臺灣博碩士論文加值系統

現今，有很多金奈米結構的電漿子效應的生物應用研究，因為金在生物體中有較佳的化學與物理穩定性。大部分的研究假設在光是垂直入射與結構交互作用下，本研究則討論在斜向入射下的交互作用金奈米結構的電漿子效應。我們利用一個波長介於0.8~2.0微米的高斯波包當作入射源來探討多重金奈米柱在操作波長1.2微米附近作為折射率感測器的靈敏度。我們藉由有限時域差分法來達成理論模擬，並得知局部表面電漿共振會存在於金奈米棒中，也計算在不同入射角度下的反射頻譜。我們嘗試在金奈米棒的垂直方向增加棒子的數量來比較其差異。此外，我們得知不僅入射角與方位角會影響反射頻譜，連金奈米柱之間互相的間距不同也會造成差異。本研究中我們利用資料傳輸介面協定(MPI)來連接多台電腦同時計算來增加程式計算模擬的效率。

The surface plasmons generated in gold nanostructures have been studied widely because of its chemical and physical stability in medical applications. Theoretical investigation of such generation has most often assumed that the excitation incident waves are shined normally onto the structure. In this thesis research, we consider the incident waves are shined in the oblique direction. We study the multi-goldnano-rod structures excited by Gaussian-pulse wave in the wavelength range from 0.8 µm to 2.0 µm to theoretically calculate the sensitivity near 1.2 µm of the nanorod structure working as a refractive-index sensor. The numerical simulation tool is based on a split-field finite-difference time-domain (FDTD) method. The electric fields existing in the gold-nano-rods resulting from the phenomenon of localized surface plasmon resonance (LSPR) and the effect on the reflection spectra of different incident angles in the obliquely incident situation are examined. Furthermore, the dependence of the reflection spectra on the number of x-direction gold-rods along the y-axis is investigated. The reflection spectra are found to depend on not only the incident and polarization angle, but the distance between the nano rods. We use the message passing interface (MPI) protocol to connect with several computers in order to improve the efficiency of computation.

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Introduction to Computational Electromagnetic . . . . . . . . . . . . . . . . . . . . . . .2
1.3 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
2 The Split-Field FDTD Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The Courant Stability Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
2.3 Modeling of Dispersive Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
2.3.1 The Drude Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 The Lorentz Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.3 The Auxiliary Differential Equation (ADE) Method . . . . . . . . . . . . . . . . . . 14
2.4 Convolutional Perfectly Matched Layer (CPML) . . . . . . . . . . . . . . . . . . . . . 17
2.5 Parallelized Split Field Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Numerical Accuracy Validation for Simulating Periodic Structures with the Split Field Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6.1 The 3D structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
3 Analysis of Coupling Effects of Nano-Scale Metal Structures . . . . . . . . . . . . 30
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 The Single-Rod Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1 Comparison among different azimuthal angles in the normal incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.2 Comparison among various incident angles in the oblique incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 The Two-Rod Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.1 Comparison among different azimuthal angles in the normal incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.2 Comparison among various incident angles in the oblique incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 The Three-Rod Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
3.4.1 Comparison among different azimuthal angles in the normal incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.2 Comparison among various incident angles in the oblique incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 The Four-Rod Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
3.5.1 Comparison among different azimuthal angles in the normal incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.2 Comparison among various incident angles in the oblique incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.6 The Five-Rod Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
3.6.1 Comparison among different azimuthal angles in the normal incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.6.2 Comparison among various incident angles in the oblique incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.7 The Seven-Rod Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.7.1 Comparison among different azimuthal angles in the normal incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.7.2 Comparison among various incident angles in the oblique incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4 The Sensitivity And Figure of Merit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81
4.1 The Definition of the Sensitiviy and FOM . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.1.1 The performance of sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.1.2 The Performance of FOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82
4.2 The Sensitivity and FOM of Single-Rod Arrays in TE and TM polarizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.3 The Sensitivity and FOM of Two-Rod Arrays in TE and TM polarizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4 The Sensitivity and FOM of Three-Rod Arrays in TE and TM polarizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.5 The Sensitivity and FOM of Four-Rod Arrays in TE and TM polarizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.6 The Sensitivity and FOM of Five-Rod Arrays in TE and TM polarizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.7 The Sensitivity and FOM of Seven-Rod Arrays in TE and TM polarizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
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