臺灣博碩士論文加值系統

本論文在二維光子晶體的三角晶格空氣孔結構上，設計並模擬基於光子晶體微共振腔的一對二分波解多工器。在數值工具上，以平面波展開法分析光子能隙以及線缺陷波導的色散曲線，並以時域有限差分法模擬光波在波導中的傳播行為。
首先，在波導中加入微共振腔濾波器，分別有單顆、雙顆及相異空氣孔的微共振腔結構，經由設計空氣孔半徑或共振腔長度，可以調整共振頻率，在適當的頻率下傳輸率可接近100%；接著，設計一對二功率分離器，分別對基本型、空氣孔位移型、增加空氣孔型、膠囊形空氣孔、水滴形空氣孔等不同結構作分析，以達到高效率的功率傳輸；最後，結合共振腔濾波器及功率分離器，設計出數種分波解多工器，包括單顆空氣孔、雙顆空氣孔、以及相異空氣孔微共振腔結構，其中採用雙顆空氣孔微共振腔的雙波長傳輸率，分別可達到95%和91%，可作為高效率的分波解多工器。
本論文所設計的分波解多工器，具有結構簡單、濾波頻率容易調整的特性，因此在高密度分波多工等光纖通信的領域上，具有潛在的應用價值。

Design and simulation of 1x2 wavelength-division demultiplexers based on two-dimensional photonic crystal microcavities in triangular air-hole lattice was conducted in this work. As for numerical techniques, plane-wave expansion method was employed to calculate photonic bandgap and waveguide dispersion curve. Finite-difference time-domain method was used to simulate wave propagation in line-defect waveguides.
Firstly, wavelength filters based on microcavity were designed, including single-hole, two-hole, and dissimilar-hole microcavities. Resonant frequency can be tuned by varying radius of air holes or length of microcavity. Power transmission can approach 100% at certain frequency ranges. Secondly, high-efficiency 1x2 power splitters were designed, including basic type, shifted hole type, additional hole type, capsule hole type, and drop hole type. Finally, microcavity filters and power splitters were combined to obtain several types of wavelength division demultiplexers, which employed single-hole, two-hole, and dissimilar-hole microcavities, respectively. High-efficiency demultiplexer based on two-hole microcavities exhibits power transmission of 95% and 91% for the two output channels, respectively.
These wavelength-division demultiplexers exhibit simple structures and their resonant frequencies can be easily tuned. Therefore, potential application of these devices will be possible in dense wavelength-division multiplexing for fiber-optic communications in the near future.

摘要 i
ABSTRACT ii
誌謝 iv
目錄 v
表目錄 viii
圖目錄 ix
第一章 導論 1
1.1 光子晶體簡介 1
1.1.1 三角晶格空氣孔結構的光子能隙分析 4
1.1.2 色散曲線 6
1.2 光子晶體分波解多工器之介紹 7
1.2.1 共振腔結構的分波解多工器 7
1.2.2 方向耦合器結構的分波解多工器 9
1.2.3 多模干涉結構的分波解多工器 11
1.2.4 光子能隙結構的分波解多工器 12
1.3 研究動機 14
1.4 論文架構 14
第二章 數值分析方法 15
2.1 馬克斯威爾方程式 15
2.2 平面波展開法 18
2.2.1 橫向電場模態 20
2.2.2 橫向磁場模態 21
2.3 時域有限差分法 22
2.4 吸收邊界條件 28
2.4.1 概要 28
2.4.2 完美匹配層的吸收邊界條件 30
2.4.3 基本方程式 31
2.4.4 完美匹配層的反射率 34
2.4.5 穩定因數 34
第三章 光子晶體分波解多工器之設計 36
3.1 光子晶體特性分析 36
3.2 光子晶體共振腔濾波器 39
3.2.1 單顆空氣孔共振腔 40
3.2.2 雙顆空氣孔共振腔 49
3.2.3 相異空氣孔共振腔 58
3.3 光子晶體一對二功率分離器 67
3.3.1 直波導結構 67
3.3.2 基本型一對二功率分離器 68
3.3.3 交界點空氣孔位移型一對二功率分離器 70
3.3.4 交界點增加空氣孔型一對二功率分離器 73
3.3.5 膠囊型一對二功率分離器 76
3.3.6 水滴型一對二功率分離器 79
3.4 光子晶體分波解多工器 82
3.4.1 單顆空氣孔分波解多工器 82
3.4.2 雙顆空氣孔分波解多工器 84
3.4.3 相異空氣孔分波解多工器 86
3.4.4 位移共振腔的位置以改善傳輸率 88
3.4.5 改變共振腔長度以調整共振頻率 92
3.4.6 分波解多工器的整理 101
第四章 結論 102
參考文獻 103

[1] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett., vol. 58, pp. 2059-2062, 1987.
[2] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett., vol. 58, pp. 2486-2489, 1987.
[3] E. Yablonovitch, “Photonic crystals: semiconductor of light,” Scientific American, vol. 285, no. 6, pp. 47-55, 2001.
[4] http://taibnet.sinica.edu.tw/chi/taibnet_species_detail.php?name_code=347116
[5] http://www.hfzqyzc.com/product/1_1.html
[6] http://www.harley.com.tw/jewels/new_page_J5.htm
[7] Y. Morita, Y. Tsuji, and K. Hirayama,“Proposal for a compact resonant-coupling-type polarization splitter based on photonic crystal waveguide with absolute photonic bandgap,” IEEE Photon. Technol. Lett., vol. 20, no. 2, pp. 93-95, Jan. 2008.
[8] Robinson S and Nakkeeran R, “Studies on photonic crystal based add drop filter by varying the dimension of inner rods,” Sustainable Energy and Intelligent Systems (SEISCON 2011), International Conference on, pp. 20-22, July 2011.
[9] Jiu-Sheng Li, Han Liu, and Le Zhang “Compact and tunable-multichannel terahertz wave filter,” IEEE Transactions on Terahertz Science and Technology (Volume:5 , Issue: 4 ), pp.551-555, July 2015.
[10] Azliza J. M. Adnan, R. Mohamad, Imran A. Tengku, and Sahbudin Shaari “1310/1550 nm photonic crystal based on multimode interference demultiplexer,” In the Joint Conference of the Opto-Electronics and Communications Conference, Australian Conference on Optical Fibre Technology (OECC/ACOFT), 7-10 July 2008.
[11] 杜俊宏，二維光子晶體之新型1.3/1.55μm分波解多工器的設計，碩士論文，龍華科技大學，電機工程研究所，桃園，2005.
[12] P. R. Villeneuve, S. Fan and J.D. Joannopoulos, “Microcavities in photonic crystal： mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B, vol. 54, pp. 7837-7842, 1996.
[13] C. Kee, J. Kim, H. Y. Park and K. J. Chang, “Defect modes in a two-dimensional square lattice of square rods,” Phys. Rev. E, vol. 58, pp. 7908-7912, 1998.
[14] R. D. Meade, A. M. Rappe, K. D. Brommer and J. D. Joannopoulos, “Accurate theoretical analysis of photonic band-gap material,” Phys. Rev. B, vol.48, pp. 8434-8437, 1993.
[15] E. Yablonovitch and T. J. Gmitter, “Photonic band structure: the face-centered
-cubic case,” Phys. Rev. Lett., vol. 63, pp. 1950-1953, 1989.
[16] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas and Propagation, vol. 14, pp. 302-307, 1966.
[17] D. Felbacq, G. Tayeb and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A, vol. 11, pp. 2526-2538, 1994.
[18] G. Tayeb and D. Maystre, “Rigorous theoretical study of finite-size two dimensional photonic crystals doped by microcavities,” J. Opt. Soc. Am. A, vol.14, pp. 3323-3332, 1997.
[19] P. P. Silvester and G. Pelosi, Finite elements for wave electromagnetics: methods and techniques, IEEE Press, New York, 1994.
[20] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: molding the flow of light, Princeton, Princeton University Press, 1995.
[21] K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett., vol. 65, pp. 2646-2649, 1990.
[22] Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell's equations,” Phys. Rev. Lett., vol. 65, pp. 2650-2653, 1990.
[23] 林振華，電磁場與天線分析-使用時域有限差分法(FDTD)，全華圖書，一版，台北，1999。
[24] G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagnetic Compatibility, vol. 23, pp. 377-382, 1981.
[25] R. L. Higdon, “Absorbing boundary conditions for difference approximation of the multi-dimensional wave equation,” Mathematics of Computation, vol. 47, no. 176, pp.437- 459, 1986.
[26] Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, “A transmitting boundary for transient wave analysis,” Scientia Sinica A, vol. 27, no. 10, pp. 1063-1076, 1984.
[27] J. P Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys, vol. 114, pp. 185-200, 1994.
[28] E. L. Lindman, “Free-space boundary conditions for the time dependent wave equation,” J. Comput. Phys., vol.18, pp. 66-78, 1975.
[29] C. Rappaport and L. Bahrmasel, “An absorbing boundary condition based on anechoic absorber for UEM scattering computation,” Journal of Electromagnetic Waves and Applications, vol. 6, no. 12, pp. 1621-1634, 1992.
[30] Z. S. Sackes, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas and Propagation, vol. 43, no.12, pp. 1460-1463, 1995.
[31] S. D. Gedeney, “An anisotropic perfectly matched layer-absorbing for the truncation of FDTD lattices,” IEEE Trans. Antennas and Propagation, vol. 44, no. 12, pp. 1630-1639, 1996.
[32] K. K. Mei and J. Fang, “Superaborption-a method to improve absorbing boundary conditions,” IEEE Trans. Antennas and Propagation, vol. 40, no. 9, pp. 1001-1010, 1992.
[33] A. Taflove and S. C. Hagness, Computational electrodynamics: the finite difference time domain method, Artech House, 2000.