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In the paper, we present a new kind of function photonic crystal of which the refractive index is a function of space position. According to Fermat principle, we give the motion equations of light in one-dimensional, two-dimensional and three-dimensional function photonic crystals. For one-dimensional function photonic crystal, we give the dispersion relation, the band gap structure and the transmissivity, and we obtain wider or narrower band gap structure than that of conventional photonic crystal. We study the effects of the refractive index, the number of period, the incidence angle and the thickness of medium layer on photonic crystal band gap, and obtain some valuable laws. Our results give the theoretical support designing the photonic crystals of different band gap structures.
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Keywords:
- photonic crystals /
- refractive index /
- transfer matrix
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[11] Wang H Q, Fang L G, Wang Y F, Yu A L 2011 Acta Phys. Sin. 60 014203 (in Chinese) [王慧琴, 方利广, 王一凡, 余奥列 2011 60 014203]
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[13] Zhang X J, Zhao J L 2010 Acta Phys. Sin. 59 6299 (in Chinese) [张晓娟, 赵建林 2010 59 6299]
[14] Pendry J B, MacKinnon A 1992 Phys. Rev. Lett. 69 2772
[15] Pendry J B 1996 J. Phys.: Condens. Matter 8 1085
[16] Ishizaki K, Noda S 2009 Nature 460 367
[17] John S 2009 Nature 460 337
[18] Wang H, Li Y P 2001 Acta Phys. Sin. 50 2172 (in Chinese) [王辉, 李永平 2001 50 2172]
[19] Chassagneux Y 2009 Nature 457 174
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[1] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
[2] John S 1987 Phys. Rev. Lett. 58 2486
[3] Tran P 1995 Phys. Rev. B 52 10673
[4] Busch K, John S 1999 Phys. Rev. Lett. 83 967
[5] Scalora M 1994 Phys. Rev. Lett. 73 1368
[6] Yurii A, Vlasov, Martin O'Boyle, Hendrik F, Hamann, Sharee J 2005 Nature 438 65
[7] Kushwaha M S 1994 Phys. Rev. B 49 2313
[8] Torrent D, Hakansson A, Cervera F, Sanchez-Dehesa J 2006 Phys. Rev. Lett. 96 204302
[9] Torrent D, Sanchez-Dehesa J 2007 New. J. Phys. 9 323
[10] Russell P 2003 Science 299 358
[11] Wang H Q, Fang L G, Wang Y F, Yu A L 2011 Acta Phys. Sin. 60 014203 (in Chinese) [王慧琴, 方利广, 王一凡, 余奥列 2011 60 014203]
[12] Wang T B, Liu N H 2007 Acta Phys. Sin. 56 5878 (in Chinese) [王同标, 刘念华 2007 56 5878]
[13] Zhang X J, Zhao J L 2010 Acta Phys. Sin. 59 6299 (in Chinese) [张晓娟, 赵建林 2010 59 6299]
[14] Pendry J B, MacKinnon A 1992 Phys. Rev. Lett. 69 2772
[15] Pendry J B 1996 J. Phys.: Condens. Matter 8 1085
[16] Ishizaki K, Noda S 2009 Nature 460 367
[17] John S 2009 Nature 460 337
[18] Wang H, Li Y P 2001 Acta Phys. Sin. 50 2172 (in Chinese) [王辉, 李永平 2001 50 2172]
[19] Chassagneux Y 2009 Nature 457 174
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