臺灣博碩士論文加值系統

時域有限差分法已用廣泛運用在諸多模擬光電電磁計算上，我們以C++語言，
自行開發時域有限差分模擬器，並且具有平行化功能，透過訊息傳遞介面協定，
一次使用多台電腦加速運算，以減少運算時間。
本論文主要分析領結天線與偶極天線陣列，且領結天線又細分為雙正三角形
領結與平頭式領結。平頭式領結天線是為雙正三角形領結天線的修正形狀，理由
是在製程過程中時常難以完美呈現尖頭的正三角形，因此修正成平頭。平頭式領
結天線的優點在於能將較多的局部場侷限在間隙中，使局部場增強的幅度提升。
首先，我們以一個寬頻的電磁波作為波源，照射在實心的領結天線陣列中，並且
計算天線間隙之局部場增強、頻譜響應及共振波長。接著，我們分別模擬了實心
偶極天線陣列及環形平頭式領結天線陣列。當環形平頭式領結天線陣列的基本參
數和條件與實心平頭式領結天線陣列相同時，模擬結果指出環形平頭式領結天線
陣列擁有較長波長的共振頻率。最重要的研究發現，陣列的週期長度，對天線陣
列的頻譜響應有重要的影響，不論在實心或空心結構中均發現此特殊現象。

The finite-difference time-domain method (FDTD) has been widely used in computational electromagnetics. We construct a parallelized three-dimensional (3-D) FDTD simulator in C++ language. The message passing interface (MPI) protocol is applied in our simulator for using several computers in the computation in order to speed up the process and shorten the simulation time.
In this research, the main topic is to analyze nanoantenna arrays having bowtie and dipole structures. We investigate two kinds of bowtie structures: the equilateral-triangle bowtie and the modified bowtie. The modified bowtie is a correction of the equilateral-triangle bowtie with the head-to-head apexes being flattened. It is more effective to confine the field within the antenna gap and increase the field enhancement. We first simulate the traditional solid bowtie arrays with a broadband source. The local field enhancement in the antenna gap is calculated, including the broadband responses and the resonant wavelengths. Then the contour bowtie nanoantenna arrays aiming at miniaturization are simulated. Contour bowtie structures has longer resonant wavelengths than the solid structures under the same circumstance. The most important discovery is that the period lengths of the array are very crucial parameters. The array period length is perpendicular to the broadside of the bowtie and dipole shapes influences the resonant wavelength in the enhancement spectrum primarily. The resonant wavelength seems to be a function of the period length. This phenomenon can be seen in both solid and contour structures.

致謝 1
摘要 2
ABSTRACT 3
CONTENTS 4
LIST OF FIGURES 6
Chapter 1 Introduction 17
1.1 Motivation 17
1.2 Introduction to Computational Electromagnetics 18
1.3 Chapter Outline 19
Chapter 2 The Finite-Difference Time-Domain Method 21
2.1 Yee Algorithm for Maxwell’s Equations 21
2.2 The Courant Stability Limit 23
2.3 Modeling of Dispersive Materials 24
2.3.1 The Drude Model 24
2.3.2 The Lorentz Model 26
2.3.3 The Auxiliary Differential Equation (ADE) Method 26
2.4 The Total-field / Scatter-field Technique 29
2.5 Convolutional Perfectly Matched Layer (CPML) 30
2.6 Periodic Boundary Conditions (PBCs) 32
2.7 Parallelized FDTD Method 32
2.8 Verification of Some FDTD Simulation Cases 34
2.8.1 Verification for 2-D Circular Cylinders 34
2.8.2 Verification for 3-D Silver Sphere 35
2.8.3 Verification for Periodic Structure of Silver Spheres 36
Chapter 3 Bowtie Nanoantenna Arrays 47
3.1 Equilateral-triangle Bowtie Nanoantenna Arrays 48
3.1.1 Comparisons between a Single Bowtie Antenna and BNA 49
3.1.2 The BNA with Various Period Lengths 49
3.1.3 The BNA with Various Period Lengths in Smaller Range 51
3.2 Modified Bowtie Nanoantenna Arrays 52
3.2.1 Comparisons between a Single Bowtie Antenna and BNA 52
3.2.2 The BNA with Various Period Lengths 52
3.2.3 The BNA with Various Period Lengths in Smaller Range 53
3.3 Modified BNA with Different Bowtie Lengths 54
Chapter 4 Nanoantenna Arrays with Dipole and Contour-Bowtie Structures 81
4.1 Dipole Nanoantenna Arrays (DNAs) 81
4.1.1 Comparison between a Single Dipole Antenna and DNA 82
4.1.2 The DNA with Various Period Lengths 82
4.2 Contour Bowtie Nanoantenna Arrays (CBNAs) 84
4.2.1 Comparison between a Single Contour Bowtie Antenna and CBNA 84
4.2.2 The CBNA with Various Period Lengths 84
Chapter 5 Conclusion 99
Bibliography 101

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