三維奈米粒子於電磁場解析研究

Abstract

摘要據Maxwell電磁理論以及並矢格林函數，整理三維奈米粒子受到平面波與電偶極波源入射的電磁場解析解。除此之外，定義量子效率、激發比率、螢光發散比率。探討當電偶極靠近奈米粒子的近遠場性質。研究首先整理平面波入射實心奈米粒子的電磁場散射問題級數解(Mie Theory)，並進一步將實心奈米粒子衍伸至核-殼奈米粒子。再來，整理電偶極入射實心奈米粒子的電磁場散射問題級數解，並且同樣將實心奈米粒子衍伸至核-殼奈米粒子。實驗上，金屬奈米粒子靠近一螢光分子的激發過程與放射過程可利用此兩部分解析解模擬。最後利用計算出來的電磁場求出量子效率與激發比率，藉以探討螢光增益。過數值計算可知，電偶極遠近只影響到各物理量值的大小，物理量最大值所對應到的波長沒有紅移或藍移的現象。另外，改變增加實心奈米粒子的半徑或是核-殼奈米粒子的核心半徑、減少金屬殼層厚度將產生紅移的現象。最後核-殼奈米粒子的結構在長波長部分比起實心奈米粒子有更高的螢光增益。

Analytic solution of three-dimensional nanoparticle under electric dipole source and plane wave is investigated. Quantum yield, excitation rate, and fluorescence enhancement can be calculated via Mie theory and dyadic Green’s function. The analytic series expansion solution of the scattering between plane wave and a solid sphere is presented. Additionally, the core-shell sphere will be presented at the same time. The analytic series expansion solution of the solid/core-shell scattering between an electric dipole is presented besides plane wave. Experimentally, these analytic solutions of electromagnetic fields can simulate two step processes. According to the numerical results, the far and near distance between electric dipole and sphere only change the value of quantum yield, excitation rate, and fluorescence enhancement. The corresponding wavelength of these maximum quantities will not be red-shift. The red-shift of the corresponding wavelength arises from the increase of solid sphere, the decrease of shell thickness, and the increase of core radius. Compared with solid sphere, core-shell sphere always has better enhancement at the region of long wavelength provided the shell is thin enough.