本論文主要在探討各向異性介質平板極化器的頻寬以及厚度靈敏度的問題，所針對的極化器為線性極化轉為圓形極化之極化器，我們利用穿透出極化器之波的軸比值，定義出極化器的頻寬以及厚度靈敏度，並加以探討。在電磁波對介質微量反射的假設前提下，為減少冗長的運算，我們提出了具物理意義的新方法來探討這類問題。以單一層各向異性介質平板而言，我們利用在極化平面上圖形求解的方法來獲得極化器的頻寬以及厚度靈敏度，經研究可發現，在極化平面上，有相同軸比值的極化軌跡形成一圓，再結合波在介質內行進所形成極化的變動軌跡，則極化器的頻寬以及厚度靈敏度可輕易求得。此外，我們亦提出將介質對波的極化效應，等效成電路模型的方法，則一些電路上的觀念，可以用來解釋極化效應，這樣的等效電路，將有助於多層各向異性介質平板極化器的探討。在本論文中，我們將探討數種無損的各向異性介質，所探討的結果將會以圖示說明，並會加以討論。

In this thesis, we investigate the transformation bandwidth and the thickness sensitivity of the anisotropic-slab linearly polarizes (LP) to circularly polarized (CP) polarizer. We define a transformation bandwidth and the thickness sensitivity based on the axial ratio. New methods are proposed that can eliminate the lengthy derivation and give deeper physical insight to the problem. Under the small reflection approximation, i.e., only the forward waves are considered, our methods can be applied to the design of the anisotropic-slab LP to CP polarizer. For the single anisotropic slab, the effect is represented graphically on the polarization ratio plane. It is shown that the polarization locus for a given axial ratio leads to a circle in the polarization state diagram. When combined with the graphical description of the change in the polarization state, the transformation bandwidth and the thickness sensitivity from an initial LP wave to a desired CP wave can be obtained easily. Furthermore, we present a method using the equivalent circuits to represent the polarization effect in anisotropic media, so that some concepts of the electric circuit can be applied. This method is more convenient in dealing with the polarization change when multiple anisotropic-slabs exist. The transformation bandwidths and the thickness sensitivities for the anisotropic-slab polarizer for several lossless media are studied. The results are discussed and illustrated.

Acknowledgement i
摘　　要 iii
Abstract iv
Contents v
List of Figures vi
List of Tables vii
Chapter 1 Introduction 1
1.1 Statement of purpose 1
1.2 Definition of transformation bandwidth and thickness sensitivity 2
1.3 Concept of equivalent circuit 2
1.4 Outline of the thesis 4
Chapter 2 Representation of Wave Polarization: Polarization Ratio 5
2.1 Complex polarization ratio (R) 5
2.2 Inverse circular polarization ratio (q) 11
Chapter 3 Wave Propagation in the Anisotropic Media 17
3.1 The R circle 17
3.2 Several examples of the R circles 21
3.2.1 Examples of the biaxial medium in the R plane 21
3.2.2 Examples of the chiral medium in the R plane 22
3.2.3 Examples of the magnetoionic medium in the R plane 26
3.3 The q circle 32
3.4 Several examples of the q circles 34
3.4.1 Example of the biaxial medium in the q plane 34
3.4.2 Examples of the chiral medium in the q plane 36
3.4.3 Examples of the magnetoionic medium in the q plane 39
Chapter 4 Transformation Bandwidth and Thickness Sensitivity 45
4.1 Transformation Bandwidth and Thickness Sensitivity by using R plane 45
4.2 Results by using R plane 50
4.2.1 Results of the biaxial slab 50
4.2.2 Results of the magnetoionic slab 55
4.2.2.1 Case 1: 57
4.2.2.2 Case 2: 58
4.3 Tolerance of alignment of the biaxial-slab LP to CP polarizer 62
4.3.1 General case of the R circle of the biaxial slab 62
4.3.2 Results of the tolerance problem 72
Chapter 5 Equivalent Circuit and Multi-layer Anisotropic-slabs Polarizer 76
5.1 Equivalent circuit 76
5.1.1 Equivalent circuit of the biaxial medium 78
5.1.2 Equivalent circuit of the chiral medium 81
5.1.3 Applying the equivalent circuit to the cascade case 81
5.2 A multi-layer anisotropic-slabs LP to CP polarizer 82
5.2.1 Design based on the binomial polynomial 89
5.2.2 Design based on the Chebyshev polynomial 97
5.2.3 Summary 101
Chapter 6 Conclusion 103
Appendix A Bilinear Transformation 107
Appendix B Symbols 111
Bibliography 114

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