由於光子晶體有能隙這個特性，許多這方面的研究被提出來。當波長在能隙範圍內，光將無法在晶體內做傳輸。所以，在晶體內放入一些缺陷，因為它破壞了原來的週期性排列，利用此方法可以使訊號沿著波導傳輸。而耦合腔波導是其中一種波導。因為光子靠著耦合且無輻射損耗在耦合腔波導內傳輸。因此，此種波導被廣泛地利用在多種元件上。
本論文我們一樣用耦合腔波導來設計元件。並討論了馬赫詹德干涉儀與分光器的一些特性。然後我們利用這些特性去設計兩個邏輯結構。其包含一個輸入訊號及兩個控制訊號端。而控制訊號端的狀態將可以控制在輸出端的電場大小。另外，我們提出一個四個通道的濾波器。此濾波器可以讓1310、1490及1550 nm等三個波長分別在不同波導管內做傳輸。因此，這個濾波器可應用在光纖到家(Fiber To The Home)中當作一個波長解多工器。最後，我們對環形波導結構的特性去做探討。藉由改變其中一個控制通道的相位，我們可以控制輸入訊號是由第一輸出端或是第二輸出端輸出。這樣我們可以利用此結構作為一個開關。

Due to the property of the photonic crystal, like bandgap, many researches on them are discussed. Photons with wavelength within the bandgap cannot propagate through the crystal. Then placing some defects in the crystal, because the periodic arrangement is destroyed, it is possible to build a waveguide to guide light along certain path. One kind is coupled cavity waveguide. The photons can propagate in a coupled-cavity waveguide by coupling without radiation losses. So it is widely used to implement a variety of optical devices.
In this thesis, we use coupled cavity waveguide to construct devices. And the characteristics of Mach-Zehnder interferometer and power splitter are discussed. Then we propose two logic gate structures with an input port and two control ports. The state of control port determines the electric field at the output port. Besides, the four-port channel drop filter is proposed. It will make the three wavelengths ─1310, 1490 and 1550 nm─ propagate in different waveguides. So it could be used as a wavelength demultiplexer for FTTH. Finally, the property of the PC-based rat-race circuit is investigated. By adjusting the phase of the control signal, we could decide the input signal to exit from output 1 or output 2. In this way, we could use it to function as a switch.

Acknowledgements i
Abstract iii
Contents v
Figures Caption vii
List of Tables xvi
List of Symbols xvii

Chapter 1： Introduction
1.1 Overview 1
1.2 Research Motivations 2
1.3 Organizations of the Thesis 3
Chapter 2： Basic Theory and Simulation Method
2.1 Introduction 6
2.2 Plane Wave Expansion Method (PWE) 6
2.3 Finite Difference Time Domain Method (FDTD) 11
Chapter 3： Mach-Zehnder Interferometer and Logic Gates Based on Coupled Cavity Waveguides
3.1 Introduction 21
3.2 Analysis 23
3.2.1 The Structures of PC Waveguide 23
3.2.2 The Transmission Characteristics of Coupled Cavity Waveguide 25
3.3 Power Splitter Based on Coupled Cavity Waveguides 26
3.4 Mach-Zehnder Interferometer employing Coupled Cavity Waveguides 28
3.5 Logic Gate Based on Mach-Zehnder Interferometer 29
3.6 Summary 32
Chapter 4： A Design of Four-Port Channel Drop Filters Based on 2D PCs
4.1 Introduction 56
4.2 Analysis 58
4.2.1 Coupled Mode Theory 58
4.3 Numerical Results 62
4.4 Summary 64
Chapter 5： Ideal 3-dB Splitter-Combiner and Switch in Photonic Crystals
5.1 Introduction 70
5.2 Analysis 71
5.3 Numerical Results 81
5.4 Summary 83
Chapter 6： Conclusions
6.1 Summary 91
6.2 Suggestions for Future Researches 92
References 92

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