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非长波极限下二维光子晶体中横电模的等效介质理论

耿滔 王岩 王新 董祥美

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非长波极限下二维光子晶体中横电模的等效介质理论

耿滔, 王岩, 王新, 董祥美

Effective medium theory of two-dimensional photonic crystal for transverse electric mode beyond the long-wavelength limit

Geng Tao, Wang Yan, Wang Xin, Dong Xiang-Mei
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  • 基于Mie散射理论, 推导、建立了适用于非长波极限的二维光子晶体中横电模的等效介质理论. 随后利用该理论探讨了二维光子晶体中横电模的负折射特性和零折射特性, 计算结果与相应的能带结构相符合, 验证了该理论在非长波极限条件下的适用性. 更进一步的是, 使用该理论能得到从能带结构中无法获取的额外信息.
    An effective medium theory of two-dimensional photonic crystal for TE mode beyond the long-wavelength limit has been established based on the Mie scattering theory. Först, the proposed theory has been used to study the negative-refractive-index photonic crystals for TE mode. This theory can be used to calculate the effective indices and the effective impedance, and to predict the position of the band gap. Results agree well with the band structures, especially when the equifrequency surface contours are almost circular. Then the proposed theory is used to study the zero-refractive-index photonic crystals for TE mode. It can be seen a triply-degenerate point at Γ point, forming a Dirac cone in the band structures. It has been called an “accidental-degeneracy-induced Dirac point”, where the effective index is zero and the effective impedance is 1. Results calculated using the proposed theory agree well with the band structures. This means that the theory can be used well beyond the long-wavelength limit. Furthermore, the additional impedance information, which cannot be obtained by band structures, can be derived from the proposed theory.
    • 基金项目: 上海市青年科技启明星计划项目(批准号: 12QA1402300)、国家自然科学基金青年科学基金(批准号: 61008044)、上海市自然科学基金(批准号: 14ZR1428500)和上海市重点学科项目第三期项目(批准号: S30502)资助的课题.
    • Funds: Project supported by the Shanghai Rising-Star Program, China (Grant No. 12QA1402300), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61008044), the Basic Research Program of Shanghai, China (Grant No. 14ZR1428500), and the Shanghai Leading Academic Discipline Project, China (Grant No. S30502).
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    Jin L, Zhu Q Y, Fu Y Q 2013 Chin. Phys. B 22 094102

    [2]

    Li Y N, Gu P F, Zhang J L, Li M Y, Liu X 2006 Acta Phys. Sin. 55 4918 (in Chinese) [厉以宇, 顾培夫, 张锦龙, 李明宇, 刘旭 2006 物理学报 55 4918]

    [3]

    Huang X, Lai L, Hang Z H, Zheng H, Chan Z T 2011 Nat. Mater. 10 582

    [4]

    Zhao H, Shen Y F, Zhang Z J 2014 Acta Phys. Sin. 63 174204 (in Chinese) [赵浩, 沈义峰, 张中杰 2014 物理学报 63 174204]

    [5]

    Ginzburg P, Fortuño F J R, Wurtz G A, Dickson W, Murphy A, Morgan F, Pollard J R, Iorsh I, Atrashchenko A, Belov P A, Kivshar Y S, Nevet A, Ankonina G, Orenstein M, Zayats A V 2013 Opt. Express 21 14907

    [6]

    Li G J, Kang X L, Li Y P 2007 Acta Phys. Sin. 56 6403 (in Chinese) [李国俊, 康学亮, 李永平 2007 物理学报 56 6403]

    [7]

    Jin L, Zhu Q Y, Fu Y Q, Yu W X 2013 Chin. Phys. B 22 104101

    [8]

    Kabashin A V, Evans P, Pastkovsky S, Hendren W, Wurtz G A, Atkinson R, Pollard R, Podolskiy V A, Zayats A V 2009 Nat. Mater. 8 867

    [9]

    Suchowski H, O’Brien K, Wong Z J, Salandrino A, Yin X, Zhang X 2013 Science 342 1223

    [10]

    Chui S T, Hu L 2002 Phys. Rev. B 65 144407

    [11]

    Sarychev A K, McPhedran R C, Shalaev V M 2001 Phys. Rev. B 64 079904

    [12]

    Koschny T, Economou E N, Smith D R, Vier D C, Soukoulis, C M 2005 Phys. Rev. B 71 245105

    [13]

    Wu Y, Li J, Zhang Z Q, Chan C T 2006 Phys. Rev. B 74 085111

    [14]

    Chern R L, Chen Y T 2009 Phys. Rev. B 80 075118

    [15]

    Jin J, Liu S, Lin Z, Chui S T 2009 Phys. Rev. B 80 115101

    [16]

    Bohren C F, Huffman D R 1983 Absorption and Scattering of Light by Small Particles (Canada: John Wiley & Sons, Inc) p195

    [17]

    Notomi M 2000 Phys. Rev. B 62 10696

    [18]

    Tang Z, Zhang H, Peng R, Ye Y, Shen L, Wen S, Fan D 2006 Phys. Rev. B 73 235103

    [19]

    Geng T, Liu T Y, zhuang S L 2007 Chin. Opt. Lett. 5 361

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  • PDF下载量:  221
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-12-22
  • 修回日期:  2015-02-04
  • 刊出日期:  2015-08-05

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