Bessel光束對多顆奈米粒子的光力操控

Abstract

本文研究奈米粒子受到結構光照射後，粒子被捕捉至特定位置或軌道的光力操控行為。其中包括線性極化高斯光束照射金奈米二聚體結構對介電粒子的捕捉；以及自帶軌道角動量(orbital angular momentum, OAM)的圓形偏極化Bessel光束照射金和二氧化矽奈米粒子後，粒子被捕捉至公轉軌道的行為。以多重中心展開法(multiple-multipole expansions method)計算電磁場，並透過Maxwell應力張量計算出粒子所受的光力，由粒子運動方程式計算軌跡並加入布朗運動的熱擾動進行模擬。在模擬實例中，找出粒子折射率與環境折射率的差異對光力行為的影響，觀察出不同性質的Bessel光束帶有的特性以及多顆粒子的交互作用對軌道運動的影響。 結果顯示，粒子折射率與環境折射率差異越大，光力的抓取會更加穩固，粒子所受到的布朗運動擾動影響更小。而Bessel光束的部分，階數大小與其錐角大小皆會影響粒子公轉軌道的大小。階數越大，光場整體的輪廓越向外，穩定公轉軌道的半徑就越大；而錐角角度越大，穩定公轉軌道的半徑會越小。金奈米粒子因具有高度吸收光子能力，在光力行為表現上會比二氧化矽奈米粒子還要明顯。在多顆粒子的模擬中，可觀察到粒子之間因交互作用力而產生的軌道偏移行為。在遠距離排列達到穩定狀態時，粒子間距大約是水中波長整數倍的距離。另外金奈米粒子在不同間距大小下會呈現不同種公轉的行為，以各粒子間距大小分為大間距排列與小間距排列。大間距排列以各粒子固定在同一軌道上穩定運行為主，粒子群的形狀會因相對位置不同而有所差異；小間距排列則能看到更加明顯的粒子間交互作用，在三顆及四顆金奈米粒子的模擬中更是能看見金奈米粒子繞著粒子群質心旋轉，同時粒子群也對光軸公轉的現象。而四顆金奈米粒子群繞著質心旋轉速度甚至出現了週期性的變化。

In this thesis, two topics were studied, the plasmon-enhanced optical trapping and the optomechanical behaviors of multiple nanoparticles (NPs) manipulated by a structured light. In the first topic, the optical trapping on a dielectric NP by a linearly polarized Gaussian beam irradiating a gold nanodimer is studied. Utilizing the multiple-multipole expansion method, we calculate the electromagnetic field, and then to analyze the optical forces, the surface integrals of Maxwell's stress tensor, upon these NPs. Based on these optical forces, the trajectories of these NPs are calculated by the dynamic equations of NPs, where the thermal disturbance for Brownian motions are considered. Our results show that the larger the difference of the refractive index between the NP and the medium the bigger the optical force. The other topic focuses on the orbital motions of multiple gold or silica NPs induced by the circularly polarized (CP) Bessel beam with orbital angular momentum (OAM). The radius of the orbit relies on the order and the cone angle of Bessel beam. The larger the order, the larger the radius of the stable orbit. Additionally, the larger the cone angle, the smaller the radius of the stable orbit. Because of the high absorption for photons by gold NPs, the optomechanical behaviors of gold NPs are more significant than those of silica NPs. The stable pattern of multiple NPs, performing an orbital motion, is according to the far-field or near-field interaction. For the far-field interaction, these gold NPs are lined up to rotate about the optical axis in a specific orbit, like a string of beads with a constant distance between adjacent NPs. In contrast, for the near-field interaction, these NPs are confined to form a cluster patter by the optical forces, rotating about their centroid; the centroid rotates nearly on a circle orbit. For example, the clusters of three and four gold NPs are a triangular and a diamond patterns, respectively. The motions of the cluster are similar to those of a planetary gear. When a steady state is reached, the distance between adjacent NPs is approximately a wavelength in water. The eventual pattern (string of beads or cluster) of the multiple gold NPs depends on their initial conditions. We also observe the deviations of their orbits; this could be due to the interaction between these NPs.