本論文針對最新之光子晶體光纖(PCF)於光纖被動元件的應用進行分析及設計。論文中利用向量邊界元素法(VBEM)和時域有限差分(FDTD)法，以模擬分析光子晶體光纖元件的傳播特性。兩種新穎的光子晶體光纖元件於論文中提出。第一種元件為八邊形(octagonal) microstructured fiber (OMF)，其具有相當寬的單模態操作波長範圍、近似圓形分布場與較少的損耗。第二種為雙橢圓核心(TEC) PCF小型極化分光器，其在相當短的分光器長度即展現高極化分離率和寬頻的優點。前述之設計概念與耦合機制皆依據正規模態耦合理論及VBEM。

The dissertation focuses on the analysis and design for the new fiber-optic passive components based on the photonic-crystal-fiber (PCF). The vector boundary element method (VBEM) and the finite-difference time-domain (FDTD) method are employed to the propagation characteristics of PCF components. A novel octagonal microstructured fiber (OMF) with eight air-holes in the first ring has been proposed. The OMF has significantly wider wavelength range for single-mode operation, more circular-like field distribution, and less confinement loss. In addition, a novel compact polarization beam splitter (PBS) based on the twin-elliptical-core PCF (TEC-PCF) has also been proposed. It behaves with high extinction ration and broad bandwidth with significantly short splitter length. The design concept and the coupling mechanism are presented in this dissertation based on the normal-mode coupling theory and VBEM.

Contents

Abstract i
Contents iii
List of Figures v
List of Tables ix

1 Introduction 1
1.1 Background 1
1.2 Photonic-Crystal-Fiber (PCF) 1
1.3 Contributions 4
1.4 Organization of the Dissertation 5

2 Numerical Methods 6
2.1 Vector Boundary Element Method (VBEM) 6
2.1.1 Theory and Formulation 7
2.1.2 Examples of the Analysis of PCF 12
2.2 Finite-Difference Time-Domain (FDTD) Method 19
2.2.1 Theory and Formulation 19
2.2.2 Examples of the Analysis of PCF 28

3 Octagonal Microstructured Fiber (OMF) 36
3.1 Design of OMF and Geometrical Parameters 36
3.2 Propagation Characteristics 40
3.2.1 Guided Modes 40
3.2.2 Single-Mode 48
3.2.3 Field Confinement 54
3.3 Summary 58

4 Polarization Beam Splitter Base on Twin-Elliptical-Core PCF 59
4.1 Polarization Beam Splitter (PBS) 59
4.2 Analysis and Design of the TEC-PCF 64
4.3 Improved Design of the TEC-PCF 70
4.4 Summary 81

5 Conclusion 82


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