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The ultra-short pulse equation in a metamaterial is solved by the extended F-expansion method. The new phenomena and characteristics of solitons, caused by the anomalous self-steepening effect and the second-order nonlinear dispersion in metamaterials, are discussed. The results show that the second-order nonlinear dispersion in the positive-index region may take the place of the linear dispersion to form the bright and dark solitons. Due to the switchable sign of the anomalous self-steepening effect in the positive-index and negative-index regions, the bright and dark solitons separately exist in the anomalous and normal dispersion regions under some specific conditions. The moving directions of the centers of bright and dark solitons can be controlled by the sign of the anomalous self-steepening effect or by the combination of the anomalous self-steepening effect and third-order linear dispersion.
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Keywords:
- soliton /
- metamaterial /
- extended F-expansion method
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[12] Wen S, Wang Y, Su W, Xiang Y, Fu X, Fan D 2006 Phys. Rev. E 73 036617
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[18] Li P G, Yang R C, Xu Z Y 2010 Phys. Rev. E 82 046603
[19] Yang R C, Zhang Y 2011 J. Opt. Soc. Am. B 28 123
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[21] Dai X Y, Wen S C, Xiang Y J 2008 Acta Phys. Sini. 57 186 (in Chinese) [戴小玉, 文双春, 项元江 2008 57 186]
[22] Xiang Y J, Dai X Y, Wen S C, Guo J, Fan D Y 2011 Phys. Rev. A 84 033815
[23] Krolikowski W, Bang O, Rasmussen J J, Wyller J 2001 Phys. Rev. E 64 016602
[24] Potasek M J 1987 Optics Letters 12 921
[25] Abdou M A 2007 Chaos, Solitons and Fractals 31 95
[26] Palacios S L, Guinea A, Fernandez-Diaz J M, Crespo R D 1999 Phys. Rev. E 60 R45
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[1] Kivshar Y S, Agrawal G 2003 Optical Solitons: From Fibers to Photonic Crystals (San Diego: Academic Press).
[2] Zharov A A, Shadrivov I V, Kivshar Y S 2003 Phys. Rev. Lett. 91 037401
[3] Shadrivov I V, Sukhorukov A A, Kivshar Y S 2004 Phys. Rev. E 69 016617
[4] Zharova N A, Shadrivov I V, Zharov A A, Kivshar Y S 2005 Opt. Express 13 1291
[5] D'Aguanno G 2004 Phys. Rev. Lett. 93 213902
[6] Scalora M, de Ceglia D, D'Aguanno G, Mattiucci N, Akozbek N, Centini M, J. Bloemer M 2007 Phys. Rev. E 75 066606
[7] Scalora M, Syrchin M S, Akozbek N, Poliakov E Y, D'Aguanno G, Mattiucci N, Bloemer M J, Zheltikov A M 2005 Phys. Rev. Lett. 95 013902
[8] Lazarides N, Eleftheriou M, Tsironis G P 2006 Phys. Rev. Lett. 97 157406
[9] Liu Y M, Bartal G A, Genov D, Zhang X 2007 Phys. Rev. Lett. 99 153901
[10] Kockaert P, Tassin P, der Sande G V, Veretennicoff I, Tlidi M 2007 Phys. Rev. A 74 033822 Tassin P, Gelens L, Danckaert J, Veretennicoff I, der Sande G V, Kockaert P, Tlidi M 2007 Chaos 17 037116
[11] Wen S, Xiang Y, Dai X, Tang Z, Su W, Fan D 2007 Phys. Rev. A 75 033815
[12] Wen S, Wang Y, Su W, Xiang Y, Fu X, Fan D 2006 Phys. Rev. E 73 036617
[13] Wen S, Xiang Y, Su W, Hu Y, Fu X, Fan D 2006 Opt. Express 14 1568
[14] Zhang J G, Wen S C, Xiang Y J, Wang Y W, Luo H L 2010 Phys. Rev. A 81 023829
[15] Dai X Y, Xiang Y J, Wen S C, Fan D Y 2010 Optics Communications 283 1607
[16] Cheng X, Zhuang B X, Dai X Y, Su W H, Wen S C 2009 Journal of Nonlinear Optical Physics and Materials 18 271
[17] Liu H L, Wen S C, Xiong M, Dai X Y 2007 Acta Physica Sinica 56 6473 (in Chinese) [刘海兰, 文双春, 熊敏, 戴小玉 2007 56 6473]
[18] Li P G, Yang R C, Xu Z Y 2010 Phys. Rev. E 82 046603
[19] Yang R C, Zhang Y 2011 J. Opt. Soc. Am. B 28 123
[20] Chen C, Dong J, Yang R C 2012 Acta Photonica Sinica 41 288 (in Chinese) [陈诚, 董佳, 杨荣草 2012 光子学报 41 288]
[21] Dai X Y, Wen S C, Xiang Y J 2008 Acta Phys. Sini. 57 186 (in Chinese) [戴小玉, 文双春, 项元江 2008 57 186]
[22] Xiang Y J, Dai X Y, Wen S C, Guo J, Fan D Y 2011 Phys. Rev. A 84 033815
[23] Krolikowski W, Bang O, Rasmussen J J, Wyller J 2001 Phys. Rev. E 64 016602
[24] Potasek M J 1987 Optics Letters 12 921
[25] Abdou M A 2007 Chaos, Solitons and Fractals 31 95
[26] Palacios S L, Guinea A, Fernandez-Diaz J M, Crespo R D 1999 Phys. Rev. E 60 R45
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