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研究生:陽明益
研究生(外文):Ming-Yi Yang
論文名稱:壓電超晶格之極子特性研究
論文名稱(外文):Characteristic research of polaritons in piezoelectric superlattice
指導教授:周元昉
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:255
中文關鍵詞:壓電超晶格極子平面波展開法能量分佈帶隙
外文關鍵詞:piezoelectric superlatticepolaritonplane wave expansion methodenergy distributionband gap
相關次數:
  • 被引用被引用:6
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週期性結構之特殊性質,不管是通帶性質或禁帶性質,皆吸引許多人爭相探討研究,並已有許多論文發表。經由介電係數週期調變之晶體,即為所謂的光子晶體,不管是其禁帶行為的頻帶間隙現象或通帶行為的負折射現象,以及利用點、線缺陷所造成的共振與波傳導現象,都有許多研究投入。另外,對於週期調變材料係數如密度、彈性係數…等之晶體,此類晶體則統稱為聲子晶體,也有許多的研究者投入,並遵循著光子晶體發展的腳步前進,然而此類週期性結構與光子晶體最大的不同在於其遵循的統御方程式不同,聲子晶體所遵循之統御方程式為牛頓第二運動定律,而光子晶體則為Maxwell’s方程式,意即一個是機械波在週期結構中的行為,另一個則是電磁波在週期結構中的行為,而聲子晶體由於可調變的參數多於光子晶體,故其行為將更具有複雜度與可調性。
除此之外,近期有研究指出利用壓電之特性並配合週期性變化,使電磁統御方程式與牛頓第二運動定律互相交互作用,而此類壓電係數週期調變之材料,即稱為壓電超晶格。而對此超晶格內之統御方程式,由於同時包含電磁波與機械波,其量子化後之粒子也有個特別的名稱,即稱為極子。本篇論文除了對一維模型進行深入探討外,並推導平板型式壓電超晶格之頻帶結構式和波傳行為,並藉由畫出此頻帶結構圖上各點之極子場形與能量比例分佈,來解釋極子中之電磁波特性與機械波特性,並配合實驗驗證理論所得之結果。另外,本文並提出一準靜電態模型,由此模型可以迅速得到在何種特定耦合激發頻率下,外界電磁波可與此超晶格平板產生激振。
There have been many researches focused on the periodic structures, inwhich the characteristics of the pass-band and the stop-band are primarily interested. The permittivity modulated structures are well known as the photonic crystals. In the applications of the photonic crystals, there are spontaneous emission suppressing, light manipulating in a specific path, and novel laser creating. In addition, the further thinking about space modulated elastic structures is called phononic crystals. The phononic crystals also have the same characteristics of the frequency band gaps, however, the factors which influence the complete band gap are more complicated than photonic crystals. These factors include the elastic constants, piezoelectric coefficients, density etc.. The governing equations for photonic crystals also are different from the phononic crystals. The physical behaviors in photonic crystals obey the Maxwell’s equations and in phononic crystals it obeys the Newton’s second law of motion.
Recently, the piezoelectric-modulated superlattices have been developed. These so called piezoelectric superlattices (PSLs) make the Maxwell’s equations and the Newton’s second law of motion couple to each other. The quantization of the interaction between the electromagnetic waves and the mechanical waves is called the polaritons. This dissertation focuses on the behaviors of the polaritons not only in 1-D PSL but also in the plate form of PSL. From the derived fields and energy distributions of the polaritons, it would have a better understanding in the PSLs.
謝致 i
中文摘要 ii
英文摘要 iii
目錄 iv
表目錄 vii
圖目錄 viii
符號表 xxiv
第一章 緒論 1
1-1 研究動機 1
1-2 文獻回顧 2
1-3 本文目的與內容 5
第二章 壓電超晶格平板之頻帶結構關係式 7
2-1 超晶格內之統御方程式 7
2-2 真空中之電磁統御方程式 14
2-3 邊界條件 15
2-4 超晶格內之平均儲存能量 18
第三章 無限域之一維超晶格結構 21
3-1 一維壓電單元超晶格 22
3-1-1 軸為極化方向 22
3-1-1-1 極子場形與能量分佈 27
3-1-1-2 等效介電係數 33
3-2 軸為極化方向 35
3-2-1 極子場形與能量分佈 38
3-2-2 等效介電係數 43
3-2-3 LiNbO3實驗 44
3-3 一維壓電-非壓電複合單元超晶格 49
3-3-1 極子場形與能量分佈 53
3-4 局域共振聲子晶體 55
第四章 壓電超晶格平板 57
4-1 軸為週期極化方向 57
4-2 軸為週期極化方向 59
4-3 軸為週期極化方向 61
4-4 PZT壓電超晶格平板 68
4-4-1 極子能量分佈 70
4-4-2 PZT超晶格平板實驗 71
4-4-2-1 實驗設計 72
4-4-2-2 試片製作 73
4-4-2-3 量測結果 75
4-4-3 實驗值與理論值之比較 77
4-4-4 PZT壓電超晶格平板之討論 78
4-4-4-1 彈性波模型 78
4-4-4-2 彈性波模型估測耦合激發頻率 81
4-4-4-3 極化週期之影響效應 81
4-5 平面波展開法之收斂性 82
第五章 結論與建議 84
參考文獻 86
附表 89
附圖 92
附錄一 252
附錄二 253
附錄三 255
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