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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 江正天 | zh_TW |
| dc.contributor.advisor | Cheng-Tien Chiang | en |
| dc.contributor.author | 李明緯 | zh_TW |
| dc.contributor.author | Ming-Wei Lee | en |
| dc.date.accessioned | 2024-02-01T16:15:53Z | - |
| dc.date.available | 2024-02-02 | - |
| dc.date.copyright | 2024-02-01 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-01-18 | - |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/91594 | - |
| dc.description.abstract | 能源利用一直是人類漫長歷史中持續尋求最佳解的議題，而其中一個焦點是如何改善能量傳遞的效率。本論文將從理論的角度切入，利用宏觀量子電動力學(macroscopic quantum electrodynamics)作為理論框架，分析介質與光子所形成的準粒子：電磁極化子(polariton)，如何影響兩個微觀材料間的共振能量轉移(resonance energy transfer)。本論文的討論涵蓋兩個部分：第一部份我們在點電偶極近似(electric point-dipole approximation)下的電漿子(plasmon)耦合共振能量轉移理論，利用米氏散射(Mie scattering)理論計算張量格林函數(tensor Green''s function)，並探討奈米銀球對共振能量轉移速率的影響和分析其中的機制；第二部份我們將聚焦於電漿子耦合共振能量轉移理論的推廣，意即消去點電偶極近似的限制，使得材料的空間構型影響能夠納入考量，其目的在於提供更全面的理論探討大體系間的能量轉移過程。此外我們也證明推廣的理論在給定特殊條件下化簡的結果能夠與其他理論取得一致性。 | zh_TW |
| dc.description.abstract | Optimal energy utilization has always been a continual pursuit throughout human history, and one of the essential issues is the improvement of the efficiency of energy transfer. This thesis approaches the topic from a theoretical perspective, utilizing macroscopic quantum electrodynamics as the theoretical framework to analyze quasi-particles formed by the interaction of media and photons: polaritons. The focus is on understanding how these polaritons affect resonance energy transfer between two microscopic materials. The discussion in this paper comprises two parts. In the first part, we explore the plasmon-coupled resonance energy transfer theory under the electric point-dipole approximation. We calculate the tensor Green's function using Mie scattering theory and investigate the impact of silver nanospheres on the resonance energy transfer rate, analyzing the underlying mechanisms. In the second part, we generalize the theory of plasmon-coupled resonance energy transfer by removing the constraints of the electric-dipole approximation, allowing consideration of the spatial configuration of materials. The aim is to provide a more comprehensive theoretical exploration of energy transfer processes in larger systems. Additionally, we demonstrate that the generalized theory, under specific conditions, yields consistent results with other theories. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-02-01T16:15:53Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-02-01T16:15:53Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xv List of Tables xix Denotation xxi Chapter 1 Introduction 1 1.1 Lord Kelvin’s Two Clouds – The Commencement of Modern Physics 1 1.2 Quantum Electrodynamics in Media – Polaritons 3 1.3 Utilization of Polaritons 4 1.4 Resonance Energy Transfer 5 1.4.1 Electrostatic Limit 6 1.4.2 Invalidity of Dissipative and Absorbing Media 7 1.4.3 Electric Point-Dipole Approximation 8 1.4.4 Prohibition of Electron Exchange 8 1.4.5 Limitation of Fermi’s Golden Rule 9 1.4.6 A Pair of Molecules 9 1.5 Motivation and Objective 10 Chapter 2 Macroscopic Quantum Electrodynamics 11 2.1 Huttner-Barnett Model 12 2.1.1 Classical Lagrangian Density 13 2.1.2 Canonical Quantization of the Transverse Lagrangian 15 2.1.3 Diagonalization of the Transverse Hamiltonian 18 2.1.4 Electromagnetic Fields in the New Representation 20 2.2 Langevin Noise Operator 22 2.3 Macroscopic Quantum Electrodynamics 23 2.4 Summary of Macroscopic Quantum Electrodynamics 26 Chapter 3 Generalized Mie Theory 27 3.1 Theoretical Background 28 3.1.1 Electromagnetic Scattering Problems and Maxwell’s Equations 28 3.1.2 Tensor Green’s Function for Maxwell’s Equations 30 3.1.2.1 Sturm-Liouville Problem and Eigenfunctions 31 3.1.2.2 Orthogonality of Vector Spherical Functions 34 3.1.2.3 Expansion of Vacuum Tensor Green’s Function 39 3.1.3 Spectral Decomposition of Electric Dipole Fields in Vacuum 44 3.1.4 Spheres and Electromagnetic Boundary Conditions 45 3.1.4.1 Single Sphere 47 3.1.4.2 Core/Shell Sphere 50 3.2 Numerical Issues 54 3.2.1 Singularities of Vacuum Tensor Green’s Function 54 3.2.2 Numerical Precision of Vector Spherical Functions 58 3.2.2.1 Radial Functions 58 3.2.2.2 Angular Functions 59 Chapter 4 Influence of Localized Surface Plasmon Polaritons on Resonance Energy Transfer 63 4.1 Plasmon-Coupled Resonance Energy Transfer 63 4.2 Design of Localized-Surface-Plasmon-Polariton Environments 65 4.3 Discussion 66 4.3.1 Coupling Factor Spectra in Plasmonic Spheres 66 4.3.2 Angle Dependence of Coupling Factors 69 4.3.3 Characteristic Distance of Core/Shell Spheres 73 Chapter 5 Resonance Energy Transfer Beyond Electric Point-Dipole Approximation 77 5.1 Theory 77 5.1.1 Hamiltonian 77 5.1.2 Transfer Rate of a Two-Entity System 81 5.2 Transition Current Density and Molecule 88 5.3 Consistency Check to Previous Theories 91 5.3.1 Transition Density Cube Method 91 5.3.2 Plasmon-Coupled Resonance Energy Transfer 93 5.3.3 Förster Resonace Energy Transfer 95 Chapter 6 Conclusion 97 References 101 Appendix A — Mathematics in Macroscopic QED 123 A.1 Fano Diagonalization on ˆH ′⊥ 123 A.2 Fano Diagonalization of ˆH ⊥ 128 Appendix B — Supplementary Information in Generalized Mie Theory 131 B.1 Derivation of Eqs. (3.5) and (3.6) 131 B.2 Derivation from Eq. (3.9) to Eq. (3.14) 132 B.3 Scalar Helmholtz Equation and its Eigenfunctions 133 B.4 Orthogonality of Angular Functions 136 B.5 Expansion of Tensor Delta Function 137 B.6 Contour Integrals in the Vacuum Tensor Green’s Function 138 B.7 Asymptotic Behavior of Vector Spherical Functions as r → 0 143 B.8 Consistent Check of Eq. (3.90) 144 B.9 Derivation of Eqs. (3.96b) and (3.96c) 147 Appendix C — Supplementary Results in Chapter 4 149 C.1 Multipole Expansion of the Coupling Factor 149 C.2 Dielectric Function of Ag Material 150 C.3 Quasi-Static Electric Field for Core/Shell Spheres 150 C.3.1 φ0(r; ω) and Vacuum Scalar Green’s Function 152 C.3.2 φscat(r; ω) and Scattering Scalar Green’s Function 153 C.3.3 Relation between Polarizability and Sphere Size 155 Appendix D — Supplementary Mathematical Derivation in Chapter 5 157 D.1 Continuous Form of ˆ Vpol,M in Eq. (5.12) 157 D.2 Derivation of Eq. (5.24) 159 D.3 ω-Integral Along the Path C2 163 D.4 Interaction of Longitudinal Transition Current Densities 165 D.5 Single-Electron Reduced Wavefunction 167 | - |
| dc.language.iso | en | - |
| dc.subject | 宏觀量子電動力學 | zh_TW |
| dc.subject | 電磁極化子 | zh_TW |
| dc.subject | 共振能量轉移 | zh_TW |
| dc.subject | 局域表面電漿子 | zh_TW |
| dc.subject | 米氏散射理論 | zh_TW |
| dc.subject | 躍遷電流密度 | zh_TW |
| dc.subject | Localized surface plasmon | en |
| dc.subject | Macroscopic quantum electrodynamics | en |
| dc.subject | Polariton | en |
| dc.subject | Resonance energy transfer | en |
| dc.subject | Transition current density | en |
| dc.subject | Mie scattering theory | en |
| dc.title | 從宏觀量子電動力學對電磁極化子耦合共振能量轉移的理論見解 | zh_TW |
| dc.title | Theoretical Insights into Polariton-Coupled Resonance Energy Transfer from Macroscopic Quantum Electrodynamics | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-1 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.coadvisor | 許良彥 | zh_TW |
| dc.contributor.coadvisor | Liang-Yan Hsu | en |
| dc.contributor.oralexamcommittee | 陳信達 | zh_TW |
| dc.contributor.oralexamcommittee | Hsing-Ta Chen | en |
| dc.subject.keyword | 宏觀量子電動力學,電磁極化子,共振能量轉移,局域表面電漿子,米氏散射理論,躍遷電流密度, | zh_TW |
| dc.subject.keyword | Macroscopic quantum electrodynamics,Polariton,Resonance energy transfer,Localized surface plasmon,Mie scattering theory,Transition current density, | en |
| dc.relation.page | 169 | - |
| dc.identifier.doi | 10.6342/NTU202400105 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2024-01-19 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 物理學系 | - |
| 顯示於系所單位： | 物理學系 | |
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