Bessel光束照射金奈米粒子之角動量轉換分析

Abstract

本研究旨在探討在平面波圓形極化光照射金奈米二聚體時，金奈米粒子之間交互作用產生逆公轉的現象，並進一步分析帶有軌道的Bessel光束照射金奈米粒子時，自旋與軌道之交互作用(spin-orbit interaction, SOI)對粒子運動軌跡、能量、動量、角動量等物理量的影響，特別是角動量之轉換分析。本研究採用多重中心展開法(multiple-multipole expansions method)計算電磁場，再以Maxwell應力張量計算奈米粒子所受到的光力與光力矩。最後，研究利用粒子運動方程式計算多顆金奈米粒子的運動軌跡以及公轉與自旋轉速。 根據數值結果顯示，平面波圓形極化光照射下，粒子的自旋角動量與多極子疊加會導致金奈米粒子之間產生逆公轉的現象。接著進一步研究帶有軌道的Bessel光束時，半徑150 nm金奈米二聚體也觀察到逆公轉的現象。 當使用Ɩ = 0階的Bessel光束在平衡位置進行照射時，不會提供軌道角動量特性。然而，在照射單顆金奈米粒子時，隨著體積的增加，由於高階模態與多極子疊加的極化方向，部分的自旋角動量被轉換到軌道角動量。因此，自旋與軌道運動行為的方向相同。此外，利用介電珠的不吸收的特性進行分析，可以驗證當不提供自旋角動量時，此時軌道角動量值極小，幾乎不會發生公轉現象。當使用Ɩ = 1~5階的Bessel光束進行照射時，隨著階數的提高使軌道半徑增加，平衡位置下入射電場強度降低，自旋與軌道之角動量與轉速也會下降。 在Bessel光束照射半徑50 nm之多顆金奈米粒子中，由於粒子之間的交互作用較弱，左旋與右旋光之間的排列圖形皆為串珠式；運動軌跡在電場最強處，粒子間距維持著1倍的水中波長。在金奈米三聚體與四聚體中，利用粒子的大小、高階數使軌道半徑增加讓側向電場較均勻，最後形成三角形、菱形之粒子群。若金奈米粒子太大顆會產生對邊或明顯的內外圈之各種變化的運動軌跡。

The aim of this study is to investigate the phenomenon of counter-rotation between gold nanoparticles under the illumination of plane waves with circular polarization, and to further analyze the effects of spin-orbit interaction (SOI) in the presence of Bessel beams with orbital characteristics on the particle's motion trajectories, energy, momentum, angular momentum, and particularly the analysis of angular momentum conversion. The multiple-multipole expansions method is employed to calculate the electromagnetic field, and then the Maxwell stress tensor is used to calculate the optical force and torque experienced by the nanoparticles. Finally, the study utilizes the particle motion equations to calculate the trajectories of multiple gold nanoparticles, as well as the revolution and spin rotation speeds. According to the numerical results, it is observed that under the illumination of plane waves with circular polarization, the superposition of spin angular momentum and multipole moments in particles leads to the phenomenon of counter-rotation between gold nanoparticles. Furthermore, further research on Bessel beams with orbital characteristics has also observed the counter-rotation phenomenon in a 150 nm radius gold nanoparticle dimer. When a zero-order Bessel beam is used for irradiation at the equilibrium position, it does not provide orbital angular momentum characteristics. However, when irradiating a single gold nanoparticle, with an increase in volume, due to the polarization direction resulting from the superposition of higher-order modes and multipole moments, a portion of the spin angular momentum is converted into orbital angular momentum. Therefore, the directions of spin and orbital motion behavior are the same. Additionally, by analyzing the non-absorbing properties of dielectric beads, it can be verified that when spin angular momentum is not provided, the orbital angular momentum value is extremely small, and revolution phenomena hardly occur. When irradiated with Bessel beams of order 1 to 5, an increase in order leads to an increase in the orbital radius, a decrease in the incident electric field intensity at the equilibrium position, and a reduction in both the spin and orbital angular momentum and rotation speed. In the case of multiple gold nanoparticles with a radius of 50 nm under Bessel beam irradiation, the interaction between particles is weak. The motion trajectories between left-hand circularly polarized light and right-hand circularly polarized light are in the form of string-like patterns at the strongest region of the electric field, with interparticle distances maintained at 1 times the wavelength in water. In the case of gold nanoparticle trimers and tetramers, by manipulating the particle sizes and higher-order modes, the orbital radius is increased to achieve a more uniform lateral electric field, resulting in the formation of triangular or rhombus-shaped particle clusters. If the gold nanoparticles are too large, various variations in motion trajectories, such as edge-to-edge or distinct inner and outer rings, can be observed.