光子晶體是介電常數在空間中呈現週期性變化的結構，它的主要特性是存在光子能隙，能夠在特定的頻率範圍內禁止光在其中的傳播。而傳統光子晶體，其光能隙的特性在光子晶體結構製作完成之後，便難再利用外在因素調變，因此發展可應用於光積體電路中的可調式光子晶體波導元件是相當重要的。
在本論文中，我們利用了模態能隙的效應，設計了含聚苯胺類電流變液體的二維可調式Y型光子晶體波導。藉由施加外加電壓於特定的區域，便能夠控制Y型波導中光的傳播方向。此外，我們也提出了一個含聚苯胺類電流變液體的可調式多通道光子晶體波導。我們接著研究了含液晶之可調式波導結構，藉由改變液晶的方向和孔洞的尺寸，我們成功地得到了以液晶為單一線缺陷之二維光子晶體波導的傳播特性。我們也模擬了以液晶當作線性缺陷的二維Y型光子晶體波導，並探討其可調式的光傳播現象。最後，我們考慮了含有液晶的三維Y型光子晶體平板波導，並探討液晶分子排列及平板厚度對其光特性之影響。

Photonic crystals (PCs) are structures with spatially periodic variations in dielectric constants. The prime property of PCs is the existence of the photonic band gaps (PBGs) which could prohibit the propagation of light within a certain frequency range. Once the PC structures are fabricated, it is hard to tune their optical properties for the fixed geometries. Thus, it is important to develop tunable PC waveguide devices for the applications in the photonic integrated circuits.
We utilize the mode-gap effect to design two-dimensional (2-D) tunable Y-shaped PC waveguides with the polyaniline type electrorheological (ER) fluids. The propagation of light on the Y-shaped waveguide can be controlled by applying the electric field in specific regions. Besides, we also propose a tunable multi-channel PC waveguide with the polyaniline type ER fluids. We then investigate the tunable propagation characteristics of a 2-D single line-defect PC waveguide with liquid crystals (LCs) by varying the direction of LCs and the hole sizes. We also simulate the tunable optical properties of a 2-D Y-shaped PC waveguide utilizing LCs. Finally, we consider a 3-D Y-shaped PC slab waveguide with LCs. The effects of the direction of LCs and the slab thickness are discussed.

1 Introduction 1

1.1 Overview 1

1.2 Chapter Outline 4

2 Numerical Methods 7

2.1 Introduction 7

2.2 Plane Wave Expansion Method 7

2.3 Finite-Difference Time-Domain Method 10

3 Tunable Photonic Crystal Waveguides Using Polyaniline Type Electrorheological Fluids 15

3.1 Mode-Gap Effect 15

3.2 Properties of Polyaniline Type Electrorheological Fluids 17

3.3 Tunable Y-Shaped Waveguides 18

3.4 Tunable Multi-Channel Waveguides 21

4 Tunable Photonic Crystal Waveguides Using Liquid Crystals 50

4.1 Optical Properties of Liquid Crystals 50

4.2 2-D Single Line-Defect PC Waveguides with LCs 51

4.3 2-D Tunable Y-Shaped Waveguides with LCs 53

4.4 3-D Tunable Y-Shaped Waveguides with LCs 55

5 Conclusions 87

Bibliography 89

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