控制光物質相互作用形成極化子是未來光子和光電器件的關鍵因素。 極化子可以通過電磁模態和電子能態之間的能量交換形成。 一般來說，在強耦合狀態下，拉比分裂大於本徵光態和物質態的線寬，在離調光譜中會觀察到能量反交叉現象。 極化子是半光、半物質的準粒子具有玻色子的性質，為探索多體物理提供了可能性，包括玻色-愛因斯坦凝聚 (BEC)、極化子激光器和一些實用的極化子器件。
在此篇著作的第一部分，我們定義了電漿子材料，並給出了它們在奈米光學、生物應用和能量傳感器中的一些應用示例。再者，介紹了基本的電漿子材料及其固有的光學特性，包括Drude和Lorentz模型。為了更詳細地了解金屬中自由和束縛電子行為的起源，討論金屬電子能帶結構對束縛電子的貢獻。特別是鋁，由於其能帶結構接近自由電子能帶，在W點和K點附近只有少量束縛電子躍遷，屬於共振型躍遷，因此是類Drude材料。然而，其他基本等離子體材料的電子能帶結構相似，它們的束縛電子是從d到sp的能帶躍遷，屬於閾值型躍遷。基於了解能帶圖和光學特性的了解後，我們沉積了晶圓級金屬薄膜並測量了它們的介電常數，使用合適的介電模型來擬合這些光學響應，並提取具有物理意義參數（例如:電漿體頻率、阻尼率和帶間躍遷能）。最後，介紹了表面電漿子的背景，包括傳播表面表面電漿極化子(SPPs)和局域表面電漿子(LSPs)，再來提及一些常見的電漿子共振模式，以及以品質因子為依據地電漿子材料排名。
著作中的第二部分，在室溫(~300 K)下，在c面藍寶石上使用分子磊晶生長磊晶鋁膜。隨後，我們介紹了鋁磊晶膜的晶體結構和光學性質。為了與使用低溫生長(refined two-step)的銀和鋁磊晶膜進行比較，我們分別計算了鋁磊晶膜在RT生長時的SPP和LSP品質因子，以及使用精細低溫生長(refined two-step)的銀和鋁外延膜。特別是室溫生長的鋁外延膜幾乎接近精細的兩步生長，但室溫生長更簡單，應用更實用。為了證明鋁是一種實用性電漿子材料，我們展示了可見光區域的高保真表面增強拉曼光譜基板(SERS substrate)和表面電漿子晶格(surface plasmonic lattice)。在表面增強拉曼光譜基板的部分，我們在鋁磊晶膜上製造奈米凹槽，並將WSe2/MoS2異質結構作為單分子分析物轉移，從樣品實空間掃描光譜的結果顯示出表面增強拉曼光譜基板高均勻性和強場增強。此外，由於強電漿子場增強，實驗中還可以清楚地觀察到MoS2 (452 cm-1)和WSe2 (266 cm-1)的2LA(M)峰，此來源於涉及縱向聲子的二階過程布里淵區的M點。在表面電漿子晶格(surface plasmonic lattice)部分，由於可見光範圍內的高輻射損耗，鋁奈米結構偶極子諧振器通常表現出小的品質因數（Q < 5）。在這裡，我們在鋁磊晶膜上製造鋁奈米孔陣列作為表面電漿子晶格，展示基於傳播性質的 SPP 所表現出高品質因子的表面電漿子晶格模式，其優化後的品質因子接近 ~25。
接著第三部分，我們關注電漿子銀奈米孔陣列與羅丹明6G (R6G)染料分子耦合系統，並探測動量空間中的極化子色散關係。為了更好地了解極化子系統，我們首先通過有限差分時域(FDTD)模擬近場分佈，以證明金屬和電介質界面之間存在傳播的SPP。其次，通過旋塗技術覆蓋在電漿子銀奈米孔陣列頂部的聚乙烯吡咯烷酮(PVP)層(~50 nm)，通過角度分辨消光系統測量具有不同週期等離子體銀納米孔陣列的色散關係，並使用耦合模式模型(coupled-mode model)來分析實驗結果。為了討論表面電漿極化子覆蓋在電漿子銀奈米孔陣列上的R6G聚合物，並測量角度分辨消光和光致螢光光譜。在此極化子系統中，通過共振離調分別觀察到強耦合現象和極化子發射。值得一提的是，在此系統還觀察到極化子帶與能隙是通過傳播性質的極化子彼此交互作用(polariton-polariton coupling)形成的。
如今，隨著量子技術的興起，高保真拓撲數或量子數越來越受到重視。許多研究集中在本徵模工程，包括 PT 對稱、拓撲能帶結構和雷射物理中的偏振奇異點。在第四項研究中，我們將討論對稱保護的 BIC 模式、極化渦旋和拓撲電荷。再來，展示了對稱保護的穩健性，並使用此高質量因子共振模式與適當的增益介質(R6G)耦合。此外，我們展示了具有 TM 偏振拓撲電荷 (+1) 的定向、室溫和單模表面發射電漿子雷射。這一成就通過電漿子能帶工程提供了一種穩健且可調諧的機制。可應用在於光物質相互作用、定向表面發射激光器和具有穩健拓撲電荷的量子信息。該原理和分析適用於電子、聲學和聲子系統。論文最後也給出了BIC雷射的雷射報告總結和文獻對比表格。

Controlling light-matter interaction forms polariton states is a key factor of future photonic and optoelectronic devices. The polaritonic systems can be formed by strongly coherent energy exchange between electromagnetic modes and electronic transition states. Generally, Rabi splitting larger than line widths of the intrinsic light and matter states in strong coupling regime, and energy anti-crossing phenomenon will be observed in detuning spectra. Polaritons are half-light, half-matter bosonic quasiparticles and offer the possibilities to explore many-body physics including Bose-Einstein condensation (BEC), polariton laser, and some practical polaritonic devices.
In the first part, we define the plasmonic materials and give some examples of their applications in nano-optics, bio-application, and energy transducer. Later, introduced to fundamental plasmonic materials and their intrinsic optical properties including Drude and Lorentz model. In order to more realize detail of the origin of the free- and bound electron behavior in metal, discuss the bound electron contribution from electronic band structures of metal. Especially, aluminum is a Drude-like material due to its band structure being close to the free-electron band, only a little bound electron transition is at near W and K point, which is resonance type transition. However, the electronic band structures of the other fundamental plasmonic materials are similar, and their bound electron is from d to sp hybrid band transition, which is the threshold type. After realizing the band diagrams and optical properties, we deposited the wafer-scale metal film, measured their dielectric constants, and used the suitable dielectric model to fit these optical responses, and extracted some physical meaning parameters (e.g. plasma frequency, damping rate, and interband transition energy). Finally, introduction to the background of surface plasmons including propagating surface plasmon polariton (SPPs) and localized surface plasmons (LSPs), some common plasmonic modes, and the quality factor for ranking of plasmonic materials.
In the second part, using molecular beam epitaxy growth epitaxial aluminum film on c-sapphire at room temperature (~300 K). Later, we introduce structural and optical properties of the aluminum epitaxial film. For comparison with silver and aluminum epitaxial film using two-step growth, we calculated the SPP and LSP quality factors of aluminum epitaxial film at RT growth, and silver and aluminum epitaxial film using refined two-step growth. Especially, the aluminum epitaxial film at room temperature growth is almost close to refined two-step growth, but room temperature growth is simpler and practical for application. For proposing that aluminum is a practical plasmonic material, we demonstrate high-fidelity surface-enhanced Raman spectroscopy (SERS) substrates and surface plasmonic surface lattice in the visible region. In the SERS part, we fabricate a nanogrooves on aluminum epitaxial film and transfer WSe2/MoS2 heterostructure as a molecular analyte. Using spatial mapping, the results show high uniformity and enhancement. Furthermore, we can also clearly observe the 2LA(M) peaks of MoS2 (452 cm–1) and WSe2 (266 cm–1) due to the strong plasmonic field enhancement, originating from a second-order process involving the longitudinal acoustic phonons at the M point of the Brillouin zone. In the surface plasmonic lattice part, aluminum nanostructure dipolar resonators can typically exhibit a small quality factor (Q < 5) due to a high radiative loss in the visible range. Here, we fabricate aluminum nanohole arrays on the aluminum epitaxial films as the plasmonic surface lattices to demonstrate high-Q plasmonic surface lattice modes based on propagating SPPs, which optimization quality factor is close to ~25.
In the third part, we focus on the Rhodamine 6G (R6G) dye molecules coupled with the plasmonic silver nanohole arrays and probe polaritonic dispersions in the momentum space. For more realizing this open system, we firstly simulated near-field distributions by finite-different time-domain (FDTD) to evidence propagating SPPs exist between the interface of a metal and dielectric medium. Secondly, polyvinylpyrrolidone (PVP) layer (~50 nm) covered on top of plasmonic silver nanohole arrays by spin-coating technique, measuring dispersions of the plasmonic silver nanohole arrays with different pitches by the angle-resolved extinction setup, and using the coupled-mode model to analyze these results. To discuss plasmon-exciton polaritons (e.g. light-matter interaction), R6G polymer matrix covered on plasmonic silver nanohole arrays and measuring angle-resolved extinction and photoluminescence spectra. In this polaritonic system, strong coupling phenomena and polariton emission are observed by angular detuning, respectively. Furthermore, we also observed polariton bands and gaps are formed by propagating plasmon-exciton polariton.
Nowadays, with the rise of quantum technology, more and more attention is paid to high-fidelity topological numbers or quantum numbers. Many studies focus on eigenmode engineering including PT-symmetric, topological band structure, and polarization singularity in laser physics. In the fourth study, we would discuss the symmetry-protected BIC mode, polarization vortex, and topological charge. Later, we demonstrate how robust is the symmetry-protected and use the high-quality factor resonance mode to be coupling with moderate gain (Rhodamine 6G). Further, we demonstrated the directional, room temperature, and single-mode surface-emitting plasmonic laser with a TM-polarized topological charge (+1). This achievement provides a robust tunability mechanism by the plasmonic band engineering. Possible applications lie in light-matter interaction, directional surface-emitting laser, and quantum information with a robust topological charge. The principle and analysis are applicable to electronic, acoustic, and phononic systems. The laser reporting summary and the comparison table of the BIC laser are also shown at the end of the thesis.

TABLE OF CONTENTS

Abstract i
摘要 iv
致謝 vi
LIST OF FIGURES x
LIST OF TABLES xxiv
Chapter 1. Introduction 1
1.1 Fundamental of plasmonic materials 1
1.2 Light in metals 4
1.3 Electronic band structures of metals 7
1.4 Optical properties of metals 9
1.5 Background of surface plasmons 18
1.5.1 Surface plasmon polaritons (SPPs) 20
1.5.2 Localized surface plasmons (LSPs) 23
1.5.3 Introduction to plasmonic modes 26
1.5.4 Quality factor (Q) of surface plasmons 28
Chapter 2. Experimental methods 30
2.1 Growth and lithography techniques 30
2.1.1 Plasma-assisted molecular beam epitaxy (PAMBE) 30
2.1.2 Thermal evaporator 31
2.1.3 Atomic Layer Deposition (ALD) 32
2.1.4 Focused ion beam (FIB) lithography 33
2.2 Optical measurements 34
2.2.1 White light interference 34
2.2.2 Micro-Raman measurement 35
2.2.3 Confocal microscopy/spectroscopy 36
2.2.4 Angle-resolved microscopy/spectroscopy 37
Chapter 3. Epitaxial aluminum films as an alternative plasmonic material 43
3.1 Growth epitaxial aluminum films on c-sapphire by PAMBE 43
3.2 Optical properties of epitaxial aluminum film 46
3.3 Surface white light interface and plasmon propagation length 48
3.4 Surface-enhanced Raman spectroscopy 52
3.5 Plasmonic surface lattice modes and optimization quality factor (Q) 54
Chapter 4. Strong coupling between surface plasmonic lattice and Rhodamine 6G dye molecules 58
4.1 Strong coupling and coupled mode model: 58
4.1.1 Coupling of classical harmonic oscillators 58
4.1.2 Strong coupling in classical description 60
4.1.3 Jaynes-Cummings model 62
4.2 Growth silver films on c-sapphire by thermal evaporator 64
4.3 Surface plasmonic lattice 66
4.3.1 Surface plasmon polaritons (SPPs) excited by periodic lattice:
66
4.3.2 Definition of transverse electric (TE) and transverse magnetic (TM) mode: 69
4.3.3 Coupled mode model including all first Bragg reflected mode:
70
4.3.4 Ag nanohole array as the surface plasmonic lattice: 72
4.3.5 Field distributions in near-field regime: 75
4.3.6 Reduce symmetry of lattice: 76
4.4 Plasmon-exciton polariton: 77
4.4.1 Principle and Design 77
4.4.2 Theoretical and Experimental observation from weak to strong coupling 80
4.4.3 Polariton Emissions and Polariton-Polariton Interaction 86
Chapter 5. Surface-emitting plasmonic laser with a topological charge
88
5.1 A brief review of plasmonic lasers: 88
5.2 Fundamental principle of bound states in the continuum (BIC):
91
5.2.1 Temporal coupled-mode theory 92
5.2.2 Measurement and observation the BIC modes 94
5.2.3 Imperfect reflection and symmetry broken 94
5.3 Topological Properties of optical BIC modes 96
5.3.1 Polarization field in momentum space 96
5.3.2 Polarization vortex in momentum space 97
5.4 Surface-emitting plasmonic laser with a topological charge 98
5.4.1 Principle and Design 98
5.4.2 Observation of the symmetry-protected BIC mode 101
5.4.3 Near-field simulations of the symmetry-protected BIC mode 103
5.4.4 TM-polarized topological charge (+1) 105
5.4.5 Lasing action in the symmetry-protected BIC mode 110
5.4.6 Conclusions 112
References 115
Curriculum Vitae (Chang-Wei Cheng) 142

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