張宏鈞臺灣大學：電信工程學研究所莊英傑Chuang, Ying-ChiehYing-ChiehChuang2007-11-272018-07-052007-11-272018-07-052004http://ntur.lib.ntu.edu.tw//handle/246246/58614摘要 有限差分法係一簡單且有效率之數值分析工具，本論文採用以有限差 分公式為基礎之全向量模態分析法來研究光波導的傳播特性。由於數值計算採用均勻格點分割，因此很容易可對任意幾何形狀的光波導結構截面進行切割。本論文採用折射率等效法處理曲形介質接面得以穩定數值計算並加速數值收斂。此外，為分析洩漏模態問題，例如計算波導Abstract Due to its simplicity and efficiency, a full-vectorial mode solver based on a finite difference scheme is applied to investigate the propagation characteristics of optical waveguides. Since uniform meshes are used in the numerical implementation, it is very easy to divide the computational window of any arbitrary cross-sectional geometries of the waveguides. An index averaging technique is employed to deal with curved dielectric interfaces for stabilizing the numerical calculation and accelerating convergence. In addition, for solving leaky-mode problems, such as the investigation of waveguide confinement loss, the perfectly matched layer (PML) absorbing boundary condition is incorporated into our finite difference formulations. The influence of the index averaging technique on the leaky-mode analysis is also discussed. We employ the shift inverse power method (SIPM) for solving the formulated eigenvalue problems. In this work, both one-dimensional and two-dimensional problems are considered, including the slab waveguide, the antiresonant reflecting optical waveguide (ARROW), the step-index optical fiber, the rectangular channel waveguide, the anisotropic embedded-channel LiNbO3 integrated optical waveguide, and microstructured optical fibers (MOFs). Comparsion of our calculation with other methods is discussed.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .1 1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 The Finite Di®erence Waveguide Mode Solver and Related Techniques 4 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Formulations . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Boundary Conditions . . . . . . . . . . . . . . . .. . . . . . . .12 2.4 The Perfectly Matched Layer . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5 The Shift Inverse Power Method . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.6 Index Averaging Method . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 Numerical Results for One-Dimensional Problems. . . . 21 3.1 Slab Waveguides . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 ARROW Waveguides . . . . . . . . . . . . . . . . . . . . . . . 22 4 Numerical Results for Two-Dimensional Problems 39 4.1 Step-Index Fibers . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.2 Rectangular Channel Waveguides . . . . . . . . . . . .. . . . . . . . . . . 41 2 4.3 Anisotropic Embedded-Channel LiNbO3 Integrated Optical Waveguides . . . . . . . . . . . . . . . . . . . . . . . 42 5 Microstructured Optical Fibers . . . . . . . . . . . . 61 5.1 Air-Hole-Assisted Optical Fibers . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.2 Photonic Crystal Fibers . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.2.1 Triangular Holey Fibers . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.2.2 Honeycomb Fibers . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . 66 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . 87en-US有限差分finite differencethesis