臺灣博碩士論文加值系統

親手性(chirality)是一種自身結構與鏡像結構不對稱的特性，此特性在自然界中十分常見。親手性分子的鏡像結構無法與自身完全重合，並存在對左手圓偏振(LCP)光與右手圓偏振(RCP)光的不同吸收率。這種對左右手圓偏振光吸收率的不同又稱作吸收圓二色性(circular dichroism, CD)，親手性分子的圓二色性可被用來鑑別或偵測該親手性分子。在自然界中常見的親手性分子如：DNA與葡萄糖中的胺基酸。
光學親手性增益(optical chirality enhancement, OCE)是針對親手性分子的光學親手性增益係數。本篇論文中，我們利用有限差分時域法(finite-different time-domain, FDTD)模擬線偏振光正向與斜向入射斜縫金屬天線，又分為vertical-cut與slant-cut兩種，並計算其OCE。我們驗證了OCE的主要貢獻來自於入射光磁場H_inc以及局域性表面電漿共振(localized surface plasmon resonant, LSPR)衰逝電場E_LSPR，而且純LSPR近場項的空間總和為0。基於以上研究，我們進一步能準確地計算受基板效應影響的不對稱OCE。
在現實實驗中，親手性分子一般存在於空氣側並且無法被基板側的OCE激發，因此我們利用矩形區塊對空氣側OCE進行積分，積分範圍則為距離金屬表面d。上方入射情況下，相比於slant-cut天線，由於vertical-cut天線具有垂直奇對稱的OCE分布，有較好的積分值。下方入射情況下，在d較小時vertical-cut天線的積分值呈現略負，並且當空氣側積分範圍越大(d越大)時轉為正值。slant-cut天線則因為具有水平奇對稱的OCE分布，隨著積分範圍d增加積分值並沒有太大的變化。

Chirality, a performance of broken mirror symmetry, common in nature. Chiral molecules whose mirror images do not overlap with the original, exhibit different absorption properties with left and right hand circular polarized incident light (LCP/RCP). The difference in absorption rate is called the absorption circular dichroism (CD) and can be used to distinguish and detect the chiral molecules. These chiral molecules are commonly present in nature such as amino acids in DNA and glucose.
Optical chirality enhancement (OCE) is a factor that enhance optical chirality of chiral molecules. In this thesis, we use finite-different time-domain (FDTD) to calculate the OCE in slant-gap metal antenna with vertical-cut/slant-cut configuration by normal and oblique incident light with linear polarization. We prove that the main contribution of OCE is originated from the inner product of the incident H field H_inc and the localized surface plasmon resonant (LSPR) evanescent E field E_LSPR. And the pure LSPR near-field term give net zero contribution. Based on these research, we can accurately count for the asymmetric OCE distribution due to the substrate effect.
In the experiments, chiral molecules typically stay on the air side and cannot experience OCE from the substrate side. Thus, we integrate OCE value by using rectangular box on the air side with distance d from metal surface. For top illumination, the vertical-cut case shows better OCE value than the slant-cut case because of the vertically odd OCE distribution. For bottom illumination, the vertical-cut case shows less net negative value for smaller d, and becomes positive when including more space (larger d) on the air side. In slant-cut case, there is not much change in the OCE value if d increases because of the horizontally odd OCE distribution.

中文摘要 I
Abstract II
致謝 III
Contents IV
List of Tables VII
List of Figures IX
List of Symbols XVI

Chapter 1 Introduction
1-1 Surface Plasmons 1
1-1-1 Dispersion of surface plasmons at interface 2
1-2 Metal Gap (MIM) and Metal Film (IMI) 6
1-2-1 Metal gap (MIM) 10
1-2-2 Metal film (IMI) 12
1-3 Pad´e Approximation 14
1-4 Reference 15

Chapter 2 Numerical Method
2-1 Finite-Difference Time-Domain (FDTD) Method 16
2-1-1 The Yee’s algorithm 16
2-1-2 Stability condition 20
2-1-3 Convolutional PML (CPML) 21
2-1-4 Total-field scatter-field (TF/SF) 30
2-1-5 Example for Ag sphere 31
2-2 Order-N Method 33
2-3 Constant-K Method 36
2-3-1 Homogeneous 38
2-3-2 Inhomogeneous with interface 40
2-3-3 Application in 2D & 3D 42
2-3-3-1 2D Periodic structure 43
2-3-3-2 2D Non-periodic structure 44
2-3-3-3 3D Periodic structure 45
2-3-3-4 3D Non-periodic structure 47
2-3-4 Example for n_1=2 to n_2=1 49
2-3-5 Example for n_1=1 to n_2=2 50
2-4 Reference 51

Chapter 3 The Mechanism of Optical Chirality Enhancement in Slant-gap Antenna
3-1 Optical Chirality Enhancement (OCE) 52
3-2 OCE Contribution 55
3-3 Antenna in Free Space 57
3-3-1 Normal incident with top and bottom illumination 59
3-3-1-1 Box integration of OCE 61
3-3-1-2 Threshold integration of OCE 63
3-3-1-3 OCE x, y and z contributions and retardation effect 68
3-3-2 Oblique incident with top and bottom illumination 70
3-4 Antenna on Substrate 72
3-4-1 Substrate effect 72
3-4-2 Oblique incident with top and bottom illumination 77
3-5 Conclusions 80
3-6 Reference 80

Chapter 4 Bound States in the Continuum in 2D Plasmonic Crystals
4-1 Bound states in Continuum (BICs) 84
4-2 Single Layer Ag Disk Arrays 86
4-2-1 Grating effect 86
4-2-2 LSPR mode 89
4-2-3 High Q mode with P-polar plane wave 93
4-2-4 IMI dispersion with periodic band folding 97
4-2-5 High Q mode with point source Hx 98
4-2-6 Radius and thickness effect 101
4-3 Double Layer Ag Disk Arrays 105
4-3-1 Hamiltonian 105
4-3-2 Symmetric geometry (r1=r2=80nm) 108
4-3-3 Asymmetric geometry (r1=70nm, r2=80nm) 117
4-4 Conclusions 121
4-5 Reference 121
 
Chapter 5 Plasmonic Resonant Modes in Highly Symmetric Multi-Branches Nanostructures
5-1 Introduction 123
5-2 Materials and Computational Method 125
5-2-1 Materials 125
5-2-2 Computational method 127
5-3 Results and Discussion 128
5-3-1 Three different cross-section of rod structure: cylindrical, hexagonal, and triangular nanorod 128
5-3-2 Spike-like, concave, and convex structure 132
5-3-3 Sea star structure 133
5-3-4 Tetrapod structure 1: cylindrical, hexagonal, and triangular tetrapod 137
5-3-5 Tetrapod structure 2: concave and convex tetrapod 139
5-3-6 Multi-branch sea urchin structure 140
5-4 Conclusions 143
5-5 Reference 145

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