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·66 北京科技大学学报 第30卷 于，=19.0时达到最大值，其后随相对介电常数的 method application:Simulating and infinite 2D photonic crystal by 增加而递减，由此可知：在所计算范围内，当，取 analyzing.sorting and suppressing the border effects.Opt Com- mun,2005,251(2):64 19.0时，两条禁带均达到最大值：而，大于12.0之 [7]Porkropivny VV.Photonic 2D crystal built from nanotubes. 后，才会出现双禁带.这表明，对于尺寸一定的正方 nanochannels.and nanowires:Review of progress in synthesis. 空气柱三角晶格光子晶体，还需选择合适的材料，才 properties.and promising application/Sizov FF.Gumenjuk- 能使得完全禁带宽度达到最大值， Sichevska J V,Kostyukevych Sergey A.Proceeding of the SPIE-The International Society of Optical Engineering 3结论 Washington:SPIE.2003.5065:196. [8]Jaskorzynska B.Properties and applications of ID and 2D photon- 研究了三种二维三角格点光子晶体禁带特征， ic crystals//Proceeding of 20046th International Conference of 结果表明空气圆柱三角晶格光子晶体要比由同种介 Transparent Optical Nnetworks.New York.2004:259 材料构成的正方介质柱三角晶格光子晶体的完全禁 [9]Celanovic I.Jovanovic N.ID and 2D photonic crystals for ther- 带要大得多，根据这两种光子晶体结构，提出了正 mophotovoltatic applications//de La Rue R M,Viktorovitch P. 方空气柱三角晶格光子晶体，对于该结构的光子晶 Sotomayor Torres C M,et al.Proceeding of the SPIE-The International Society of Optical Engineering.Washington: 体，当相对介电常数6，大于12.0时，将出现双禁 SPIE,2004,5450:416 带；且在计算的范围内，当6等于19.0时，两条禁 [10]Cheryl M,Anderson,Konstantins P.Large two-dimensional 带均达到最大值，这些结果对三角晶格光子晶体的 photonic band gaps.Phys Rev Lett,1996.77(14):2949 应用具有一定的参考价值， [11]LiZ Y.Gu B Y.Yang GZ.Large absolute band gaps in 2D anisotropic photonic crystals.Phys Rec Leut.1998.81(12): 参考文献 257 [1]Yablonovitch E.Inhibited spontaneous emission in solid state [12]Zhuang F.He S L,He J P.Large complete band gap of a two- physics and electronics.Phys Rev Lett.1987.58(20):2059 dimensional photonic crystal consisting of anisotropic elliptic [2]John S.Strong localization of photons in certain disorded dielectric cylinders.Acta Phys Sin,2002,51(2):355 (庄飞，何赛灵，何江平。大带隙的二维各向异性椭圆介质光 superlattices.Phys Rev Leut,1987.58(23):2486 子晶体.物理学报，2002,51(2)：355) [3]Netti M C,Harris A,Brumber JJ.Optical trirefringence in pho- tonic crystal waveguides.Phys Rev Lett,2001.86(8):1526 [13]Joannopoulos J D,Meade R D.Winn J N.Molding the Flow of [4]Happ T D.Kamp M,Klopf F.Bent laser cavity based on 2D Light.New York:Princeton University Press,1995. photonic crystal waveguide.Electron Lett.2000,36(4):324 [14]Feng S,Shen L F,He S L.A two-dimensional photonic crys- [5]Masashi N.Staoshi O.Hidenao T.Fabrication of GaAs hole ar- tal formed by a triangular lattice of square dielectric rods with a ray as a 2D-photonic crystal and their to photonic bandgap waveg- large absolute band gap.Acta Phys Sin.2004.53(4):1540 (冯尚申，沈林放，何赛灵.大带隙二维正方介质柱三角晶格 uide.Opt Quantum Electron.2002.34(1):183 [6]Bonnefois J J.Guida G,Priou A.A new multiple scattering 光子晶体，物理学报，2004,53(4)：1540)于εr＝19∙0时达到最大值其后随相对介电常数的 增加而递减．由此可知：在所计算范围内当 εr 取 19∙0时两条禁带均达到最大值；而εr 大于12∙0之 后才会出现双禁带．这表明对于尺寸一定的正方 空气柱三角晶格光子晶体还需选择合适的材料才 能使得完全禁带宽度达到最大值． 3 结论 研究了三种二维三角格点光子晶体禁带特征 结果表明空气圆柱三角晶格光子晶体要比由同种介 材料构成的正方介质柱三角晶格光子晶体的完全禁 带要大得多．根据这两种光子晶体结构提出了正 方空气柱三角晶格光子晶体．对于该结构的光子晶 体当相对介电常数 εr 大于12∙0时将出现双禁 带；且在计算的范围内当 εr 等于19∙0时两条禁 带均达到最大值．这些结果对三角晶格光子晶体的 应用具有一定的参考价值． 参 考 文 献 ［1］ Yablonovitch E．Inhibited spontaneous emission in solid state physics and electronics．Phys Rev Lett198758（20）：2059 ［2］ John S．Strong localization of photons in certain disorded dielectric superlattices．Phys Rev Lett198758（23）：2486 ［3］ Netti M CHarris ABrumber J J．Optical trirefringence in photonic crystal waveguides．Phys Rev Lett200186（8）：1526 ［4］ Happ T DKamp MKlopf F．Bent laser cavity based on 2D photonic crystal waveguide．Electron Lett200036（4）：324 ［5］ Masashi NStaoshi OHidenao T．Fabrication of GaAs hole array as a2D-photonic crystal and their to photonic bandgap waveguide．Opt Quantum Electron200234（1）：183 ［6］ Bonnefois J JGuida GPriou A．A new multiple scattering method application：Simulating and infinite2D photonic crystal by analyzingsorting and suppressing the border effects．Opt Commun2005251（2）：64 ［7］ Porkropivny V V．Photonic 2D crystal built from nanotubes nanochannelsand nanowires：Review of progress in synthesis propertiesand promising application ∥ Sizov F FGumenjukSichevska J V Kostyukevych Sergey A． Proceeding of the SPIE— The International Society of Optical Engineering． Washington：SPIE20035065：196． ［8］ Jaskorzynska B．Properties and applications of1D and2D photonic crystals∥ Proceeding of 20046th International Conference of T ransparent Optical Nnetworks．New York2004：259 ［9］ Celanovic IJovanovic N．1D and2D photonic crystals for thermophotovoltatic applications∥de La Rue R MViktorovitch P Sotomayor Torres C Met al． Proceeding of the SPIE— The International Society of Optical Engineering． Washington： SPIE20045450：416 ［10］ Cheryl MAndersonKonstantins P．Large two-dimensional photonic band gaps．Phys Rev Lett199677（14）：2949 ［11］ Li Z YGu B YYang G Z．Large absolute band gaps in 2D anisotropic photonic crystals．Phys Rev Lett199881（12）： 257 ［12］ Zhuang FHe S LHe J P．Large complete band gap of a twodimensional photonic crystal consisting of anisotropic elliptic cylinders．Acta Phys Sin200251（2）：355 （庄飞何赛灵何江平．大带隙的二维各向异性椭圆介质光 子晶体．物理学报200251（2）：355） ［13］ Joannopoulos J DMeade R DWinn J N．Molding the Flow of L ight．New York：Princeton University Press1995． ［14］ Feng S SShen L FHe S L．A two-dimensional photonic crystal formed by a triangular lattice of square dielectric rods with a large absolute band gap．Acta Phys Sin200453（4）：1540 （冯尚申沈林放何赛灵．大带隙二维正方介质柱三角晶格 光子晶体．物理学报200453（4）：1540） ·66· 北 京 科 技 大 学 学 报 第30卷