本論文係利用全波向量方程，以向量邊界元素法作為分析及設計光子晶體光纖（微結構光纖或孔隙光纖）之工具。首先，將模擬結果與文獻資料比較確認向量邊界元素法計算光子晶體光纖結構之正確性及效率。接著以之探討光子晶體光纖之優異特性之一—極化特性；分析橢圓形氣孔光子晶體光纖的極化效應及將之埋入步階變化折色率纖核中的極化特性的變化。為分析色散特性，應用所發展之高效且精確之色散參數計算演算法在光子晶體色散特性的分析。探討均勻大小氣孔之光之晶體光纖、最內圈氣孔小於外圈氣孔之光子晶體光纖及最內兩圈氣孔小於外圈氣孔之光子晶體光纖的色散特性。最後據以設計出高寬頻超平坦色散之光子晶體光纖，其零色散及色散平坦波段從波長1.2微米到1.7微米，頻寬達400奈米以上，足以涵蓋整個光通訊波段。

Based on a full-wave formulation, a vector boundary element method (VBEM) is proposed to model the photonic crystal fibers (PCFs) (microstructured fibers). The accuracy and efficiency of the approach are confirmed by comparing the results calculated with those in previous literatures. With employing the VBEM, the guiding characteristics, including the effective indexes, vector mode patterns, and the polarization properties of the PCFs are investigated. There polarization characteristics of the PCFs with elliptical air holes (EPCFs) and the one ring air-hole EPCF embedded in the step-index core are studied and discussed. In addition, based on the VBEM formulations, a novel and efficient numerical approach to calculate the dispersion parameters of the PCFs is also proposed. The effect of the PCF geometrical structure on the group velocity dispersion property is reviewed, and then the one-ring defect and two-ring defect PCFs are studied and designed for the ultra-flattened dispersion applications. As an example, a four-ring (two-ring defect) PCF with flattened dispersion of ±0.25 ps/km/nm from 1.295μm to 1.725μm wavelength is numerically demonstrated.

Abstract………………………………………………………………...Ⅰ
Contents………………………………………………………………...Ⅳ
List of Figures……………………………………………………...…..Ⅶ
1 Introduction…………………………………………………………1
1.1 Motivation and Literature Survey……………...…………………………….1
1.2 Contributions of This Work……………………………………………….…4
1.3 Chapter Outlines………………………………………………………..……5
2 Vector Boundary Element Method……..………………………….8
2.1 Overview…………………………………………………………………...8
2.2 Surface Integral Equation Formulations (SIEFs)……………………..……9
2.3 An Efficient Approach for Dispersion Calculation……………………….11
2.3.1 Formulations………………………………………………………….12
2.3.2 Numerical Procedures………………………………………..………...15
2.4 Accuracy and Efficiency Check…………………………………..…...….20
2.5 Leakage Property of PCF and Loss Issue in VBEM……………..……….21
2.6 Some Numerical Issues…………………………………………………...23
2.6.1 Numerical Convergence……………………………………………...23
2.6.2 Consideration of Ring Number………………………………………24
2.6.3 Wavelength Dependence of Refractive Index……..…………………27
2.7 Summary………………………………………………………………….29
3 Polarization Effect of Elliptical Holey Fibers……………………47
3.1 Introduction………………………………………………………….……47
3.2 Birefringence of Elliptical Hole PCF…………………………………..…48
3.3 Field Confined High Birefringent HF………………………………..…...51
3.3.1 Overview……………………………………………………………...51
3.3.2 Polarization Properties of FCHFs………………………………….…52
3.3.3 Central Hole Assistance on Birefringence in FCHF…………..……...54
3.4 Summary………………………………………………………………….56
4 Dispersion Control in Photonic Crystal Fibers………...………...72
4.1 Introduction……………………………………………………………….72
4.2 Dispersion Characteristics of PCF……...……………………………...…73
4.2.1 Waveguide Dispersion and Scaling Transformation……..………..….73
4.2.2 Applications Related to Chromatic Dispersion………………………75
4.2.3 Dispersion Properties of the One-ring Defect PCF……..…………....76
4.3 Design of Ultra-flattened Dispersion………..………………………..…..78
4.3.1 Overview……..………………………………………………………78
4.3.2 Design of Novel Ultra-flattened Dispersion PCF……………….……79
4.4 Summary………………………………………………………………….83
5 Conclusion………………………………………………………….99
Bibliography………………………………………………………..…101
Biography……………………………………………………….….…109
Publication List………………………………………………….……110

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