漸變式光子晶體透鏡研究

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姓名

簡宏達(Hung-Ta Chien) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

漸變式光子晶體透鏡研究
(Study of Graded Photonic Crystal Lens)

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摘要(中)

本研究討論一個漸變式光子晶體，其結構為一個以四方晶格排列的空氣柱所組成。空氣柱的大小由中心至外圍在水平方向逐漸增大，而在每一直行中的空氣柱大小是相同的。經由有限時域差分法的計算，我們發現這個漸變式光子晶體可將電磁波聚焦，我們更進一步研究其幾何參數對於焦距、光點大小及聚焦強度的影響。由於此結構可將電磁波聚焦到約兩個晶格常數的範圍內，兩個晶格常數約是等於一個光子晶體波導的寬度，因此我們將此結構應用至光子晶體波導與傳統介電質波導的耦合。並和其它光子晶體波導耦合器進行比較。我們比較的光子晶體波導耦合器包括:光子晶體錐形波導、傳統錐形波導和拋物面鏡耦合器。所以的元件被設計並製作在一個 silicon-on-insulator 基板上。從模擬和量測結果得知，我們所設計的漸變式光子晶體波導耦合器可以在較短的耦合長度限制下提供較高的耦合效率。而我們也討論了其它光子晶體波導耦合器的優缺點。

摘要(英)

In this work, we studied the graded photonic crystal consisting of spatial-varying air holes in a square array theoretically and experimentally. The radii of the air holes are identical in each column and modified from the central column to the edge column. We found that the graded photonic crystal could focus the electromagnetic waves. Through finite-difference time-domain method, we studied the relations between the geometry of the graded photonic crystal, focal length, spot size, and the intensity at focal point. The structure focuses the electromagnetic waves to a focal point measuring only two lattice constants which is close to the width of a single-line-defect photonic crystal waveguide. Therefore, the graded photonic crystal is applied to the issue of the coupling between photonic crystal waveguides and conventional dielectric waveguides. The coupling efficiency is compared with various couplers including the photonic crystal taper, the waveguide taper, and the parabolic mirror coupler. All of the couplers were designed and fabricated on a silicon-on-insulator substrate. The simulation and experimental results suggest that the graded photonic crystal coupler could offer a higher coupling efficiency in a shorter coupling length. Besides, the innate properties of each coupler are discussed.

關鍵字(中)

★ 光子晶體
★ 漸變式光子晶體
★ 漸變式光子晶體透鏡
★ 波導耦合器

關鍵字(英)

★ Photonic crystal.
★ Waveguide coupler
★ Graded photonic crystal lens
★ Graded photonic crystal

論文目次

ABSTRACT i
摘要 iii
謝誌 v
CONTENTS vii
LIST OF FIGURES xi
LIST OF TABLES xix
LIST OF ACRONYMS/ABBREVIATIONS xxi
CHAPTER 1 INTRODUCTION 1
1.1 Photonic Crystals 1
1.2 Photonic Crystal Lenses 6
1.2.1 Operating in the Linear-dispersion Region 6
1.2.2 Operating in the Negative Refraction Region 7
1.3 Graded Photonic Crystals 9
1.4 The Couplers 11
1.4.1 Photonic Crystal Tapers 11
1.4.2 Waveguide Tapers 14
1.4.3 Parabolic Mirror Coupler 14
1.4.4 The Graded Photonic Crystal Lens Coupler 15
1.5 Summary 16
CHAPTER 2 THEORY AND SIMULATION METHODS 17
2.1 Equifrequency Contour 17
2.2 Snell’s Law in Anisotropic Media 19
2.3 Finite-Difference Time-Domain Method 20
2.4 Plane Wave Expansion 27
2.5 Solve the Eigenmodes of the Waveguides 29
2.5.1 Wave Equations 29
2.5.2 Calculate the Modes in One Dimensional Waveguide 31
2.5.3 Matrix Wave Equations 32
2.5.4 Effective Index Approximation 34
2.6 Summary 35
CHAPTER 3 GRADED PHOTONIC CRYSTAL LENS 37
3.1 Structure and Parameters 37
3.2 Simulation Method and Results 38
3.2.1 Pulse Response 39
3.2.2 Continuous Wave Simulations 41
3.2.3 Further Analyses of the Graded Photonic Crystal Lens 44
3.3 The Focusing by the Graded PC Lens 50
3.4 Summary 55
CHAPTER 4 COUPLERS 57
4.1 Dielectric Waveguides 57
4.2 Photonic Crystal Waveguides 59
4.3 Graded Photonic Crystal Couplers 61
4.4 Other Couplers 62
4.4.1 Photonic Crystal Tapers 62
4.4.2 Waveguide Tapers 64
4.4.3 Parabolic Mirror Coupler 66
4.5 Results 68
4.6 Summary 70
CHAPTER 5 FABRICATION AND MEASUREMENT 71
5.1 Fabrication 71
5.2 Sample Preparation 72
5.2.1 Lapping and Polish 73
5.2.2 Thin Out the Sample and Cleavage 74
5.3 Measurement Process 76
5.3.1 Measurement Setup 76
5.3.2 Measurement Steps 77
5.4 Measurement Results 78
5.5 Summary 80
CHAPTER 6 DISCUSSION AND CONCLUSION 83
6.1 Graded PC Lens and Couplers 83
6.2 Future Work 86
REFERENCE 89
APPENDIX: LIST OF PUBLICATIONS 95

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指導教授

陳啟昌(Chii-Chang Chen)

審核日期

2009-6-23

推文