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,1168 北京科技大学学报 第31卷 表1不同微腔尺寸及介质柱半径的归一化谐振频率 Table 1 Resonant frequencies of two-dimensional photonic crystal microcavities with different microcavity sizes and dielectric rod radii 介质柱半径 归一化谐振频率，∫ 归一化谐振频率，f 归一化谐振频率，∫ 归一化谐振频率， r (L.=7,L,=17) (L.=9,L,=17) (L.=11,L,=17) (L,=13,L,=17) 0.200 0.327770 0.328020 0.328065 0.328073 0.225 0.318720 0.318840 0.318870 0.318870 0.250 0.310800 0.310900 0.310930 0.310934 0.275 0.303060 0.303130 0.303140 0.303150 0.300 0.294530 0.294560 0.294680 0.294680 0.325 0.284800 0.284960 0.284996 0.285004 3结论 defect modes in two-dimensional metallic photonic crystals.J Appl Phys,1999,85(12):8499 本文采用多重散射法对具有五个缺陷点的氧化 [5]Painter O.Lee R K.Scherer A.et al.Two-dimensional photonic 铝介质柱四方晶格二维光子晶体微腔的透过率T band-gap defect mode laser.Science,1999.284:1819 [6]Berggren M,Dodabalapur A.Slusher R E.Timko A.et al.Or- 和品质因子Q进行了研究，计算表明，随着微腔尺 ganie solid state laser with imprinted gratings on plastic sub 寸的增加，微腔的品质因子Q增加，而微腔的透过 strates.Appl Phys Lett.1998.72(4):410 率T先增加后减小.在固定微腔尺寸的情况下，随 [7]Fan S H,Villeneuve PR,Joannopoulos J D.et al.Channel drop 着介质柱半径的增加，微腔的品质因子Q和透过率 tunneling through localized states.Phys Rev Leut,1998.80(5): 960 T先增加后减小.综合各项计算结果，当L,=13, L,=17,介质柱半径=0.25时微腔的品质因子和 [8]Notomi M.Taniyama H.Mitsugi S,et al.Optomechanical wavelength and energy conversion in high-double-layer cavities 透过率达到了比较大的值，分别为49270和91%. of photonic erystal slabs.Phys Rev Lett,2006.97:023903 当微腔尺寸不变时，各光子晶体微腔的谐振频率随 [9]Srinivasan K.Barclay P E.Painter O.et al.Experimental 着介质柱半径的增加而减小. demonstration of a high quality factor photonic crystal microcavi- ty.Appl Phys Leu.2003.80(10):1915 参考文献 [10]Jugessur A S.Pottier P.De La Rue R M.Microcavity filters [1]Yablonovitch E.Inhibited spontaneous emission in solid state based on hexagonal lattice 2-D photonic crystal structures embed- physics and electronics.Phys Rev Lett.1987.58(20):2059 ded in ridge waveguides.Photon Nanostruct.2005.3:25 [2]John S.Strong localization of photons in certain disorded dielectric [11]Subramania G.Lin Y,Wendt J R,et al.Tuning the micro- superlattices.Phys Rev Lett.1987.58(23):2486 cavity resonant wavelength in a two-dimensional photonic crystal [3]McCall S L:Platzman P M.Microwave propagation in two di- by modifying the cavity geometry.Appl Phys Lett.83(22): mensional dielectric lattices.Phys Rev Lett.1991.67(15): 4491 2017 [12]Li L M.Zhang Z Q.Multiple-scattering approach to finite sized [4]Gadot F,De Lustrac A.Lourtiog J M.et al.High transmission photonic band-gap meterials.Phys Rev B.1998.58(15):9587表1 不同微腔尺寸及介质柱半径的归一化谐振频率 Table1 Resonant frequencies of two-dimensional photonic crystal microcavities with different microcavity sizes and dielectric rod radii 介质柱半径 r 归一化谐振频率f （ L x＝7L y＝17） 归一化谐振频率f （ L x＝9L y＝17） 归一化谐振频率f （ L x＝11L y＝17） 归一化谐振频率f （ L x＝13L y＝17） 0∙200 0∙327770 0∙328020 0∙328065 0∙328073 0∙225 0∙318720 0∙318840 0∙318870 0∙318870 0∙250 0∙310800 0∙310900 0∙310930 0∙310934 0∙275 0∙303060 0∙303130 0∙303140 0∙303150 0∙300 0∙294530 0∙294560 0∙294680 0∙294680 0∙325 0∙284800 0∙284960 0∙284996 0∙285004 3 结论 本文采用多重散射法对具有五个缺陷点的氧化 铝介质柱四方晶格二维光子晶体微腔的透过率 T 和品质因子 Q 进行了研究．计算表明随着微腔尺 寸的增加微腔的品质因子 Q 增加而微腔的透过 率 T 先增加后减小．在固定微腔尺寸的情况下随 着介质柱半径的增加微腔的品质因子 Q 和透过率 T 先增加后减小．综合各项计算结果当 L x ＝13 Ly＝17介质柱半径 r＝0∙25时微腔的品质因子和 透过率达到了比较大的值分别为49270和91％． 当微腔尺寸不变时各光子晶体微腔的谐振频率随 着介质柱半径的增加而减小． 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］ McCall S LPlatzman P M．Microwave propagation in two-dimensional dielectric lattices． Phys Rev Lett199167（15）： 2017 ［4］ Gadot FDe Lustrac ALourtioz J Met al．High-transmission defect modes in two-dimensional metallic photonic crystals． J Appl Phys199985（12）：8499 ［5］ Painter OLee R KScherer Aet al．Two-dimensional photonic band-gap defect mode laser．Science1999284：1819 ［6］ Berggren MDodabalapur ASlusher R ETimko Aet al．Organic solid-state laser with imprinted gratings on plastic substrates．Appl Phys Lett199872（4）：410 ［7］ Fan S HVilleneuve P RJoannopoulos J Det al．Channel drop tunneling through localized states．Phys Rev Lett199880（5）： 960 ［8］ Notomi MTaniyama H Mitsugi Set al．Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs．Phys Rev Lett200697：023903 ［9］ Srinivasan KBarclay P EPainter Oet al．Experimental demonstration of a high quality factor photonic crystal microcavity．Appl Phys Lett200380（10）：1915 ［10］ Jugessur A SPottier PDe La Rue R M．Microcavity filters based on hexagonal lattice2-D photonic crystal structures embedded in ridge waveguides．Photon Nanostruct20053：25 ［11］ Subramania GLin S YWendt J Ret al．Tuning the microcavity resonant wavelength in a two-dimensional photonic crystal by modifying the cavity geometry．Appl Phys Lett83（22）： 4491 ［12］ Li L MZhang Z Q．Multiple-scattering approach to finite-sized photonic band-gap meterials．Phys Rev B199858（15）：9587 ·1168· 北 京 科 技 大 学 学 报 第31卷