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We introduce graphene into conventional photonic crystals to build new photonic crystal structures, and strictly derive the dispersion relations of the structures based on the electromagnetic boundary conditions and the Maxwell's equations required. The dispersion relations are different from that of the conventional photonic crystals, and the optical properties of the structures may also differ from that of the conventional photonic crystals because of the presence of graphene conductivity in the dispersion relations. By changing the Fermi energy of graphene, the conductivity of it can be changed, the dispersion relations adjusted, the energy band structure altered, and its light propagation manipulated as well. With increasing Fermi energy, the energy band can be transformed from the allowed bands to the prohibited bands and then transformed along the opposite direction to the allowed bands. Because the conductivity changes rapidly in low frequency range, while changes slowly in high frequency range, as the Fermi energy increases, the energy band in the low frequency region will move quickly to higher frequency region, and the energy band in the high frequency region moves slowly, leading to the band compression and mutual conversion between the allowed and the prohibited bands. The larger the Fermi energy, the more obvious the band compression, and the more easy the mutual conversion.
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Keywords:
- graphene /
- terahertz /
- photonic crystal structures
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[1] Shen Y C, Lo T, Taday P F, Cole B E, Tribe W R, Kemp M C 2005 Appl. Phys. Lett. 86 241116
[2] Jacobsen R H, Mittleman D M, Nuss M C 1996 Opt. Lett. 21 2011
[3] Markelz A G, Roitberg A, Heilweil E J 2000 Chem. Phys. Lett. 320 42
[4] Yoneyama H, Yamashita M, Kasai S, Kawase K, Ito H, Ouchi T 2008 Opt. Commun. 281 1909
[5] Li Z Y, Yao J Q, Xu D G, Zhong K, Wang J L, Bing P B 2011 Chin. Phys. B 20 054207
[6] Chen D P, Xing C F, Zhang Z, Zhang C L 2012 Acta Phys. Sin. 61 024202 (in Chinese) [陈大鹏, 邢春飞, 张峥, 张存林 2012 物理学报 61 024202]
[7] Pendry J B 2000 Phys. Rev. Lett. 85 3966
[8] Zhang S, Fan W, Panio N C, Malloy K J, Osgood R M, Brueck S R J 2005 Phys. Rev. Lett. 95 137404
[9] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
[10] Lee S H, Choi M, Kim T T, Lee S, Liu M, Yin X, Choi H K, Lee S S, Choi C G, Choi S Y, Zhang X, Min B 2012 Nature Materials 11 936
[11] Rodriguez B S, Yan R, Kelly M M, Fang T, Tahy K, Hwang W S, Jena D, Liu L, Xing H G 2012 Nature Communications 3 780
[12] Zuo Z G, Wang P, Ling F R, Liu J S, Yao J Q 2013 Chin. Phys. B 22 097304
[13] Xie L Y, Xiao W B, Huang G Q, Hu A R, Liu J T 2014 Acta Phys. Sin. 63 057803 (in Chinese) [谢凌云, 肖文波, 黄国庆, 胡爱荣, 刘江涛 2014 物理学报 63 057803]
[14] Zhang Y P, Zhang H Y, Yin Y H, Liu L Y, Zhang X, Gao Y, Zhang H Y 2012 Acta Phys. Sin. 61 047803 (in Chinese) [张玉萍, 张洪艳, 尹贻恒, 刘陵玉, 张晓, 高营, 张会云 2012 物理学报 61 047803]
[15] Mao Q, Wen Q Y, Tian W, Wen T L, Chen Z, Yang Q H, Zhang H W 2014 Opt. Lett. 39 5649
[16] Wang F, Zhang Y, Tian C, Girit C, Zettl A, Crommie M, Shen Y R 2008 Science 320 206
[17] Hanson G W 2008 J. Appl. Phys. 103 064302
[18] Koppens F H L, Chang D E, Garca de Abajo F J 2011 Nano Lett. 11 3370
[19] Bao Q L, Zhang H, Wang B, Ni Z H, Lim C H Y X, Wang Y, Tang D Y, Loh K P 2011 Nat. Photonics 5 411
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