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系統識別號 U0026-1401201502562100
論文名稱(中文) 手性介質(Chiral medium)的能帶結構之探討與研究
論文名稱(英文) A study on band structure of Chiral medium
校院名稱 成功大學
系所名稱(中) 數學系應用數學碩博士班
系所名稱(英) Department of Mathematics
學年度 103
學期 1
出版年 104
研究生(中文) 王益宏
研究生(英文) Yi-Hong Wang
學號 L16011085
學位類別 碩士
語文別 英文
論文頁數 54頁
口試委員 指導教授-舒宇宸
口試委員-侯世章
口試委員-陳旻宏
中文關鍵字 超材料  手性材料  介面條件  能帶結構  虛擬網格方法 
英文關鍵字 chiral mediums  metamaterials  interface conditions  band structures  ghost point method 
學科別分類
中文摘要 在這篇論文中,我們探討手性材料的第一條與第二條能帶,並藉由推導介面條件得到波方程在週期結構的解析解。然而,由於係數矩陣的行列式過於複雜,我們無法直接從中得到手性材料頻率與波數的確切關係,因此我們提出了一個數值方法去克服這個困難。我們運用了有限差分法來解特徵值問題,得到頻率並代回係數矩陣的行列式,最後檢驗其誤差收斂性。從我們的數值結果顯示,我們得到第一條與第二條能帶的特徵值的二階收斂。除此之外,我們發現當在z方向的波數等於零的情況下,會有四階收斂現象發生。
英文摘要 In this thesis, we discuss the first and second band of chiral medium and derivate the interface conditions for obtaining electromagnetic plane wave solutions. Owing to the complicated determinant of coefficient matrix, we cannot obtain the explicit relation of frequency and wavenumber of chiral medium directly. Thus we propose the numerical method to overcome this difficulty. Furthermore, we apply finite difference method to solve the eigenvalue problem and substitute the frequency into the determinant of coefficient matrix. And we investigate the rate of convergences. From the numerical results, we obtain the second-order convergences of the first and second band. Besides, we discover forth-order convergences when wavenumber of z component is equal to zero.
論文目次 1 Introduction 1
1.1 Photonic Crystal.......... 1
1.2 Metamaterials............ 4
1.3 Chiral mediums of Metamaterials....... 5
1.4 Aim of This Study........... 6
2 Chiral Mediums 8
2.1 Maxwell’s Equations.......... 8
2.2 Wavenumbers of Electromagnetic Wave in Complex Mediums... 10
2.3 Interface Conditions.......... 16
3 Numerical Method 22
3.1 Discretization of Maxwell’s equations....... 22
3.2 Discretization for Chiral Mediums....... 25
3.3 Ghost Point Method for Eigenfunction...... 27
4 Numerical Results 36
4.1 Band Structures of Conventional Mediums...... 36
4.1.1 Conventional Mediums without Interface..... 36
4.1.2 Periodic Conventional Mediums with Interface.... 38
4.2 Band Structures of Chiral Mediums........ 40
4.3 Interface Conditions between Vacuum and Chiral Mediums.. 42
5 Conclusion 51
Bibliography 52
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