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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.
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Keywords:
- effective medium theory /
- beyond long-wavelength limit /
- photonic crystal /
- transverse electric mode
[1] 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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[1] 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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