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研究生:陳廷仰
研究生(外文):Tyng-Yang Chen
論文名稱:光子晶體微共振腔輻射特性之模擬
論文名稱(外文):Simulation on Radiation Characteristics of a Photonic Crystal Microcavity
指導教授:江衍偉江衍偉引用關係
指導教授(外文):Yean-Woei Kiang
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:光電工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:91
中文關鍵詞:光子晶體
外文關鍵詞:photonic crystal
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本論文中,我們模擬分析了各種光子晶體平板微共振腔的輻射特性。由於光子晶體具有布拉格反射和全反射的效應,光可以侷限在缺陷中,這類光子晶體可用於製作發光二極體。吾人利用三維之有限時域差分法,分別針對方形晶格和三角形晶格缺陷結構的輻射特性進行模擬。吾人先探討缺陷附近空氣洞大小和輻射特性的關係,接著調整空氣洞的位置和形狀。在某些結構下,只需稍微適當的改變缺陷附近的結構,便可有效增進輻射效率,而不需大幅改變整體的結構或介質的折射率。最後我們歸納一些結論,以供設計高效能發光二極體參考。
Abstract


In this thesis, the radiation characteristics of various kinds of photonic crystal slab microcavites are numerically investigated. Light is confined within the defect region by the combined action of distributed Bragg reflection and total internal reflection. This kind of photonic crystal has been employed in making a semiconductor light-emitting diode (LED). By using the three-dimensional finite-difference time-domain (FDTD) method, we calculate the radiation characteristics for the square-lattice or triangular-lattice microcavity consisting of a single defect. The relation between the radiation characteristics and the radii of air holes around the defect is discussed. Then, the positions and shapes of nearest holes are adjusted. In some structures, we only need to perform small adjustment of the defect geometry to get better radiation characteristics, without significantly changing the photonic crystal structure and refractive index of dielectric material. Some conclusions are drawn, which may be helpful for designing efficient LEDs.
Contents
Contents


Chapter 1 Introduction 1
1.1 Background 1
1.2 Semiconductor light-emitting diodes 2
1.3 Motivation of this study………………………………..4
Chapter 2 Theoretical Formulations 7
2.1 Problem geometry 7
2.1.1 Introduction…………………………………………7
2.1.2 Single-point defect in square lattice…………7
2.1.3 Single-point defect in triangular lattice……..10
2.2 Maxwell’s equations……………………………11

Chapter 3 Finite-Difference Time-Domain Method………………………….18
3.1 Introduction 18
3.2 Three-dimensional FDTD algorithms 19
3.3 Stability criterion and Mur’s absorbing
boundary condition 23
3.4 Definitions of parameters………………………………….25

Chapter 4 Simulation Results 29
4.1 Square lattice………………………………………….29
4.1.1 Square-lattice point defect ………………………….29
4.1.2 Changing the radius rx near the defect…………………...32
4.1.3 Changing the positions of the nearest holes
in the x-direction………………………………………..33
4.1.4 Changing the radius ry near the defect……………..……34
4.1.5 Changing the positions of the nearest holes
in the y-direction...………………………………...……35
4.1.6 Elliptical holes in the x-direction near the defect…..........36
4.1.7 Elliptical holes in the y-direction near the defect…..........36
4.1.8 Discussions……………………………..............…37
4.2 Triangular lattice……………………….………...…………41
4.2.1 Triangular-lattice point defect…………………………...41
4.2.2 Changing the radius of rx near the defect……………….43
4.2.3 Changing the positions of the nearest holes
in the x-direction………..………………………………44
4.2.4 Changing the radius of holes near the defect……………44
4.2.5 Elliptical holes in the x-direction near the defect…….....45
4.2.6 X-directed point dipole source in triangular lattice……...46
4.2.7 Discussions……………………………………..……….46

Chapter 5 Conclusions 86

References…………………………………………………..88
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