含螢光分子之多層奈米粒子的平均螢光增益

Abstract

根據Maxwell方程式、Mie理論與並矢格林函數，整理球型奈米粒子受平面波與電偶極波源的電磁場解析解，並進一步將散射體由實心球推廣至多層結構。除此之外，再定義激發效率、量子效率、螢光增益以及考慮螢光分子隨機分佈、任意極化方向的平均螢光增益。 螢光增益與螢光分子位置、震盪方向、入射平面波極化方向三者有密切的關係，考慮一般實驗螢光分子均勻分布、極化方向難以控制的情況，以平均螢光增益的概念來解釋各種散射體的光學特性較為恰當，可避免過於高估或低估的情形產生。另外，再加入史托克位移(Stokes shift)效應，即入射平面波波長與螢光分子放出螢光波長不同的情況，討論核殼散射體、奈米殼散射體與觀察對平均螢光增益的影響。 由數值模擬結果得知，當激發雷射波長與該奈米粒子的表面電漿共振波段重疊時，就可以得到最大的平均螢光增益效果。最後，我們發現銀奈米殼具有最大的平均螢光增益，其值高達225倍。

According to Maxwell equations, Mie theory and dyadic Green’s functions, analytical solutions of the incident plane wave and electric dipole source in the multi-layer structure are derived. In addition, we also define the excitation rate, quantum yield, enhancement factor and average enhancement factor. The average enhancement factor (AEF) by considering the arbitrary orientation and location of molecule with respect to the polarization of the incident wave is proposed to explain the overall performance of a large number of nanoparticles. The concept of AEF can avoid overestimating or underestimating fluorescent intensity. Furthermore, with Stokes shift effect, we observe the difference of AEF between three kinds of nanoparticles:core-shell, nanoshell and nanoshell@SiO2. To obtain the maximum AEF, the excitation spectra had better overlap the surface plasmon resonance(SPR) band. Finally, our results indicate that Ag nanoshell has the highest AEF. The AEF of optimal size of Ag nanoshell (radius of SiO2: 20 nm, thickness of Ag shell: 5nm) is 225.