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研究生:趙竑鈞
研究生(外文):Hong-Jyun Jhao
論文名稱:二維光子晶體瑕疵共振腔內模態之分析
論文名稱(外文):Analysis of Defect Modes of Two-Dimensional Photonic Crystal Nano-Cavities
指導教授:李柏璁李柏璁引用關係
指導教授(外文):Po-Tsung Lee
學位類別:碩士
校院名稱:國立交通大學
系所名稱:光電工程系所
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:2005
畢業學年度:93
語文別:英文
論文頁數:43
中文關鍵詞:光子晶體瑕疵共振腔瑕疵模態時域有限差分法
外文關鍵詞:photonic crystalsdefect cavitiesdefect modesfinite difference time domain
相關次數:
  • 被引用被引用:0
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  • 下載下載:8
  • 收藏至我的研究室書目清單書目收藏:1
在這篇論文裡研究的是二維光子晶體瑕疵共振腔內的模態。
首先,我們介紹時域有限差分法和相關的邊界值條件。
其次,一些對稱性的分析和共振腔的設計原則將被討論。
最後,我們將展示一些模擬的技巧和光子晶體模擬的結果。
In this thesis, defect modes of two-dimensional photonic crystal nano-cavity are analyzed.
The defect is formed by removing a single air hole from array of air holes of hexagonal lattice arrangement on a dielectric slab.
First, the finite difference time domain method with various boundary conditions is introduced.
Second, symmetry analysis of defect modes and design rules for high quality factor cavities are presented.
Finally, techniques of the simulation and the results of the simulation, like photonic band structures, resonant frequencies, mode profiles, and quality factors are exhibited.
Abstract in Chinese i
Abstract in English ii
Acknowledgements iii
Contents iv
List of Tables vi
List of Figures viii
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Simulation Principles for the FDTD Method 4
2.1 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Yee’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Heaviside-Lorentz Unit System . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Sullivan’s Implement for Perfectly Matched Layer Absorbing Boundary
Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.5 My Implement for PML ABC . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.6 Bloch’s Boundary Conditions for Periodic Structures . . . . . . . . . . . . 11
2.7 Symmetric Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 11
2.8 Poynting Vector and EM-Energy in Yee’s Lattice . . . . . . . . . . . . . . 13
2.9 Time Step Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Symmetry Analysis 16
3.1 Some Terminologies and Useful Theorems . . . . . . . . . . . . . . . . . . 16
3.1.1 Basic Concepts of Group . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1.2 Representation of a Group . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.3 Basis Functions and Projection Operators . . . . . . . . . . . . . . 20
3.2 Classification of Defect Modes in Hexagonal Lattice . . . . . . . . . . . . . 22
3.2.1 Symmetry Group of Photonic Crystals . . . . . . . . . . . . . . . . 22
3.2.2 Symmetry of 2D Photonic Crystals of Finite Thickness . . . . . . . 23
3.2.3 Symmetry of Defect Modes . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Some Design Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4 Simulation Results 27
4.1 Photonic Band Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.1 2D PWE Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.2 3D PWE Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1.3 3D FDTD Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Defect Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.1 Resonant Frequencies of Defect Modes . . . . . . . . . . . . . . . . 31
4.2.2 Mode Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2.3 Quality Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5 Summary 40
References 41
[1] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,”
Phys. Rev. Lett., vol. 58, pp. 2059–2062, 1987.
[2] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals. Princeton,
New York: Princeton Univ. Press, 1995.
[3] O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I.
Kim., “Two-dimensional photonic band-gap defect mode laser,” Science, vol. 284,
pp. 1819–1821, 1999.
[4] O. Painter, K. Srinivasan, J. D. O’Brien. A. Scherer and P. D. Dapkus, “Tailoring
of the resonant mode properties of optical nanocavities in two-dimensional photohic
crystal slab waveguides,” J. Opt. A: Pure Appl. Opt., vol. 3, pp. 161–170, 2001.
[5] H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, Y. H. Lee, and J. S. Kim, “Nondegenerate
monopole-mode two-dimensional photonic band gap laser,” Appl. Phys. Lett.
vol. 79, pp. 3032–3034, 2001.
[6] H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee,
“Characteristics of modified single-defect two-dimensional photonic crystal lasers,”
IEEE J. Quantum Electron., vol. 38, pp. 1353–1365, 2002.
[7] Vˇuckovi´c, Marko Lon´car, Hideo Mabuchi, and Axel Scherer, “Design of photonic
crystal microcavities for cavity QED,” Phys. Rev. E, vol. 65, 016608, 2001.
[8] Vˇuckovi´c, Marko Lon´car, Hideo Mabuchi, and Axel Scherer, “Optimization of the Q
factor in photonic crystal microcavities,” IEEE J. Quantum Electron., vol. 38, pp.
850–856, 2002.
[9] P. T. Lee, J. R. Cao, S. J. Choi, Z. J. Wei, J. D. O’Brien, and P. D. Dapkus,
“Operation of photonic crystal membrane lasers above room temperature,” Appl.
Phys. Lett., vol. 81, pp. 3311–3313, 2002.
[10] P. T. Lee, J. R. Cao, S. J. Choi, Z. J. Wei, J. D. O’Brien, and P. D. Dapkus, “Roomtemperature
operation of VCSEL-pumped photonic crystal lasers,” IEEE Photon.
Technol. Lett., vol. 14, pp. 435–437, 2002.
[11] E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev.,
vol. 69, p. 681, 1946.
[12] M. Boroditsky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, E. Yablonovitch, “Spontaneous
emission extraction and Purcell enhancement from Thin-Film 2-D Photonic
Crystals,” J. Lightwave Technol., vol. 17, pp. 2096–2112, 1999.
[13] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s
equations in isotropic media,” IEEE Trans. Antennas Propag., vol. 14, pp. 302–307,
1966.
[14] J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic
waves,” J. Comput. Phys, vol. 114, pp. 185–200, 1994.
[15] Sullivan, “An unsplit step 3-D PML for use with the FDTD method,” IEEE Microwave
Guided Wave Lett., vol. 7, pp. 184–186, 1997.
[16] Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic
absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propagat.,
vol. 43, pp. 1460–1463, 1995.
[17] J. D. Moerloose and D. D. Zuttler, “Poynting’s theorem for the finite-difference-timedomain
method,” Micro. Opt. Technol. Lett. Vol. 8, pp. 257–260, 1995.
[18] A. Taflove and S. C. Hagness, Computational Electrodynamics : the finite-difference
time-domain method, 2nd ed., Boston: Artech House, 2000.
[19] M. Tinkham, Group Theory and Quantum Mechanics, New York: McGraw-Hill,
1964.
[20] K. Sakoda, Optical Properties of Photonic Crystals, Berlin: Springer, 2001.
[21] E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and
J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys.
Rev. Lett., vol. 67, pp. 3380–3383, 1991.
[22] L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits,
New York: John Wiley & Sons, 1995.
[23] J. D. Jackson, Classical Electrodynamics, 3rd ed., New York: Wiley, 1999.
[24] W. H. Press, et al., Numerical Recipes in C: The Art of Scientific Computing, 2nd
ed., New York: Cambridge, 1992.
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