二维斜三角晶格及棋盘格子直波导光子晶体带隙研究
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摘要
光子晶体(Photonies crystals)是一种能够产生光子禁带的周期性光学微结构材料。它具有极其独特的光学性质和导光机制,在实际生活中具有多种潜在的应用价值。目前,关于光子晶体的研究已经成为光学和光电子学领域最前沿的项目之一。
本文第一章详细介绍了光子晶体的概念、性质、应用领域和研究现状。由于此论文主要是利用平面波展开方法对二维光子晶体能带结构进行数值计算。因此,在第二章中对平面波展开法及其数值算法的推导做了详细的分析。
第三章中,在二维正三角晶格光子晶体的基础上,通过改变晶体的晶格基矢构造了-种全新的周期结构。该周期结构的最小周期单元不再是传统意义上的等边三角形,而是一种更为优化的斜三角形结构。利用平面波展开法理论模拟了二维斜三角品格光子晶体完全带隙的情况,发现所设计结构的完全带隙宽度是二维正三角晶格光子晶体完全带隙宽度的4.32倍。分析了介质柱宽度,介质柱旋转角度以及相对介电常数对所构造结构的完全带隙的影响,所得结果对二维光子晶体的理论研究和实际应用有所帮助。为任意角度的二维光子晶体集成波导的研究和制作提供了理论基础。
最后一章的主要研究工作是研究光子晶体波导的能带结构。同时,结合超原胞技术,计算出二维光子晶体波导的能带结构,并且根据计算讨论了介质柱宽度和缺陷介质柱介电常数对能带结构的影响。这些研究对光子晶体波导的设计具有实际指导意义。
Photonic crystals were periodic optical micro-structure that were capable of generating photonic band gaps. It has many peculiar optical properties and unique light-guiding principle, so it has a number of potential applications in real life. Presently, the researching of PC has become the most advanced project in the optical and optoelectronic field.
In chapter one, initial introduction about the concept, properties, application domain and research status quo of PC. In this thesis, Photonic band struetures of Two-dimensional (2D) Photonic crystals have been calculated based on Plane-wave expansion (PWE) method. So the plane-wave expansion method (PWE) and it's numerical arithmetic are analyzed in the second chapter.
In chapter three, Based on the two-dimensional equilateral triangular lattice photonic crystals, a new periodic structure is constructed by changing the unit cell-vector of the photonic crystals. The minimum construction unit of the periodic structure is no longer the traditional equilateral triangle, but an optimal oblique triangle. With the method of plan wave expansion, the band gap of two-dimensional oblique triangular lattice photonic crystals were simulated. The result shows that the absolute band gap width be 4.32 times wider than it produced by the two-dimensional equilateral triangular lattice photonic crystals. The influence on oblique triangular lattice photonic crystals by changing the width, rotation angle and relative dielectric constant of the dielectric column is analyzed. The results are very useful to the theoretical research and practical application of two-dimensional photonic crystals, and also provide a rationale for the research and fabrication of integrated two-dimensional photonic crystal waveguide at any angle.
The main work of the last chapter is the analysis of Photonic Band Structures with photonic crystal waveguides. Then, combined with supercell technique, Photonic Band Structures of 2D photonic crystal waveguides were calculated. And, the influence factors on photonic band structures, such as width of Medium column and dielectric constant of defective Medium column, were discussed. These results have practical function to direct waveguide designing.
本文第一章详细介绍了光子晶体的概念、性质、应用领域和研究现状。由于此论文主要是利用平面波展开方法对二维光子晶体能带结构进行数值计算。因此,在第二章中对平面波展开法及其数值算法的推导做了详细的分析。
第三章中,在二维正三角晶格光子晶体的基础上,通过改变晶体的晶格基矢构造了-种全新的周期结构。该周期结构的最小周期单元不再是传统意义上的等边三角形,而是一种更为优化的斜三角形结构。利用平面波展开法理论模拟了二维斜三角品格光子晶体完全带隙的情况,发现所设计结构的完全带隙宽度是二维正三角晶格光子晶体完全带隙宽度的4.32倍。分析了介质柱宽度,介质柱旋转角度以及相对介电常数对所构造结构的完全带隙的影响,所得结果对二维光子晶体的理论研究和实际应用有所帮助。为任意角度的二维光子晶体集成波导的研究和制作提供了理论基础。
最后一章的主要研究工作是研究光子晶体波导的能带结构。同时,结合超原胞技术,计算出二维光子晶体波导的能带结构,并且根据计算讨论了介质柱宽度和缺陷介质柱介电常数对能带结构的影响。这些研究对光子晶体波导的设计具有实际指导意义。
Photonic crystals were periodic optical micro-structure that were capable of generating photonic band gaps. It has many peculiar optical properties and unique light-guiding principle, so it has a number of potential applications in real life. Presently, the researching of PC has become the most advanced project in the optical and optoelectronic field.
In chapter one, initial introduction about the concept, properties, application domain and research status quo of PC. In this thesis, Photonic band struetures of Two-dimensional (2D) Photonic crystals have been calculated based on Plane-wave expansion (PWE) method. So the plane-wave expansion method (PWE) and it's numerical arithmetic are analyzed in the second chapter.
In chapter three, Based on the two-dimensional equilateral triangular lattice photonic crystals, a new periodic structure is constructed by changing the unit cell-vector of the photonic crystals. The minimum construction unit of the periodic structure is no longer the traditional equilateral triangle, but an optimal oblique triangle. With the method of plan wave expansion, the band gap of two-dimensional oblique triangular lattice photonic crystals were simulated. The result shows that the absolute band gap width be 4.32 times wider than it produced by the two-dimensional equilateral triangular lattice photonic crystals. The influence on oblique triangular lattice photonic crystals by changing the width, rotation angle and relative dielectric constant of the dielectric column is analyzed. The results are very useful to the theoretical research and practical application of two-dimensional photonic crystals, and also provide a rationale for the research and fabrication of integrated two-dimensional photonic crystal waveguide at any angle.
The main work of the last chapter is the analysis of Photonic Band Structures with photonic crystal waveguides. Then, combined with supercell technique, Photonic Band Structures of 2D photonic crystal waveguides were calculated. And, the influence factors on photonic band structures, such as width of Medium column and dielectric constant of defective Medium column, were discussed. These results have practical function to direct waveguide designing.
引文
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[3]I. Abarm. G. Bourdon. Photonic-well microcavities for spontaneous emission control [J]. phys. Rev. (A).1996,54(8):3476-3479
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[6]M. M. Sigalas, C. T. Chan, K. M. Ho, et al. Metallic photonic band-gap materials [J]. Phys. Rev. (B).1995,52(161):11744-11751
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[8]Villeneuve P. R, Piche M. Photonic Band Gaps in Two-dimentional Square and Hexagonal Lattices [J]. Phys. Rev. B.,1992,46 (8):4969-4972
[9]Plihal M, Maradudin A. A. Photonic Band Structure of Two-dimentional Systems:The Triangular Lattice [J]. Phys. Rev. B,1991,44(16):8565-8571
[10]Gadot F, Chelnokov A, De Lustrac A, et al. Experimental Demonstration of Complete Photonic Band Gap in Graphite Structure [J]. Appl. Phys. Lett.,1997,71 (13) 1780-1782
[11]Anderson C. M, Giapis K. P. Larger Two-Dimentional Photonic Band Gaps. Phys. Rev. Lett., 1996,77 (14):2949-2952
[12]仇高新,林芳蕾,李永平.利用复式晶胞实现二维正方形布拉菲格子光子晶体的完全带隙[J].物理学报,2003,52(3)：600-603
[13]谢双媛,羊亚平,林志新,吴翔,驱动场作用下光子晶体中三能级原子的自发辐射[J].物理学报,1999,48(8)：1459-1469
[14]K. M. Leung, Y. F. Liu. Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media[J]. Phys Rev Lett,1990,65(21):2646-2649
[15]E. Yablonovitch, T. J. Gmitter, K. M. Leung. Photonic Band Structure:The Face-centered-cubic Case Employing Nonspherical Atoms. Appl. Phys. Lett.,1991,67 (17):2295-2298
[16]Zhou Y S. Wang X H. Gu B Y etal. Switching control of spontaneous emission by polarized atoms on two-dimensional photonic crystal[J] Phys. Rev. Lett,2006,96:103601
[17]X. H. Wang, R. Z. Wang, B. Y. Gu, etal. Decay dist ribution of spontaneous emission from an assembly of atoms in photonic crystals wit h pseudo gaps[J]. Phys. Rev. Lett, 2002,88 (9):093902-093904
[18]E. Cubukeu. Negative refraction by Photonie Crystals[J]. Nature,2003,423 (6940):604-605
[19]P. V. Parimi. Photonic crystals:Imaging by flat lens using negative refraetion [J]. Nature,2003,426:404-405
[20]L. J. WU, M. Mazilu, J. F. Gallet, et al. Planar Photonic crystal Polarization splitter[J]. OPtics.Lett.,2004,29(14):1620-1622
[21]李明宇,顾培夫.光子晶体偏振分光镜的优化设计[J].物理学报.2005,54(5)：2358-2363
[22]L. P. Randolph, J.N. Lee, R. B. Oswald. Luminescence of ZnS and Znse Window and filter materials [J], IEEE Trans. Nuclear Seienee.1975,22(6):2265-2272
[23]E.Chow, S. Y. Lin,J. R. Wendt, et al. Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ=1.55μm wavelengths [J]. Opt. Lett., 2001,26(50):286-288
[24]E.Chow, S. Y. Lin,J. R., V. Hietala, et al. Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal [J]. Science.1998,282(5387):274-276
[25]K. Taesung, P. O. Leisher, A. J. Danner, et al.Photonic crystal structure effect on the enhancement in the external quantum efficiency of a red LED [J].IEEE photon. Technol. Lett.,2006,18(17):1876-1878
[26]K. Asakawa, Y. Sugimoto, Y. Watanabe. New design for wide/flat bandwidth in Photonic crystal-based SMZ all-optical device (PC-SMz)[C]. ICTON.2006, Jun,18-22, Nottingham UK:146-149
[27]M. C. Lee, M. Hah, D. E. K. Lau, et al. MEMS-actuated photonic crystal switehes [J]. IEEE Photonics Tech. Lett.,2006,18(2):358-360
[28]Kanamor. iY, InoueK, HorieK and Hane K. Photonic crystal switch by inserting nano-crystal defects using MEMS actuator [J]. Optical MEMS,2003,18:107-108.
[29]江海涛,李云辉,李宏强等.光子晶体在微波技术中的应用[J].物理,2003,12：799-803
[30]T. Lopetegi, M. A. G. laso, M. J. Erro, et al. Novel photonic bandgap microstrip structures using network topology [J]. Microwave. Opt.Technol.Lett.,2000,25(1):33-36
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