以有限差分時域法分析二維奈米電漿子結構之光散射與導波問題

Abstract

摘要 本篇論文採用二維有限時域差分法來研究奈米電漿子圓柱間的耦合現 象及一維的電漿子波導。我們使用Drude 色散模型模擬金屬，並使用 具有色散的單軸異向性完美匹配層作為相對應的計算空間吸收邊界。 首先，在色散材料的曲面模型中，我們比較了index-average scheme 和 conformal scheme 之間的差異。接著我們使用conformal scheme 來分析 奈米電漿子圓柱的散射截面積。近場強度和一維圓柱陣列的散射截面 積之間的關係也會在此做一些討論。此外，我們分別針對下列幾種不 同條件來計算散射截面積和近場強度: 1、不同的圓柱半徑 2、不同圓 柱間的距離 3、不同的入射波方向。最後，我們將有限時域差分法計 算出來的圓柱陣列結構色散關係圖與有限元素法得到的結果做比較; 另一方面，我們改變薄膜陣列的厚度並觀察色散關係和磁場分佈情形 的變化。

Abstract In this research, a two-dimensional (2-D) finite-difference time-domain (FDTD) analysis method is applied to study the coupling between nano-plasmonic cylinders and mode characteristics 1-D nano-plasmonic waveguides. The Drude model for metallic material dispersion is implemented into the FDTD algorithm along with the dispersive uniaxial perfectly matched layer (UPML) as the absorbing boundary condition for the computational domain. For the modeling of the curved surfaces for the dispersive materials, we first compare the index-average scheme with the conformal scheme. We then apply the conformal scheme to analyze the total scattering cross section (TSCS) of the nano-plasmonic cylinders. The relation between the near field intensity and the TSCS of 1-D cylinder arrays are discussed. We calculate the TSCS and the near field intensity by changing the size of the cylinder radius, the distance between the neighboring cylinders, and the direction of the incidence wave. Rather than applying frequency-domain methods, we try to use the FDTD method to analyze the guiding conditions for 1-D nano-plasmonic cylinder and film arrays. For the cylinder arrays, we compare the results calculated by the FDTD method with those by the finite-element method (FEM) in our group. For the film arrays, we vary the thickness of the films and observe the change of the dispersion curves and magnetic field distributions of each guided mode.