以全向量虛軸有限元素波束傳播法分析具垂直尖角與側邊之電漿子波導

Abstract

在這篇論文中，我們採用以曲線混和型元素為基底的全向量有限元素虛軸波束傳播法搭配完美匹配層來精準地分析幾種電漿子波導。 整篇我們的研究方向主要著重於方形的3D 結構電漿子波導。因此一開始我們將藉由一些長或寬是無限長的波導來了解電漿子模態在直角結構上的現象。 建立了一些基本觀念後，接著我們再分析一條金屬薄線在二氧化矽基板上的條形電漿子波導。我們找到了三種模態，分別為束縛模態、逸漏式模態及邊緣模態。我們理論分析了高階束縛模態在條形波導上寬度的限制，並且與數值計算的結果有不錯的一致性。接下來，我們會討論兩個條形波導的電磁場耦合問題。當兩個波導的電磁場互相耦合時，會產生對稱及反對稱模態，我們分別找出兩種模態的場形圖及計算出它們的等效傳播常數及耗損。我們也計算了幾個頻率的結果並比較兩種模態的色散關係圖。最後，我們由等效傳播常數及耗損的結果，可以推算出兩條形波導之間的電磁干擾問題。

In this thesis, we adopt the full-vectorial finite element imaginary-distance beam propagation method (FE-ID-BPM) based on the hybrid edge/nodal elements and the incorporated perfectly matched layers (PMLs) to analyze several plasmonic waveguides. We start from the simplest, infinite 3-D plamonic waveguide, which is uniform in propagating direction, for investigating the basic characteristics. Then based on those concepts, we introduce some waveguides, such as edge and stripe plasmonic waveguides. We investigate how the size of the edge will affect the confinement and attenuation of surface plasmon polariton (SPP) edge mode. We show three types of SPP modes, including leaky, bound, and edge modes, supported by the stripe waveguide. The limited width of a thin stripe, which can support the bound mode, is analyzed by some approximation, and the results agree with that calculated by the FE-ID-BPM numerical model. Comparison among the modes is discussed. Then, we look into the coupling phenomenon of two single elements. The coupling in- duces symmetry and antisymmetry modes, which can both be numerically obtained using the FE-ID-BPM. Related plasmonic slot and stripe waveguides are studied, and their mode patterns and dispersion diagrams presented. We calculate the effective propagating constant and attenuation for different spacings of the two adjacent stripes. The crosstalk between the coupled stripes is then evaluated.