.06, r2/a=0.01, w/a=0.02; and The largest relative full band gap in kagome crystals is 42.6% appears when the crystals is solid with hexagram connected by dielectric rectangular rods, the ε=77, r/a=0.07, w/a=0.02. (2) In kagome crystals with no connected by dielectric rectangular, there are more kinds of the dielectrics and radiuses can make the band gap bigger. Otherwise, it will make the band gap appear in the high band. (3) The band gaps in the kagome crystals connected with dielectric rectangular rods is much bigger than no connected with dielectric rectangular rods, Otherwise, the width of dielectric rectangular rods are always small. (4) In high dielectric kagome crystals, the largest full band gaps appear in low band, that is difference with honey, triangle crystals, square crystals, unless there are more kinds of the dielectrics or radiuses in the kagome crystals. (5) When we change the rods from solid to hollow, in kagome crystals only has one structure that is better for band gap. But on the other hand, When changing the rods from solid to hollow in honey, triangle crystals, square crystals, that are always better for band gaps. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T00:24:01Z (GMT). No. of bitstreams: 1 ntu-101-R98543067-1.pdf: 17371675 bytes, checksum: 1981467cb956c9f65992dc22f1e36073 (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | 致謝................................. ii
中文摘要................................. iv ABSTRACT................................. vi 總目錄................................. viii 圖目錄................................. xii 表目錄................................. xxiv Chapter 1 緒論.................................... 1 1.1 研究動機 ................ ..................... 1 1.2 光子晶體 ...................................... 3 1.2.1 局部化與重光子現象 ............................ 4 1.3 相關之文獻回顧 ................................. 6 1.4 論文導覽 ...................................... 10 Chapter 2 基本理論................................. 11 2.1 電磁波的種類 ................................... 11 2.2 計算方法及馬克斯威爾方程式理論 .................... 12 2.2.1 平面波展開法 ................................. 12 2.3 米氏散射 ...................................... 15 2.4 布拉格散射 ..................................... 16 2.5 光子晶體之進階延伸應用 ........................... 17 2.5.1 TE模態電磁波方程式 ............................ 17 2.5.2 淺水波方程式 ................................. 18 2.5.3 流場與磁場關隙式 .............................. 20 Chapter 3 倒晶格空間與布洛赫理論 ..................... 21 3.1 倒晶格與布里淵區 ................................ 21 3.2 布洛赫理論 ..................................... 23 3.3 電磁波在光子晶體中傳播 ........................... 25 Chapter 4 結果與討論 ............................... 27 4.1 可果美晶格-無橋實心圓柱 .......................... 29 4.1.1 無連接橋的原始可果美實心圓柱體 .................. 29 4.1.2 單位晶格內不同幾何尺寸之可果美晶格 ............... 31 4.1.3 單位晶格內不同介電常數之可果美晶格 ............... 36 4.2 可果美晶格-無橋空心圓柱 .......................... 41 4.2.1 無連接橋的可果美空心圓環柱體 .................... 41 4.3 可果美晶格-有橋實心圓柱 .......................... 45 4.3.1 有連接橋的可果美實心圓柱體 ...................... 45 4.3.2 六芒星式連接橋的可果美實心圓柱體 ................. 48 4.4 可果美晶格-有橋空心圓環柱 ......................... 52 4.4.1 有連接橋的可果美空心圓環柱體 ..................... 52 4.4.2 六芒星式連接橋的可果美空心圓環柱體 ................ 57 4.5 分析參數與完全能隙的分析 .......................... 62 4.5.1 完全能隙與介電常數之分析 ........................ 62 4.5.2 完全能隙對幾何圓柱參數的分析 ..................... 66 4.5.3 完全能隙與連接橋寬度之分析 ....................... 70 4.5.4 完全能隙與內圓空氣圓柱之分析 ..................... 73 4.6 頻帶圖分析 ...................................... 76 4.6.1 分析介電常數與頻帶關係 .......................... 77 4.6.2 分析幾何圓柱參數與頻帶關係 ....................... 85 4.6.3 分析橋寬參數與頻帶關係 ........................... 92 Chapter 5 不同晶格之計算結果與比較 ..................... 100 5.1 六角晶格 ........................................ 100 5.1.1 無連接橋之空心圓環柱 ............................ 100 5.1.2 有連接橋之空心圓環柱 ............................ 103 5.1.3 單位晶格內不同介電常數之六角晶格 .................. 108 5.2 三角晶格 ........................................ 112 5.2.1 無連接橋之空心圓環柱-60度三角晶格 ................. 112 5.2.2 無連接橋之空心圓環柱-50度三角晶格 ................. 115 5.2.3 有連接橋之實心圓環柱-50度三角晶格 ................. 118 5.3 四角晶格 ........................................ 122 5.3.1 增橋式之實心圓柱-(c)構型 ........................ 122 5.3.2 無連接橋之空心圓環柱-(d)構型 ..................... 126 5.3.3 有連接橋之空心圓環柱-(e)構型 ..................... 129 5.3.4 增橋式之空心圓環柱-(f)構型 ....................... 134 Chapter6 光子晶體之進階應用............................ 141 6.1 流場與磁場關係式 .................................. 141 6.2 電磁場場強分析 .................................... 142 6.2.1 可果美晶格 ..................................... 142 6.2.2 六角晶格 ....................................... 144 6.2.3 三角晶格 ....................................... 148 6.2.4 四角晶格 ....................................... 150 6.3 實驗架設 ......................................... 153 Chapter 7 結論與未來展望 .............................. 156 7.1 結論 ............................................ 156 7.2 未來展望 ......................................... 159 參考文獻 ............................................. 160 附錄一 格點精度收斂表 ............................................. 164 附錄二 基本原始晶格最大完全能隙比較表 ............................................... 166 附錄三 Installation of MBP............................................... 168 | |
| dc.language.iso | zh-TW | |
| dc.subject | 重光子態 | zh_TW |
| dc.subject | 光子晶體 | zh_TW |
| dc.subject | 光子能隙 | zh_TW |
| dc.subject | 可果美 | zh_TW |
| dc.subject | 米氏共振 | zh_TW |
| dc.subject | Photonic crystals | en |
| dc.subject | Heavy photon | en |
| dc.subject | Mie resonance | en |
| dc.subject | kagome | en |
| dc.subject | Photonic band | en |
| dc.title | 二維可果美晶格光子晶體最大完全能隙之計算 | zh_TW |
| dc.title | Calculation of Maximal Full Band Gaps for Two-Dimension Kagome Photonic Crystal | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 楊照彥(Jaw-Yen Yang),朱錦洲(Chin-Chou Chu),欒丕綱(Pi -Gang Luan) | |
| dc.subject.keyword | 光子晶體,光子能隙,可果美,米氏共振,重光子態, | zh_TW |
| dc.subject.keyword | Photonic crystals,Photonic band,kagome,Mie resonance,Heavy photon, | en |
| dc.relation.page | 171 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2012-05-17 | |
| 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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