在本論文中，我們應用特殊電磁場關係，所開發出來稱為電場-磁場耦合方程 (Coupled Electric-Coupled Magnetic Field Method, CE-CH)的新方法來求解抗共振反射光波導(Antiresonant Reflecting Optical Waveguides, ARROW’s) 的模態問題。相較於傳統方法，這個方法的優點，在於它能夠直接處理波導中逸漏式模態(leaky mode)；且本法有較佳的數值特性，特別是在電磁場量的計算中，其精確性因特殊的方程式設定，而顯得更為出色。
本文中，我們先簡單介紹傳統上，用於求解多層介質波導的幾種方法以及常見的抗共振反射光波導模態解法，接著將介紹如何以電場/磁場耦合方程解抗共振反射光波導結構，並分析光波在抗共振反射光波導中傳播時能量損耗與場量的分佈情形。同時也會探討當結構有所變化時，對整個波導特性所產生的影響。
由於矩陣找根比較麻煩，所以我們亦藉由矩陣行列式的簡化，推導出極為精確的一階近似公式，這些式子對於一個芯層厚度為8微米(

We have developed a rigorous leaky-mode analysis on the antiresonant reflecting optical waveguides (ARROW’s) using a so-called “coupled electric (CE) coupled magnetic (CH) field method.” Radiation loss characteristics and the field distribution of the ARROW are analyzed in detail. Meanwhile, both the refractive indices and the thickness dependence for the isolation and distinction of modes are also investigated in this thesis. From the CE–CH method, the associated complex symmetric tridiagonal matrices are derived to solve the modal solutions via the eigenvalue-eigenvector technique. The uniquely designed formulation of CE–CH method yields better numerical properties, specifically in calculating the field distribution. This is suitable for any combination of materials and is capable of handling complex problems such as the leaky characteristics for both lossless and lossy cases.
To quickly solve the complex roots of the ARROW, a set of accurate closed-form approximations for estimating both the field distribution and complex propagating constant have been derived from the CE–CH matrices. These first-order approximations provide six significant figures of the real part of the propagation constant

1. Introduction 1
1.1 The Opto-Electronic Integrated Circuits (OEIC’s) 2
1.2 Anti-Resonant Reflecting Optical Waveguide 4
1.3 Motivations 6
1.4 Contributions of The Present Work 7
1.5 Chapter Outline 8
2. Review of Mode Solving Techniques 11
2.1 General Analytical Methods 12
2.1.1 The ABCD Matrix Method 12
2.1.2 Transfer Matrix Method 16
2.1.3 Impedance Transformation 21
2.2 Frequent Applications Employing ARROW Solutions 24
2.2.1 Transverse Resonant Method 25
2.2.2 Mode Analysis Method Using The
System Interference Matrix 28
2.3 Numerical Techniques 31
3. The CE-CH Method 46
3.1 Introduction 46
3.2 Formulate The CE-CH Matrices 48
3.3 ARROW Waveguide Design 56
3.4 Close-Form First-Order Approximation 58
3.5 Root Solving with Impedance Transformation 65
4. Numerical Results and Discussion 68
4.1 Characteristics of The Traditional ARROW 68
4.2 The Impedance Contrast Booster 73
4.3 Waveguide with A Lossy Substrate 79
4.4 Detune From the Antiresonance 82
4.4.1 Thickness Variation of The First Cladding 82
4.4.2 Index Variation of The First Cladding 85
4.4.3 Variation of The Core Region 86
4.5 The Application of Polarizer 92
5. Conclusion 136
References 139
Publication List 152

[1]. Pallab Bhattacharya, Semiconductor Optoelectronic Devices., 2nd ed. 1997.
[2]. R. Swoboda, and H. Zimmermann, “A 2.5-Gb/s Receiver OEIC in 06-