金奈米孔洞陣列量測環境折射率變化之探討

Measurement of the Change in Refractive Index of Surrounding Medium by Gold Nanohole Array

陳炳憲(Bing-Xian Chen)

指導教授 ： 郭茂坤

國立臺灣大學/工學院/應用力學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202203315

摘要

本論文探討自旋軌道力矩效應和金奈米孔洞陣列量測環境折射率兩部分。第一部分為金奈米粒子與光作用的自旋-軌道交互作用，探討當奈米結構於光軸中心時其自旋行為。後續對Maxwell應力張量計算奈米結構所受之總光力矩，以及zilch張量計算自旋角動量轉換力矩，對兩者相減而得到的軌道角動量轉換力矩，當光源為非平面波時，消散場會對軌道角動量轉換力矩產生貢獻。針對單一奈米粒子在搭配具有軌道角動量的Bessel光束或在高斯光束聚焦平面下游處，因光與粒子結構的交互作用下，部分的自旋角動量轉換到軌道行為上，導致軌道公轉運動行為。因光源提供自旋及軌道角動量，在自旋與軌道角動量密度較大處，對粒子產生的自旋與軌道公轉力矩也較為強烈，且均發生在平衡位置周遭。軌道運動的方向與Bessel光束的階數正負號有關，自旋的方向會受到Bessel光束的極化方向影響。
第二部分為金奈米孔洞陣列量測環境折射率變化，當圓形極化光穿過孔洞陣列後，於遠場的穿透能量頻譜上看到低谷的產生，因Bloch條件為週期性邊界方向上的交互干涉作用，而孔洞之間表面波的相向傳播，將形成駐波將能量留在金屬表面上，導致在共振波長發生時，於穿透能量上有相對低谷。Wood異常為入射光穿透孔洞或光柵時，繞射波沿平行於金屬表面方向傳播，於介質中傳遞時，形成建設性或非建設性干涉。Bloch條件與Wood異常發生的共振波長於穿透能量上有所影響。由於Bloch條件與金屬和環境介質有關，當環境折射率改變時，其共振波長會隨之改變，可作為折射率感測器使用。而本研究使用COMSOL去模擬在四方、六方排列方式下，調整孔洞間距及孔洞形狀對環境折射率敏感度及品質因子(Figure of Merit)進行比較，提供優化敏感度的準則來進行後續孔洞結構設計之方向。

關鍵字

光力 ； 高斯光束 ； Bessel光束 ； 光力矩 ； 軌道角動量 ； zilch張量 ； Bloch 條件 ； Wood anomaly ； 表面電漿共振 ； 金屬奈米孔洞

並列摘要

This thesis includes two topics: the spin-orbit interaction of light upon the optomechanics of nanoparticle (NP), and the measurement of refractive index using nanohole array in gold film.
In the first topic, the spin-orbit interaction of a structured light interacting with a silica NP, gold NP, or gold nanorod (NR) is studied. When a NP is illuminated by a circularly polarized (CP) Bessel beam, it performs an orbital motion with spinning. This is because that a part of the orbital angular momentum (OAM) and spin angular momentum (SAM) of Bessel beam are transferred into the NP by the light scattering and absorption. We use the multiple multipole (MMP) method to simulate the electromagnetic field. The total optical torque exerted on NP is calculated by the surface integral of Maxwell’s stress tensor, and the SAM transfer torque is calculated by the surface integral of zilch stress tensor. The OAM transfer torque, which is the difference of the two torques, is also analyzed. We find that the maximum OAM transfer torque occurs at the stable orbit of the NP. The rotation of the orbital motion depends on the sign of the order of Bessel beam, and the spin direction of the NP depends on the handedness of the CP Bessel beam.
The second topic focuses on the analysis on the measurement of the change of the refractive index of surrounding medium using a nanohole array in gold film. When a CP light irradiates a periodic nanohole array in gold film, the transmission spectrum shows a deep profile at certain specific wavelengths. If Bloch condition is satisfied, the surface plasmon polaritons originating from these nanoholes form a standing wave. At this resonant wavelength of Bloch dip, most energy is confined on the metal surface, resulting in a deep in the transmission spectrum. From the shift of Bloch dip, we can measure the change of the medium’s refractive index. We use COMSOL to simulate the transmission spectra of a variety of nanohole arrays; square or hexagonal arrays of different shaped nanoholes with different pitches. The sensitivity and the figure of merit (FoM) of the nanohole array are investigated to optimize the design for sensor.

並列關鍵字

Optical force ； Gaussian beam ； Bessel beam ； optical torque ； orbital angular momentum ； zilch stress tensor ； Bloch condition ； Wood anomaly ； surface plasmon resonance ； metallic nanohole array

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