臺灣博碩士論文加值系統

In recent years, with growing interests to Photonic Crystals (PhCs) and their applications, many researchers have studied PhCs. 2-Dimensional PhC laser is one of the interesting research topics due to its strong light confinement in a small wavelength-scale volume.
Liquid Crystal (LC) infiltrated 2D PhC laser has also been investigated for the laser wavelength tuning, yet its theoretical study seems insufficient. Thus, in this research, we developed 3D Finite-Difference Time-Domain (FDTD) program which can simulate the light propagation in LCs, and analyzed the characteristics of LC infiltrated 2D PhC laser.
In several characteristic PhC structures, the lasing wavelength shift of a single mode, the degeneracy splitting, the lasing mode change and the quality factor (Q-factor) change are found as the arrangement of LCs changes. Moreover, by properly designing the defect, we can expect the intrinsic polarization of the lasing mode.

Contents


Abstract
Acknowledgment

Chapter 1 : Introduction 1
1.1. Photonic Crystal and 2-Dimensional Photonic Crystal Laser 1
1.1.1. Photonic Crystal 1
1.1.2. 2-Dimensional Photonic Crystal Laser 4
1.2. Liquid Crystal 5
1.3. Liquid Crystal Infiltrated Tunable Photonic Crystal Laser 8
References 10

Chapter 2 : Simulation of Light Propagation using Finite-Difference Time-Domain Method 12
2.1. Finite-Difference Time-Domain (FDTD) Method 12
2.2. Simulation of Light Propagation 19
2.2.1. Light Propagation in Air 19
2.2.2. Light Propagation in Nematic Liquid Crystal 20
2.2.3. Light Propagation in Twisted Nematic Liquid Crystal 22
References 24


Chapter 3 : Design of the Liquid Crystal Infiltrated Photonic Crystal Laser 25
3.1. Choice of Liquid Crystal 25
3.2. Design of 2-Dimensional Photonic Crystal Slab 26
3.2.1. Slab Thickness 27
3.2.2. Hole Radius 27
3.2.3. Lattice Constant 29
3.2.4. Defect Design 30
References 32

Chapter 4 : Characteristics of the Liquid Crystal Infiltrated Photonic Crystal Laser 33
4.1. Simulation Conditions 33
4.2. Several Characteristics of the Liquid Crystal Infiltrated Photonic Crystal Laser 37
4.2.1. Lasing Wavelength Shift of Single Mode (Design A)37
4.2.2. Degeneracy Splitting (Design B) 43
4.2.3. Lasing Mode Change (DesignC) 46
References 49

Chapter 5 : Conclusion 50

Chapter 1

[1] E. Yablonovitch, “Inhibited spontaneous emission in solid-stat physics and electronics”, Phys. Rev. Lett. 58, 2059-2062 (1987).
[2] Alongkarn Chutinan and Susumu Noda, “Waveguides and waveguide bends in two dimensional photonic crystal slabs”, Phys. Rev. B 62, 4488-4492 (2000).
[3] S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure”, Nature 407, 608-610 (2000).
[4] 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, 284, 1819-1821 (1999).
[5] Hong-Gyu Park, Se-Heon Kim, Min-Kyo Seo, Young-Gu Ju, Sung-Bock Kim, and Yong-Hee Lee, “Characteristics of Electrically Driven Two-Dimensional Photonic Crystal Lasers”, IEEE J. Quantum Electron., 41 1131 (2005).
[6] T.Yoshi, A.Scherer, J.Hendrickson, G.Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O.B. Schekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity”, Nature 432, 200-203 (2004).
[7] A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu, P. Petroff, and A. Imamoglu, “Deterministic coupling of single quantum dots to single nanocavity modes”, Science 308, 1158-1161 (2005).
[8] Kurt Busch and Sajeev John, “Liquid-Crystal Photonic-Band-Gap Materials: The Tunable Electromagnetic Vacuum”, Phys. Rev. Lett. 83, 967 (1999).
[9] Ryotaro Ozaki, Yuko Matsuhisa, Masanori Ozaki, and Katsumi Yoshino, “Electrically tunable lasing based on defect mode in one-dimensional photonic crystal with conducting polymer and liquid crystal defect layer”, Appl. Phys. Lett. 84, 1844-1846 (2004).
[10] B. Maune, M. Loncar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85, 360-362 (2004).
[11] Brett Maune, Jeremy Witzens, Thomas Baehr-Jones, Michael Kolodrubetz, Harry Atwater, and Axel Scherer, Rainer Hagen, Yueming Qiu, “Optically triggered Q-switched photonic crystal Laser”, OPTICS EXPRESS 13, 4699 (2005).
[12] John D. Joannopoulos, Robert D. Meade, and Joshua N. Winn, Photonic Crystals:
Molding the Flow of Light, Princeton University Press (1995).
[13] Hong-Gyu Park, Jeong-Ki Hwang, Joon Huh, Han-Youl Ryu, Se-Heon Kim, Jeong-Soo Kim, and Yong-Hee Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers”, IEEE JOURNAL OF QUANTUM ELECTRONICS 38, 1353 (2002).
[14] Y. Akahane, T. Asano, B. S. Song and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal”, Nature 425, 944–947 (2003).
[15] Pochi Yeh and Claire Gu, Optics of Liquid Cyrstal Displays, Wiley Interscience (1999).
[16] Peter J. Collings and Michael Hird, Introduction to Liquid Crystals, Taylor & Francis (1997).

Chapter 2

[1] A. Taflove and Susan C. Hagness, Computational Electrodynamics—The Finite-Difference Time-Domain Method, 2nd ed., Artech House (2000).
[2] Pochi Yeh and Claire Gu, Optics of Liquid Cyrstal Displays, Wiley Interscience (1999).

Chapter 3

[1] B. Maune, M. Loncar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85, 360-362 (2004).
[2] S. T. Wu, C. S. Wu, M. Warenghem, and M. Ismaili, Opt. Eng. 32, 1775 (1993).
[3] S. T. Wu, Phys. Rev. A, 33, 1270 (1986).
[4] Hong-Gyu Park, Jeong-Ki Hwang, Joon Huh, Han-Youl Ryu, Se-Heon Kim, Jeong-Soo Kim, and Yong-Hee Lee, “Characteristics of Modified Single-Defect Two-Dimensional Photonic Crystal Lasers”, IEEE JOURNAL OF QUANTUM ELECTRONICS 38, 1353 (2002).
[5] P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, Clarendon Press (1993).
[6] Se-Heon Kim and Yong-Hee Lee, “Symmetry Relations of Two-Dimensional Photonic Crystal Cavity Modes”, IEEE JOURNAL OF QUANTUM ELECTRONICS, 39, 1081 (2003).

Chapter 4

[1] B. Maune, M. Loncar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85, 360-362 (2004).
[2] Se-Heon Kim and Yong-Hee Lee, “Symmetry Relations of Two-Dimensional Photonic Crystal Cavity Modes”, IEEE JOURNAL OF QUANTUM ELECTRONICS, 39, 1081 (2003).