Analysis of Dielectric Pipe Waveguides and Plasmonic Slot Waveguides Using the Finite-Difference Frequency-Domain Method

本論文使用全向量有限差分頻域法分析管狀介質波導與槽形電漿子波導，並引入完美匹配層做為計算區域外圍的吸收邊界，以便分析洩漏波導。對於介質接面的處理，係採用階梯式近似法或折射率平均法。 本論文分析研究不同形狀的管狀介質波導在兆赫頻率下傳播的等效折射率和衰減係數，包括圓形、半圓形、四分之一圓形、正方形與二十四多邊形等形狀，特別討論其基本模態的特性。另外，對於各波導結構亦探討其空氣核心模態與殼層模態耦合所產生的法諾效應。 本論文亦分析研究槽形電漿子波導的模態特性，針對其中間凹槽的寬度、金屬薄膜的高度與曲率半徑、兩側的薄膜寬度等參數，討論其基本模態的特性。對於有限差分網格點的大小與位置和計算空間大小對數值計算精準度的影響，亦詳加探討。此外，經由忽略金屬的材料損耗，探討對稱與非對稱槽形結構的洩漏性質。In this thesis, the full-vectorial finite-difference frequency-domain (FDFD) method based on Yee''s mesh is utilized to analyze optical waveguides. The perfect matched layer (PML) is employed as the absorbing boundary of the computational window in this FDFD solver. Moreover, the FDFD model adopts two approximation methods for dealing with dielectric interfaces: the stair-case approximation method and the index average scheme. Effective indices and attenuation constants are calculated for pipe waveguides with different forms of the core region at terahertz frequencies, such as circular, semi-circular, quarter-circular, square, and 24 sided polygonal pipe waveguide. Fano resonances, which are caused by the coupling between the core modes and the cladding modes, are observed inside transmission bands in the above-mentioned structures. As for the subwavelength plasmonic slot waveguide, its basic characteristics for various slot widths, film thicknesses, radii of rounded edges, and finite strip widths are analyzed and discussed. The effect of some parameters of calculation on the accuracy of the numerical results is also examined. Moreover, by ignoring the material loss of the metal in both symmetric and asymmetric slot waveguides, the possible leakage characteristics are investigated.1 Introduction 1 1.1 Numerical Schemes for the Analysis of Optical Waveguides . . . . . . 1 1.2 Overview of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 The Finite-Diff erence Frequency-Domain Method 6 2.1 The Central Di fference Scheme . . . . . . . . . . . . . . . . . . . . . 7 2.2 Mode Solvers for 1-D Problems . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 The TE Polarized Wave . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 The TM Polarized wave . . . . . . . . . . . . . . . . . . . . . 11 2.3 Mode Solvers for 2-D Problems . . . . . . . . . . . . . . . . . . . . . 12 2.4 The FDFD Method with Perfectly Matched Layers . . . . . . . . . . 16 2.5 Approximation at Dielectric Interfaces . . . . . . . . . . . . . . . . . 20 2.5.1 The Stair-Case Approximation Method . . . . . . . . . . . . . 20 2.5.2 The Index Average scheme . . . . . . . . . . . . . . . . . . . . 21 2.5.3 Comparison between FDFD Solutions and Analytic Solutions of the Optical Fiber . . . . . . . . . . . . . . . . . . . . . . . . 21 3 Analysis of Pipe Waveguides for Terahertz Waveguiding 31 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Guiding Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3 Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.1 Circular Pipe Waveguides . . . . . . . . . . . . . . . . . . . . 35 3.3.2 Semi-circular and Quarter-circular Pipe Waveguides . . . . . . 36 3.3.3 Square and 24 Sided Polygonal Pipe Waveguides . . . . . . . . 36 3.4 Fano Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.4.1 Circular and 24 Sided Polygonal Pipe Waveguides . . . . . . . 39 3.4.2 Square Pipe Waveguides . . . . . . . . . . . . . . . . . . . . . 40 3.4.3 Semi-circular and Quarter-circular Pipe Waveguides . . . . . . 40 4 Analysis of Subwavelength Plasmonic Slot Waveguides 69 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.1.1 The Surface Plasmon Polariton . . . . . . . . . . . . . . . . . 70 4.1.2 Surface Plasmon Polariton Waveguides . . . . . . . . . . . . . 72 4.2 Modal Analysis of Slot Waveguides . . . . . . . . . . . . . . . . . . . 73 4.2.1 Symmetric Slot Waveguides . . . . . . . . . . . . . . . . . . . 74 4.2.2 Asymmetric Slot Waveguides . . . . . . . . . . . . . . . . . . 78 4.2.3 Slot Waveguides with Rounded Edges . . . . . . . . . . . . . . 80 4.2.4 Slot Waveguides with Finite Metal-Film Width . . . . . . . . 81 5 Conclusion 10