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平面波展開法研究蜂巢狀光子晶體之光學性質

时间:2010年03月02日来源:职称论文网 作者:翁台宜 点击:
  【关键词】研究,平面,and,of,Phys.,Photonic,Re

中文關鍵字 平面波展開法 光子晶體
英文關鍵字 plane-wave method photonic crystals
學科別分類 學科別>自然科學>物理

中文摘要 繼電子產品改善人類生活之後,科學家們試圖尋找類似晶體結構的材料以控制光學性質,光子晶體的構想由此而生。由於和晶體具許多相似之處,亦可用類似的分析方式探討光於光子晶體內各種表現。本研究主要探討二維及有限高度蜂巢狀光子晶體之光學性質。蜂巢狀光子晶體由圓柱體和連接圓柱體的長方體所組成,此結構容易產生大的完全光學能隙。我們採用平面波展開法計算頻率能帶,以線性三角形法計算能態密度,有限高度的平板光子晶體我們還另外採用了超晶格計算法以及投影能帶結構以獲得在平板中的傳播模態。

對於二維蜂巢狀光子晶體,我們分析頻率能帶、能態密度以得知能隙所在頻率範圍及大小,討論長方體寬度對於能隙的影響,另外分析等能量曲線探討此光子晶體內的負折射性質。對於蜂巢狀平板光子晶體,我們探討了幾何參數和周圍材質對於能隙大小範圍的影響。
英文摘要 In order to control the propagation of electromagnetic waves, photonic crystals exhibiting large photonic band gaps have generated considerable attention. Honeycomb photonic crystals with cylinders and connecting walls have the potential to have large full band gap. The system is analyzed by the band calculation approach analogous to electronic band in semiconductor. The band structures are calculated by the plane wave expansion method, using MPB, a freely available software package. For two-dimensional honeycomb photonic crystals, the equifrequency contours are plotted as well as the band structures. The photon density of states is also obtained by linear triangle method. The band structure and the density of states tell how light propagates in photonic crystals, and the negative refraction behavior can be understood by the equifrequency contours. For honeycomb photonic crystals slabs, projected band diagrams are plotted by supercell technique and the geometric and substrate effects on band gaps are also discussed.
論文目次 Acknowledgments vi

1 Introduction 1
1.1 Overview of Photonic Crystals......1
1.2 Motivations of This Study......3
1.3 Overview of This Thesis......4

2 Theoretical Background 6
2.1 Electromagnetism in Inhomogeneous Dielectric Media......6
2.1.1 Scaling Law of Maxwell's Equations......7
2.1.2 Electromagnetic Variational Theorem......8
2.2 Eletromagnetism in Periodic Dielectric Media......10
2.3 Plane-wave Method......12
2.4 Triangle Method for Photon Density of States......16
2.5 Techniques for Photonic Crystal Slabs......20
2.5.1 Supercell Method......20
2.5.2 Projected Band Diagram......21
2.6 Equifrequency Contour for Negative Refraction Behavior......22

3 Simulation Results of Two-dimensional Honeycomb Photonic Crystals 24
3.1 Band Structure of Two-dimensional Honeycomb Photonic Crystals......24
3.2 Gap Map of Two-dimensional Honeycomb Photonic Crystals......27
3.3 Density of States of Two-dimensional Honeycomb Photonic Crystals......28
3.4 Equifrequency contour of Two-dimensional Honeycomb Photonic Crystals......29

4 Simulation Results of Honeycomb Photonic Crystal Slabs 34
4.1 Band Structure of Honeycomb Photonic Crystal Slabs......34
4.2 Geometric Effects on Honeycomb Photonic Crystal Slabs......35
4.2.1 Effects of Slab Thickness......35
4.2.2 Effects of Wall Thickness......36
4.3 Substrate Effects on Honeycomb Photonic Crystal Slabs......37
4.3.1 Symmetric Structures......37
4.3.2 Asymmetric Structures......40

5 Conclusions 42

Bibliography 44
參考文獻 [1] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals, Princeton University Press, 1995.
[2] E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[3] E. Burstein and C. Weisbuch, editors, Confined Electrons and Photons, Plenum Press, 1995.
[4] P. Vukusic and J. R. Sambles, Nature 852, 424 (2003).
[5] A. Birner, R. B. Wehrspohn, U. M. Gosele, and K. Busch, Adv. Mater. 13, 377 (2001).
[6] K. Busch, S. Lolkes, R. B. Wehrspohn, and H. Foll, editors, Photonic Crystals, Wiley-Vch, 2004.


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