張宏鈞臺灣大學：電信工程學研究所張峰偉Chang, Feng-WeiFeng-WeiChang2007-11-272018-07-052007-11-272018-07-052007http://ntur.lib.ntu.edu.tw//handle/246246/58866摘要 本論文使用有限差分頻域法搭配適當邊界條件匹配處理來分析 不同截面之介電質光波導，並在程式中引入完美匹配層做為計算視窗 之吸收邊界以分析具有損耗的光波導。我們將不同結構的光波導分成 兩類來分析討論：線性介電質界面光波導與曲線介電質界面光波導。 線性介電質界面光波導包括方型埋入式波導、瘠形波導、斜面瘠形 波導。此外，數值範例的討論也包括多模態干涉現象的傳播問題。光 纖與光子晶體光纖被視為具有曲線介電質界面的光波導，光子晶體光 纖的特殊性質，如色散和雙折射性，以及單環與多環光子晶體光纖的 損耗特性都在此論文中詳加分析與討論。除了瞭解這些光波導不同的 特性外，我們也測試了有限差分頻域法的準確性和收斂性並且觀察到 不同網格規劃對計算結果之影響。我們比較使用適當邊界條件匹配與 使用傳統階梯式近似在分析處理不同波導上的效率來突顯前者具有 較高的處理效能。Abstract In this research, the finite-difference ferquency-domain (FDFD) method with the proper boundary-condition (BC) matching scheme is adopted to analyze optical waveguides with different cross-sectional dielectric interfaces. The perfectly matched layer (PML) is incorporated into our algorithm as the absorbing boundary of the computing window for analyzing leaky waveguides. Several optical waveguides are analyzed and discussed by assorting them into two categories: optical waveguides with linear dielectric interfaces and those with curved ielectric interfaces. The optical waveguides with linear dielectric interfaces include the square channel waveguides, rib waveguides, and sloped-side rib waveguides. The propagation problems of the multi-mode interference (MMI) phenomenon are also discussed and taken as numerical examples. The optical fibers and the photonic crystal fibers (PCFs) are considered as waveguides with curved dielectric interfaces. The novel properties of the PCFs, such as dispersion and birefringence are studied, and the leakage loss characteristics of the sigle- and multiple-ring of PCFs are investigated. Besides understanding various properties of these optical waveguides, we examine the accuracy and convergence characteristics of our FDFD method and observed the effect of the grid mesh arrangement on the obtained results. We compare the proper BC matching scheme with the conventional stair-case approximation in the analysis of different waveguides to mark advantages of the former scheme.Contents 1 Introduction 1 1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 The Finite-Difference Frequency-Domain Method 4 2.1 Centeral Difference Scheme . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Mode Solvers for 1-D Waveguide Problems . . . . . . . . . . . . . . . 5 2.2.1 The TE Polarized Wave . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 The TM Polarized Wave . . . . . . . . . . . . . . . . . . . . . 7 2.3 Mode Solver for 2-D Waveguide Problems . . . . . . . . . . . . . . . 8 2.4 FDFD Method with Perfectly Matched Layers . . . . . . . . . . . . . 11 2.5 Improved Treatment for the Dielectric Interfaces . . . . . . . . . . . . 15 2.5.1 Index Average scheme . . . . . . . . . . . . . . . . . . . . . . 15 2.5.2 Proper Boundary Condition Matching . . . . . . . . . . . . . 15 3 2-D Optical Waveguides with Linear Dielectric Interfaces 24 3.1 Channel Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 Rib waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 Sloped-Side Rib Waveguides . . . . . . . . . . . . . . . . . . . . . . . 27 3.4 Multi-Mode Interference Based on Self-Imaging . . . . . . . . . . . . 28 3.4.1 Self-Imaging Principle . . . . . . . . . . . . . . . . . . . . . . 28 3.4.2 Multi-Mode Waveguides . . . . . . . . . . . . . . . . . . . . . 28 3.4.3 Guided-Mode Propagation Analysis . . . . . . . . . . . . . . . 30 3.4.4 Multi-Mode Interference . . . . . . . . . . . . . . . . . . . . . 31 3.4.5 Self-Imagimg in Multi-mode Waveguides . . . . . . . . . . . . 34 4 2-D Optical Waveguides with Curved Dielectric Interfaces 56 4.1 Optical Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2 Photonic Crystal Fibers . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.2.1 Photonic Crystal Fibers with Single- and Multiple-Ring of Air Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2.2 Single-Polarization Single-Mode PCFs . . . . . . . . . . . . . 60 4.3 Dispersion Design of Photonic Crystal Fibers . . . . . . . . . . . . . . 61 4.3.1 Ultra-Flattened-Dispersion Photonic Crystal Fibers . . . . . . 62 4.3.2 High Negative Dispersion Photonic Crystal Fibers . . . . . . . 63 5 Conclusion 862215445 bytesapplication/pdfen-US有限差分多模干涉FDFDMMIthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/58866/1/ntu-96-R94942075-1.pdf