金、銀奈米粒子之光束縛力

Abstract

以線性極化平面電磁波或Gaussian光束，照射金、銀奈米二聚體(dimer)，產生表面電漿子共振(surface plasmon resonance；SPR)，並出現控制著兩粒子穩定距離的光束縛力(optical binding force)。在幾種波長下，由多重中心展開法(multiple-multipole expansions method)計算電磁場，並透過Maxwell應力張量得知粒子所受光力，與二聚體間距改變的關係。結果顯示，在各波長下，粒子會出現幾個穩定平衡距離，並束縛住彼此，而這距離皆為略小於在介質中波長的整數倍。在這些特定的距離下，當兩粒子靠近或遠離時，二聚體間的光力會如同彈簧般，產生斥力或吸力，且當二聚體相距一倍波長時，這虛擬彈簧中的恢復力與彈簧常數往往是最大的，表示這是最穩定的狀態，此外，兩粒子球心連線(中心線)總是傾向於垂直電場極化的方向。至於由不相同的兩粒子所組成的異型二聚體，其穩定平衡距離仍然存在，但會出現光泳力，驅使整個二聚體系統作剛體運動。另一方面，以Gaussian光束為光源時，會產生朝向中心的梯度力，對平衡位置產生影響，甚至破壞。而三顆粒子所組成的三聚體，同樣以接近介質中波長的距離，保持平衡，並仍有光泳力的產生。 除此之外，任意角度平面波，照射金奈米桿的平均吸收與散射效應，及金奈米桿的去極化效率(depolarization ratio)，也在本文作討論。結果指出，金奈米桿的長軸表面電漿子共振(longitudinal SPR；LSPR)，會隨著桿的細長比(aspect ratio；AR)增加而紅位移。至於金奈米桿的去極化效率，與LSPR並無太大關係，但會隨著AR值加大而增加，且紅位移。

This study theoretically investigates that plasmon-mediated optical forces, exerted on metal dimers, consisting of two gold or silver nanoparticles (NPs), induced by the normal illumination of a linearly polarized plane wave or Gaussian beam. Using the multiple multipole method, we analyzed the optical force in terms of Maxwell’s stress tensor versus the inter-particles distance for some specific wavelengths. Numerical results show that for a given wavelength there are several stable equilibrium distances between NPs, which is slightly shorter than some integer multiples of the wavelength in medium, for metal dimer acting as bonded together. At these specific distances, the optical force between dimer will become a repulsive or an attractive force when the two NPs are close to or away from each other. The spring constant of the restoring force at the first stable equilibrium is always the maximum, indicating that the first stable equilibrium distance is the most stable one. Moreover, the central line of a dimer tends to be perpendicular to the polarization of light. For a heterodimer, which consists of two NPs of different sizes or different materials, the phenomenon of stable equilibrium distance still exists but with a net driving photophoretic force to move the heterodimer. In addition, a Gaussian beam provides a gradient force reducing the stability of these equilibriums. For a trimer, consisting of three gold NPs, there still exists stable distance between NPs and also a photophoretic force. Moreover, the average scattering and absorption efficiencies as well as depolarization ratio of a randomly oriented gold nanorod are also studied. Our results indicate that the depolarization spectrum is broader than those of scattering and absorption efficiencies. The maximum depolarization ratio can be raised and the corresponding wavelength (not at the longitudinal SPR) is red-shifted by increasing the aspect ratio.