Investigation of Surface Plasmonic Structures and Photonic Devices Using the Pseudospectral Time-Domain Method

此論文研究在於運用高精準的多區域「時域擬譜方法」來研究表面電漿結構的現象及元件應用，主要著重於計算奈米尺度大小的金屬結構和光波交互反應而產生的共振頻譜。研究上分為兩主題，在前半段中，我們首先會分別研究介質波導以及表面電漿波導構成之環型共振器的光學行為。在模擬二維介質環型共振器中，我們會先驗證我們使用的時域擬譜方法可和另一高精準的時域不連續賈勒津方法提供相同精確的結果。同時，我們也使用此時域擬譜方法來模擬三維環型共振器結構的頻譜來和其二維結構做比對。緊接著，時域擬譜方法會被應用於分析表面電漿波導構成之環型共振器。在計算時，我們採用了合適曲線擬合的色散模型來近似銀金屬在近紅外線及可見光波段的特性。一開始我們會先分析一些先前研究者提出不同於傳統圓形之方型和六邊形環型共振器結構。藉由修改其它共振器結構的缺失，我們進一步最佳化和改善而成了一個能在所需的波長範圍內可提供較佳頻譜結果之跑道型環型共振器。論文的後半段中，我們主要研究三維奈米銀粒子間的局部化表面電漿共振與近場交互耦合作用，並著眼於時域擬譜方法可提供的高精度計算。藉由分析消光、散射、和吸收截面積頻譜，我們可以詳細地研究在不同入射波傳播與極化方向下，改變球體尺寸、間距、周圍介質、以及球體數量對於共振頻譜的光特性之影響。同時，我們也可藉由計算在特定共振頻譜高點或低點的光學近場來瞭解其近場耦合行為和獲知其背後的物理意義。In this research, the high-accuracy multi-domain pseudospectral time-domain (PSTD) method is utilized to study the phenomena and device applications of several surface plasmon structures, with the emphasis on resonant spectra of nanometer-sized metallic structures interacting with optical waves. In the first part, optical behaviors of dielectric as well as surface plasmonic waveguide-coupled ring resonators are investigated. The PSTD method is first shown to provide accurate results in simulating two-dimensional (2-D) dielectric ring resonators as compared with another high-accurate method, the discontinuous Galerkin time-domain (DGTD) method, and the PSTD simulation of a 3-D ring structure is also performed for comparing spectra with its 2-D counterpart. The PSTD analysis is then applied to surface plasmonic waveguide ring resonators, in which a well-fitted dispersive model to approximate the characteristics of silver in the near-infrared and visible parts of the light spectrum is adopted. Previously proposed rectangular- and hexagonal-shaped structures that are different from traditional circular-ring ones are analyzed. A race-track-shaped ring structure is then further optimized and improved based on fixing drawbacks of other structures so that the resultant ring gives better spectral characteristics in the required wavelength range. In the second part, localized surface plasmonic resonance and near-field couplings between 3-D nanometer-sized silver particles are investigated, with the emphasis on the high-accuracy calculations the PSTD method can offer. By analyzing spectra of extinction, scattering, and absorption cross-sections, influences of varying spherical dimension, spacing, surrounding medium, and the number of spheres upon resonant spectra under different incident wave propagation directions and polarizations are studied in detail. Calculated optical near fields are examined to understand coupling behaviors at specific resonant peaks or dips and gain more physical features