Dirichlet-to-Neumann 映射法應用於光子晶體能帶結構之計算

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：68

、訪客IP：3.15.10.190

姓名

張凱程(Zhang Kaicheng) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

Dirichlet-to-Neumann 映射法應用於光子晶體能帶結構之計算

相關論文

★ 平坦化陣列波導光柵分析和一維光子晶體研究	★ 光子晶體波導與藕合共振波導之研究
★ 光子晶體異常折射之研究	★ 光子晶體傳導帶與介電質柱波導之研究
★ 平面波展開法在光子晶體之應用	★ 偏平面光子晶體能帶之研究
★ 通道選擇濾波器之探討	★ 廣義光子晶體元件之研究與分析
★ 新式光子晶體波導濾波器之研究	★ 廣義非均向性介質的光傳播研究
★ 光子晶體耦合濾波器之研究	★ 聲子晶體傳導帶與週期性彈性柱波導之研究
★ 對稱與非對稱波導光柵之特性研究	★ 雙曲透鏡之研究
★ 電磁波與聲波隱形斗篷之研究	★ 一維光子晶體等效非均向介值之研究

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

本論文採用數值分析方法Dirichlet-to-Neumannu映射(DtN map)來計算光子晶體的頻帶結構。由Dirichlet-to-Neumann映射的基本原理開始，探討DtN映射法在常見二維光子晶體結構：正方晶格、三角晶格、超晶格結構與蜂巢狀晶格中的應用。我們引入色散性介質，以DtN映射法模擬正方晶格頻帶結構，調配其參數使晶體具有雙負折射性質。在晶柱介質為Drude色散模型，背景介質為Lorentz色散模型的情況下，晶柱介質的電漿頻率( )為2.0，背景介質的無阻尼震盪頻率( )為0.38且填充率( )為0.56時，其雙負折射效應最為明顯。

摘要(英)

This thesis introduce a numerical analysis method,the Dirichlet-to-Neumann map(DtN map), to calculate the band structure of photonic crystals. From the basic principle of Dirichlet-to-Neumann map, we investgate the applications on general two-dimensional photonic crystal structures: such as square lattice, triangular lattice, super lattice and honey-comb lattice. We introduce dispersion material to simulate band structure of square lattice by DtN map, change the parameter that makes doule negative refractive medium. In Drude model cylinder and Lorentz model background crystal structure, the cylinder plasma frequency 2.0 and background non-damping resonant frequency 0.38 with filling rate 0.56 makes better double negative refractive medium.

關鍵字(中)

★ 光子晶體
★ DtN映射法
★ 正方晶格
★ 色散性介質

關鍵字(英)

★ photonic crystal
★ Dirichlet-to-Neumann map
★ square lattice
★ dispersion medium

論文目次

摘要 I
誌謝 III
目次 IV
圖目錄 V
第一章簡介 1
第一節研究背景 1
第二節研究目的 2
第二章 DTN映射法於波頻帶分析的應用 3
第一節波頻帶分析常見方法 3
第二節 DTN頻帶分析法與其應用 4
一、正方晶格頻帶分析 6
二、三角晶格頻帶分析 12
第三節 DTN頻帶分析法進階應用 17
一、超晶胞(super cell)頻帶分析 17
二、蜂巢狀晶格頻帶分析 22
第三章色散性金屬介質柱光子晶體頻帶特性 28
第一節低填充率色散金屬柱光子晶體等效模型 29
第二節 DTN映射法等效電漿模型驗證 31
第三節色散金屬柱光子晶體頻帶分析 36
第四章雙負折射介質光子晶體頻帶特性 39
第一節色散背景光子晶體頻帶分析 39
第二節雙負折射介質光子晶體頻帶分析 45
第三節雙負折射介質光子晶體準頻率曲線圖分析 47
第五章結論 48
第一節研究發現 48
第二節未來展望 49
參考文獻 50

參考文獻

E.Yablonovitch et. al. “Inhibited Spontaneous Emission in Solid-state Physics and Electronics”, Phys. Rev. Lett. ,Vol. 58, pp. 2059, 1987.
S. John et. al. “Strong localization of photons in certain disordered dielectric super lattices,” Phys. Rev. Lett. ,Vol. 58, pp. 2486, 1987.
Loncar, T. Doll J. Vuckovic, and A. Scherer et. al. “Design and Fabrication of Silicon Photonic Crystal Optical Waveguides” J. Lightwave Tech., Vol. 18, pp. 1402-1411, 2000.
O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, I.Kim “Two-Dimensional Photonic Band-Gap Defect Mode Laser” SCIENCE, Vol. 284, pp.1819, 1999.
Hwang, J.-K., H.-Y. Ryu, “Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 μm” Appl. Phys. Lett. Vol. 76, p.2982, 2000.
M. Boroditsky et. al. “ Spontaneous Emission Extraction and Purcell Enhancement from Thin-film 2-D Photonic Crystal” IEEE LIGHTWAVE TECHNOLOGY, Vol. 17, pp. 2096, 1999.
J. Yuan, Y. Lu, “Photonic bandgap calculations with Dirichlet-to-Neumann maps,” J. Opt. Soc. Am. A., Vol. 23, 3217-3222, 2006.
Jianhua Yuan , Ya Yan Lu “Computing photonic band structures by Dirichlet-to-Neumann maps: The triangular lattice” Opt, 2007.
H. Xie and Y. Lu, “Modeling two-dimensional anisotropic photonic crystals by Dirichlet-to-Neumann maps,” J. Opt. Soc. Am. A., Vol. 26, 1606-1614, 2009.
Vala, A. S., A. Sedghi, et al “Detailed study of flat bands appearing in metallic photonic crystals.” Physica Status Solidi, Vol. 8(9): 2965-2968, 2011.
Moreno, E., Erni, D., & Hafner, C. Band structure computations of metallic photonic crystals with the multiple multipole method. Physical Review B, Vol. 65(15), 155120, 2002.
S. Guo and S. Albin et. al. “Simple plane wave implementation for photonic crystal calculations” Opt. Express Vol. 11, pp. 167-175, 2003.
Dennis M. Sullivan, Electromagnetic Simulation Using The FDTD Method, Wiley-IEEE Press, New York, 2001.
Kane S.Yee et. al. “Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media” , IEEE. Trans. Antennas. Propag. ,Vol.14, pp. 302-307, 1966.
O. C. Zienkiewicz, Robert Leroy Taylor, J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, Butterworth-Heinemann press, 2005.
Rahman, B.M.A.; “A review on the characterization of photonic devices using the finite element method,” Electrotechnical Conference, 1996. MELECON ‘96., 8th Mediterranean , vol.2, no., pp.705-708 vol.2, 13-16 May, 1996.
Chuan, C., X. Can, et al. “Temperature dependent complex photonic band structures in two-dimensional photonic crystals composed of high-temperature superconductors.” Journal of Physics: Condensed Matter, Vol. 20(27): 275203, 2008.
Takigawa, S. and S. Noda “Gain analysis in photonic crystal lasers using modified complex plane-wave expansion method.” Solid-State Electronics, Vol. 73(0): 37-43, 2012.
Manzanares-Martinez, B., J.-Y. Kim, et al. “Determination of ultrasonic vibration modes of a graded solid cylinder using a modified wave-expansion technique.” The Journal of the Acoustical Society of America, Vol. 125(4): 2634-2634, 2009.
Manzanares-Martinez, B., F. Ramos-Mendieta, et al. “Ultrasonic elastic modes in solid bars: An application of the plane wave expansion method.” The Journal of the Acoustical Society of America, Vol. 127(6): 3503-3510, 2010.
Peier, P., H. Merbold, et al. Imaging of THz waves in 2D photonic crystal structures embedded in a slab waveguide.” New Journal of Physics, Vol. 12(1): 013014, 2010.
El-Naggar, S. A., S. I. Mostafa, et al. “Complete band gaps of phononic crystal plates with square rods.” Ultrasonics, Vol. 52(4): 536-542, 2012.
Hagstrom, T., T. Warburton, et al. “Radiation boundary conditions for time-dependent waves based on complete plane wave expansions.” Journal of Computational and Applied Mathematics, Vol. 234(6): 1988-1995, 2010.
Frezza, F., G. Schettini, et al. “Generalized plane-wave expansion of cylindrical functions in lossy media convergent in the whole complex plane.” Optics Communications, Vol. 284(16–17): 3867-3871, 2011.
Mehrem, R. “The plane wave expansion, infinite integrals and identities involving spherical Bessel functions.” Applied Mathematics and Computation, Vol. 217(12): 5360-5365, 2011.
Oviedo-de-Julian, I., R. A. Mendez-Sanchez, et al. “The plane wave expansion method applied to thin plates.” The Journal of the Acoustical Society of America, Vol. 130(4): 2346-2346, 2011.
Hsue, Y.-C., A. J. Freeman, et al. “Extended plane-wave expansion method in three-dimensional anisotropic photonic crystals.” Physical Review B, Vol. 72(19): 195118, 2005.
Chuang, Y. C. and T. J. Suleski “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation.” Journal of Optics, Vol. 12(3): 035102, 2010.
Zhilin, H. and M. A. Badreddine “Numerical investigation of the propagation of elastic wave modes in a one-dimensional phononic crystal plate coated on a uniform substrate.” Journal of Physics D: Applied Physics, Vol. 42(8): 085103, 2009.
Zhang, C.-X. and X.-S. Xu “Low group velocity in a photonic crystal coupled-cavity waveguide.” Chinese Physics B, Vol. 21(4): 044213, 2012.
Liang-Yu, W., C. Lien-Wen, et al. (2008). “The nondiffractive wave propagation in the sonic crystal consisting of rectangular rods with a slit.” Journal of Physics: Condensed Matter, Vol. 20(29): 295229, 2008.
欒丕綱、陳啟昌，光子晶體：從蝴蝶翅膀到奈米光子學，五南出版社，台北市，民國九十九年。
Moreno, E., D. Erni, et al. “Band structure computations of metallic photonic crystals with the multiple multipole method.” Physical Review B, Vol. 65(15): 155120, 2002
Pendry, J. B., A. J. Holden, et al. “Extremely Low Frequency Plasmons in Metallic Mesostructures.” Physical Review Letters, Vol. 76(25): 4773-4776, 1996.
V. Liu and S. Fan, “Efficient computation of equifrequency surfaces and density of states in photonic crystals using Dirichlet-to-Neumann maps,” J. Opt. Soc. Am. B, Vol. 28, 1837-1843, 2011.
Li, F.-L., Y.-S. Wang, et al. “Bandgap calculation of two-dimensional mixed solid–fluid phononic crystals by Dirichlet-to-Neumann maps.” Physica Scripta, Vol. 84(5): 055402, 2011.
S. Li and Y. Lu, "Multipole Dirichlet-to-Neumann map method for photonic crystals with complex unit cells," J. Opt. Soc. Am. A, Vol. 24, 2438-2442, 2007.
S. Li and Y. Lu, "Computing Photonic Crystal Defect Modes by Dirichlet-to- Neumann Maps," Opt. Express, Vol. 15, 14454-14466, 2007.
Yuexia Huang, Y. Y. L. “Modeling Photonic Crystals With Complex Unit Cells By Dirichlet-to-Neumann Maps.” Journal of Computational Mathematics, Vol. 25(3): 337-349, 2007.

指導教授

欒丕綱

審核日期

2013-1-23

推文