光與電漿子結構的交互作用之模擬分析

Abstract

表面電漿子(surface plasmon polaritons, SPPs)在奈米光學上有許多應用，不同的奈米結構將會增強表面電漿子效應，因此本文以邊界元素法(Boundary element method, BEM)與有限元素法(Finite element method, FEM)分析不同奈米結構所激發出的表面電漿子的光學現象。邊界元素法是在表面創造網格並與基本解建立積分表示式(integral representations, SIRs)，可以分析整體電磁場分布，具有半解析與較少的未知係數的優點，對於分析表面電漿子在無窮域與表面物理現象是一項有利的數值方法。在結構的邊角處與曲率較大的地方會有劇烈的電漿子震盪，不只有電場能量的增強，Poynting向量的流線也會被扭曲纏繞改變傳播流向，並且在尖角處有光渦旋的行為發生，使奈米結構的表面上在特定方向上形成明顯的光化學合成，從無手徵性(chiral)結構變成帶有手徵性的結構。表面電漿子的電磁場會在物體表面上形成光曳引力，表面電位移的強度與Maxwell應力張量在正向應力的關係可以提供奈米結構的光變形，對於不同波長下的表面電漿子共振的電漿模態將能夠在局部位置上形成光拉力。 有限元素法將分析區域建立立體網格並來展現去域內的物理分量，將微分方程變成弱形式(weak from)去數值模擬，可以分析較複雜幾何形狀的電磁波問題。第二部份研究奈米孔洞的光學性質中，將利用圓柱座標下向量波函數所建構的超越方程式分析奈米單一孔洞的解析解中不同的SPPs傳播模態在無窮長的傳播特性，對於孔洞內所傳遞的模態會有顯著差距在模態的傳播長度(propagation length)上，其中以Mode-1為主要能夠通過奈米孔洞的光學訊息。從無窮長的模態分析轉換至有限厚度的奈米孔洞，本文使用有限元素套裝軟體COMSOL來分析圓形平面波激發奈米孔洞的光學特性。入射的圓形平面波所帶有的手徵性以及奈米孔洞的邊緣提供的光子動量轉換使奈米孔洞內激發出傳播模態，而從洞內帶有螺旋(helical)的Mode-1傳遞到洞口後會激發出在表面上帶有螺旋(spiral)的表面電漿子，並且可以簡化分析模型來設計表面電漿子的干涉樣式，增強金屬表面的能量分布。在週期性排列的孔洞分析中，不同的晶格長度將會改變孔洞間的表面電漿子干涉，當滿足布洛赫條件(Bloch condition)時會使光場會在特定波長侷限能量在金屬表面上，將會增強金屬吸收光子轉換成熱電子的效應，並且對應到量測穿透頻譜之低谷上。

In nano-optics, a variety of applications and researches of surface plasmon polaritons (SPPs) have drawn a lot of attentions recently. In this first topic of this thesis, we developed a boundary element method (BEM) based on surface integral equations (SIEs) to calculate the electromagnetic (EM) fields on the surface of plasmonic nanostructures. The surface EM fields can be used to reconstruct EM fields in the domain by using the surface integral representations (SIRs) for the study of plasmonic behaviors. Since only the physical unknowns at the discrete meshes on the boundary need to be solved, BEM has the advantages of matching the radiation condition semi-analytically and less unknowns for numerical calculation. Because plasmon effect is particularly significant at the corners of a nanostructure, the intensity of electric field is enhanced to twist the streamlines of the Poynting vector to perform a winding behavior; there are optical vortices of energy flow at these sharp corners. When a gold nanocuboid is excited by the right-handed circularly polarized plane wave, the plasmon-enhanced photochemistry reaction would occur at the sharp corners to produce a chiral nanostructure. The phenomenon also enhances the optical traction, in terms of Maxwell stress tensor, on the surface of the nanostructure to induce the optomechanical motion and optical deformation. In the second part, we analyzed the propagation characteristics of surface plasmon polarition (SPP) via nanoholes in metallic film. The propagation modes of different SPPs in an infinitely-long nanohole are solved by a transcendental equation. The Mode-1 SPP is a dominant mode though a nanohole because that its propagation loss is less than the other modes. For a finite nanohole, we used the finite element method (COMSOL) for study. We found a mode-1 spiral SPP propagating from the outlet of nanohole, which is converted from the mode-1 helical SPPs in the nanohole. Moreover, periodic nanohole array induces multiple SPPs causing interference at the surface of metal film to change the transmission power at certain specific wavelengths. Particularly when the Bloch condition is satisfied, the nanohole array confines the light energy on the surface. Consequently, there is a Bloch dip at the transmission spectrum. Additionally, the constructive interference of SPPs at the near field of metal might be useful for biosensor.