金屬奈米殼之電漿子模態分析

Abstract

本研究利用Mie理論及並矢格林函數，分別分析球型金屬(金、銀)奈米粒子或奈米殼(nanoshell)受到平面波及電偶極波源在不同波長激發下，所表現的各種模態，例如偶極模態、四極模態、六極模態。對於平面波激發，分析奈米粒子的吸收截面積與散射截面積行為。對於電偶極激發，則分析受到奈米粒子或奈米殼的影響下之近場及遠場行為，例如輻射功率與非輻射功率。為進一步探討這些模態對兩個螢光體(予體、受體)之間的Förster共振能量轉移(Förster resonance energy transfer; FRET)之影響，本研究以雙電偶極(bi-dipole)波源模擬之，依據雙電偶極的方向，分成同向(反對稱)及反向(對稱)兩種波源。 數值模擬結果顯示，同向(反對稱)的雙電偶極可以激發出奇數項的模態(偶極模態、六極模態)；而反向(對稱)的雙電偶極，則可激發出偶數項的模態(四極模態、八極模態)，這些模態與平面波激發的結果一致。金奈米粒子及金奈米殼僅有偶極與四極模態表現，其他高階模態因波長較短，易被金吸收故不表現，另外在510-540 nm之間有極強的材料吸收。銀奈米殼則有各個模態的表現，且不同階模態的波長會隨內徑對殼層厚度的比值增大而增長，另外在330-355 nm之間有極強的材料吸收。其中四極模態的波寬較窄，且其近場及遠場行為皆優於其他模態，可被利用形成一個小型共振腔，幫助兩個位於南北極的螢光體(予體、受體) 之Förster共振能量轉移，適合實現奈米雷射的構想。 最後分析不同比例的金銀合金奈米殼，結果顯示其模態(偶極、四極模態)依據合金比例介於金、銀奈米殼的模態之間。

The plasmonic modes of Au and Ag nanoparticles (NPs) and nanoshells (NSs) excited by plane waves and electric dipoles are studied by using Mie theory and dyadic Green’s functions; e.g. the dipole, quadrupole and sextupole modes. For the plane wave excitation, the absorption and scattering cross sections are analyzed. For the dipole excitation, the near-field and far-field responses (e.g. radiative and nonradiative powers) are analyzed. Furthermore, to study the enhanced FRET between a donor and acceptor by these modes, two types (symmetric and anti-symmetric) of bi-dipole are used for simulation. Numerical results show that anti-symmetric bi-dipole can excite the dipole and sextupole modes, and the symmetric one the quadrupole and octupole modes. These modes are in agreement with those excited by a plane wave. For Au NP and NS, only the dipole and quadrupole modes are observed, while the other higher-order modes are not. In addition, there is a strong absorption band at 510-540 nm. For the Ag NS, the dipole, quadrupole, sextupole, and octupole modes are observed. Moreover, these modes are red-shifted as the ratio of the core radius to the shell thickness increases. In addition, the strong absorption band is at 330-355 nm. The quadrupole mode exhibits its superiority in the near and far fields. Therefore it can be utilized to form a resonant cavity for enhancing the FRET of a donor and acceptor. This is to say the quadrupole mode of Ag NS can be used to realize the spaser-based nanolaser. Finally, the plasmonic modes of Ag/Au alloy NS are studied. These modes are in between those of Ag NS and Au NS, depending on the ratio of alloy.