||Theoretical Studies on Localized Surface Plasmon Resonances of Nanoparticle Arrays—Standing-Wave Modes, Optical Phase Characteristics, and Rayleigh Anomalies
||Department of Photonics
localized surface plasmon resonance
refractive index sensing
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 standing-wave modes in split-ring resonators (SRRs), the optical phase characteristics of nanodot arrays, and the impacts of Rayleigh anomalies on LSPR spectra.
We investigate the excitations of standing-wave 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 left-handed 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 P-factor to characterize the ability of incident fields to excite standing-wave modes.
We analytically model the intensity and the phase spectra of silver nanodots with temporal-coupled 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 figure-of-merit is greatly enhanced.
We have developed a theoretical model based on TCMT for LSPRs coupled with Rayleigh anomalies (TCMT-RA). TCMT-RA 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 size-to-period ratio of nanodot array enhances the effects of Rayleigh anomalies.
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 Quasi-Static Approximation for Small Nanospheres 1
1.2.2 Plasmon Resonances Beyond Quasi-Static Approximation 4
1.3 Thesis Overview 5
Chapter 2 Excitations of Standing-Wave Modes in Split-Ring Resonators 7
2.1 Introduction 7
2.2 Simulation Structures and Methods 8
2.3 Qualitative Interpretation of Excitations of Standing-Wave Modes 9
2.3.1 Standing-Wave Modes in Split-Ring 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 Standing-Wave 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 Coupled-Mode 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 Figure-of-Merit 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 Line-Shapes of Transmission and Reflection 50
4.3 Temporal Coupled-Mode Theory for Plasmon Resonances Coupled with Rayleigh Anomalies 51
4.4 Analysis of Spectra of Nanodot Arrays 56
4.4.1 Procedure for Acquiring TCMT-RA Parameters from Spectra 56
4.4.2 Correlations Between TCMT-RA Parameters and Geometry of Nanodot Arrays 59
4.4.3 Universal Scaling of External Quality Factor 61
4.4.4 Reduction of Full-Width 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
Appendix A Analyzing Spectra of Split-Ring Resonator Arrays with Temporal Coupled-Mode 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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