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

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。

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.