
系統識別號 
U00261002201416174700 
論文名稱(中文) 
奈米粒子陣列侷域性表面電漿共振之理論研究—駐波模態、光學相位特性以及瑞利異常 
論文名稱(英文) 
Theoretical Studies on Localized Surface Plasmon Resonances of Nanoparticle Arrays—StandingWave Modes, Optical Phase Characteristics, and Rayleigh Anomalies 
校院名稱 
成功大學 
系所名稱(中) 
光電科學與工程學系 
系所名稱(英) 
Department of Photonics 
學年度 
102 
學期 
1 
出版年 
103 
研究生(中文) 
陳文瑜 
研究生(英文) 
WenYu Chen 
學號 
L78981212 
學位類別 
博士 
語文別 
英文 
論文頁數 
93頁 
口試委員 
指導教授林俊宏 口試委員藍永強 口試委員張世慧 口試委員陳學禮 口試委員李佳翰

中文關鍵字 
侷域性表面電漿共振
折射率感測
橢圓偏振術
瑞利異常
奈米點陣列
分裂共振環

英文關鍵字 
localized surface plasmon resonance
refractive index sensing
ellipsometry
Rayleigh anomaly
nanodot array
splitring resonator

學科別分類 

中文摘要 
本論文探討週期性奈米粒子陣列之侷域性表面電漿共振所引發的光學現象，共有三個主題:分裂共振環的駐波模態、奈米點陣列的光學相位特性以及瑞利異常對共振頻譜的影響。
我們改變入射光的入射角以及偏振態，探討這些條件對分裂共振環的駐波模態所產生的影響。由模擬的頻譜發現，斜向入射的線偏振光能激發正向入射時的暗模態；且斜向入射時，左、右圓偏光的頻譜不再重疊。這些光學現象能以入射電場及共振模態的駐波電流之間的平行度解釋，因此，我們提出平行度計算公式，以此公式預測入射光與駐波模態的耦合程度。
我們利用時態模態耦合理論分析銀點陣列之頻譜，並將焦點放在表面電漿共振引發之光學相位特徵。表面電漿共振在反射光的頻譜中引發相位反轉的現象；在穿透光的相位頻譜中引發z形轉折。我們利用時態模態耦合理論推導z形轉折的相位斜率公式，由公式可知，金屬的歐姆吸收會降低相位的斜率。接著我們探討非等向性銀點陣列之相位延遲現象，表面電漿共振在互為垂直偏振光之間引發相位差，此相位差的頻寬遠窄於表面電漿共振的頻寬。我們將相位延遲現象應用於折射率感測，極窄的頻寬能使感測器之品質因素大幅提升。
我們利用時態模態耦合理論探討侷域性表面電漿共振與瑞利異常現象耦合對頻譜產生的影響。我們分析各種週期及點尺寸的金屬點陣列之頻譜，發現一個普適的尺度法則:表面電漿模態在每個共振週期中輻射到遠場的能量與金屬點的覆蓋率成正比。由理論可知，瑞利異常對表面電漿共振頻譜產生四個影響:共振位置紅移、頻譜不對稱、頻寬變窄、相位斜率變陡。由模擬可知，當金屬陣列的點尺寸對週期的比值愈小，瑞利異常的影響愈大。

英文摘要 
This thesis presents theoretical studies on the optical characteristics of localized surface plasmon resonances (LSPRs) in spectra of periodic nanoparticle arrays. Three subjects have been discussed: the excitations of standingwave modes in splitring resonators (SRRs), the optical phase characteristics of nanodot arrays, and the impacts of Rayleigh anomalies on LSPR spectra.
We investigate the excitations of standingwave modes of SRRs with different incident angles and polarizations. Two changes at oblique incidence with respect to normal incidence are investigated—the excitations of dark modes with linear polarizations and the deviation of spectra of right and lefthanded circular polarizations. We find that the parallelism between the incident electric field and the induced plasmon current is the key factor affecting the excitation. We propose the use of a Pfactor to characterize the ability of incident fields to excite standingwave modes.
We analytically model the intensity and the phase spectra of silver nanodots with temporalcoupled mode theory (TCMT). The focus is on phase characteristics that are a π jump for reflection and a zigzag transition for transmission. We derive the equation of phase slope at the zigzag transition of transmission. The equation shows that the Ohmic absorption decreases the phase slope. We further investigate plasmonic phase retardation in anisotropic nanodot arrays. We discovered that the bandwidth of phase retardation could be much narrower than the LSPR bandwidth if the long and the short side lengths of the nanodots are very close. We propose the application of plasmonic phase retardation in refractive index sensing. In this sensing algorithm, the sensor figureofmerit is greatly enhanced.
We have developed a theoretical model based on TCMT for LSPRs coupled with Rayleigh anomalies (TCMTRA). TCMTRA is used for analyzing the spectra of nanodot arrays with various periods and dot sizes. We calculate the reciprocal of external quality factor, which means the percentage of LSPR energy radiating to far field per oscillation cycle, and find that the value is universally proportional to the nanodot coverage. The Rayleigh anomalies have four effects on the LSPR spectra, namely, redshift of LSPR, asymmetric line shape, bandwidth reduction, and increased phase slope. The results show that the decrease in the sizetoperiod ratio of nanodot array enhances the effects of Rayleigh anomalies.

論文目次 
Contents i
List of Tables iv
List of Figures v
List of Symbols vii
Chapter 1 Introduction 1
1.1 Motivation 1
1.2 Localized Surface Plasmon Resonance 1
1.2.1 QuasiStatic Approximation for Small Nanospheres 1
1.2.2 Plasmon Resonances Beyond QuasiStatic Approximation 4
1.3 Thesis Overview 5
Chapter 2 Excitations of StandingWave Modes in SplitRing Resonators 7
2.1 Introduction 7
2.2 Simulation Structures and Methods 8
2.3 Qualitative Interpretation of Excitations of StandingWave Modes 9
2.3.1 StandingWave Modes in SplitRing Resonators 9
2.3.2 Excitations of Odd Modes of Perpendicular Polarization at 45° Incidences 11
2.3.3 Excitations of Mode 1L and 1R at 45° Incidences 12
2.4 Mathematical Interpretation of Excitations of StandingWave Modes 13
2.4.1 Parallelism Factor 13
2.4.2 Phase Change of Mode 3L with Different Angles of Incidences 15
2.4.3 Parallelism Factor as a Function of Geometry 16
2.5 Summary 17
Chapter 3 Plasmonic Phase Transition and Phase Retardation 27
3.1 Introduction 27
3.2 Plasmonic Phase Transition 29
3.2.1 Spectra of Square Nanodot Array 29
3.2.2 Temporal CoupledMode Theory for Nanodot Arrays 29
3.2.3 Procedure for Acquiring TCMT Parameters from Spectra 33
3.2.4 Phase Slope 34
3.3 Plasmonic Phase Retardation 36
3.3.1 Spectra of Anisotropic Nanodot Array 36
3.3.2 FigureofMerit of Anisotropic Nanodot Array 37
3.3.3 Experiment: Phase Sensor of an Anisotropic Nanodot Array 38
3.4 Summary 39
Chapter 4 Coupling Between Localized Surface Plasmon Resonances and Rayleigh Anomalies 48
4.1 Introduction 48
4.2 Asymmetric LineShapes of Transmission and Reflection 50
4.3 Temporal CoupledMode Theory for Plasmon Resonances Coupled with Rayleigh Anomalies 51
4.4 Analysis of Spectra of Nanodot Arrays 56
4.4.1 Procedure for Acquiring TCMTRA Parameters from Spectra 56
4.4.2 Correlations Between TCMTRA Parameters and Geometry of Nanodot Arrays 59
4.4.3 Universal Scaling of External Quality Factor 61
4.4.4 Reduction of FullWidth at Half Maximum 62
4.4.5 Increase of Phase Slope 63
4.4.6 Four Impacts of Rayleigh Anomalies on Plasmon Resonance Spectra 66
4.5 Summary 66
Chapter 5 Conclusions 76
5.1 Summary 76
5.2 Outlook 77
References 78
Appendix A Analyzing Spectra of SplitRing Resonator Arrays with Temporal CoupledMode Theory 84
Appendix B Ellipsometric Parameters of a Silver Nanorod Array 85
Appendix C Fabrication of Anisotropic Nanodot Array 87
Appendix D Analysis for Spectra of Silver Nanodot Arrays with Fixed Period of 800 nm and Varied Dot Sizes 89
Appendix E Publications 92

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