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Based on the developed optically pumped graphene multilayer terahertz surface plasma structures, this paper calculates the real part of propagation index and amplification coefficient in optically pumped graphene multilayer structures, discusses the inluences of momentum relaxation time, temperature, numbers of grapheme layers, and the quasi-Fermi energy in the topmost grapheme layer on the real part of propagation index and amplification coefficient. It is shown that when the real part of dynamic conductivity becomes negative in the terahertz range of frequencies in the optically pumped graphene multilayer structures, the surface plasma of graphene layers can achieve gain. By comparing the peeling-graphene-structure with the graphene structure that has a high conducting bottom graphene layer in optically pumped scheme, it can be said that the surface plasma of the peeling-graphene-structure can get a high efficient amplification. Meanwhile, the structure having properly numbers of graphene layers can get a larger amplification than the simple graphene structure in an optically pumped scheme at low temperatures.
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Keywords:
- terahertz /
- multiple grapheme layer /
- surface plasma /
- gain
[1] Han P Y, Liu W, Xie Y H, Zhang X C 2009 Physics 38 06 (in Chinese) [韩鹏昱, 刘伟, 谢亚红, 张希成2009 物理 38 06]
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[7] Ryzhii V, Ryzhii M, Satou A 2009 J. Appl. Phys. 106 084507
[8] Ryzhii V, Ryzhii M, Otsuji T 2008 Phys. Stat. Sol. (c) 5 261
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[11] Ryzhii M, Ryzhii V 2007 J. Appl. Phys. 46 08151
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[13] Zhang Y P, Liu L Y, Chen Q, Feng Z H, Wang J L, Zhang X, Zhang H Y, Zhang H Y 2013 Acta Phys. Sin. 62 097202 (in Chinese)[张玉萍, 刘陵玉, 陈琦, 冯志红, 张晓, 张洪艳, 张会云2013 62 097202]
[14] Ryzhii V, Dubinov A A, Otsuji T, Mitin V, Shur M S 2010 Appl. Phys. 107 054505
[15] Dubinov A A, Aleshkin V Y, Ryzhii M, Otsuji T, Ryzhii V 2009 Appl. Phys. 2 092301
[16] Aleshkin V Ya, Dubinov A A, Ryzhii V 2009 JETP Letters 89 63
[17] Wu S Q, Liu J S, Wang S L, Hu B 2013 Chin. Phys. B 22 104207
[18] Hanson G W 2008 J. Appl. Phys. 103 064302
[19] Vafek O 2006 Phys. Rev. Lett. 97 266406
[20] Falkovsky L A, Varlamov A A 2007 Eur. Phys. J. B 56 281
[21] Jablan M, Buljan H, Solijacic M 2009 Phys. Rev. B 80 245435
[22] Watanabe T, Fukushima T, Yabe Y, Boubanga-Tombet S A, Satou A, Dubinov A A, Aleshkin V Ya, Mitin V, Ryzhii V, Otsuji T 2013 New J. Phys. 15 075003
[23] Dubinov A A, Aleshkin V Ya, Mitin V Otsji T, Ryzhii V 2010 J. Phys. 23 145302
[24] Vakil A 2011 Science 332 1291
[25] Chen P Y, Alu A 2011 ACS Nano 5 5855
[26] Lin C, Tian Z, Xun L, Guoping W 2013 Optics Express 21 28628
[27] Rana F 2008 IEEE Trans. Nanotechnol. 7 91
[28] Zhang Y P, Liu L Y, Zhang X, Zhang H Y, Zhang H Y 2012 Journal of Optoelectronics. Laser 23 832 (in Chinese)[张玉萍, 刘陵玉, 张晓, 张洪艳, 张会云2012 光电子 激光23 832]
[29] Satou A, Otsuji T, Ryzhii V 2011 J. Appl. Phys 50 070116
[30] Satou A, Ryzhii V, Kurita Y, Otsuji T 2013 J. Appl. Phys. 113 143108
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[1] Han P Y, Liu W, Xie Y H, Zhang X C 2009 Physics 38 06 (in Chinese) [韩鹏昱, 刘伟, 谢亚红, 张希成2009 物理 38 06]
[2] Geim A K MacDonald A H 2007 Phys. Today 60 35
[3] Castro Neto A H Guinea F Peres N M R Novoselov K S Geim A K 2009 Rev. Mod. Phys. 81 109
[4] Wu H Q, Linghu C Y, Lv H M, Qian H 2013 Chin. Phys. B 22 098106
[5] Rzhii V, Rzhii M, Otsuji T 2007 J. Appl. Phys. 101 083114
[6] Satou A, Vasko F T, Ryzhii V 2008 Phys. Rev. B 78 115431
[7] Ryzhii V, Ryzhii M, Satou A 2009 J. Appl. Phys. 106 084507
[8] Ryzhii V, Ryzhii M, Otsuji T 2008 Phys. Stat. Sol. (c) 5 261
[9] Zhang Y P, Zhang X, Liu L Y, Zhang H Y, Gao Y, Xu S L, Zhang H Y 2009 Chinese Journal of Lasers 39 0111002 (in Chinese) [张玉萍, 张晓, 刘陵玉, 张洪艳, 高营, 徐世林, 张会云2009 中国激光39 0111002]
[10] Ryzhii V, Ryzhii M, Mitin V, Otsuji T 2011 J. Appl. Phys. 110 094503
[11] Ryzhii M, Ryzhii V 2007 J. Appl. Phys. 46 08151
[12] 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 61 047803]
[13] Zhang Y P, Liu L Y, Chen Q, Feng Z H, Wang J L, Zhang X, Zhang H Y, Zhang H Y 2013 Acta Phys. Sin. 62 097202 (in Chinese)[张玉萍, 刘陵玉, 陈琦, 冯志红, 张晓, 张洪艳, 张会云2013 62 097202]
[14] Ryzhii V, Dubinov A A, Otsuji T, Mitin V, Shur M S 2010 Appl. Phys. 107 054505
[15] Dubinov A A, Aleshkin V Y, Ryzhii M, Otsuji T, Ryzhii V 2009 Appl. Phys. 2 092301
[16] Aleshkin V Ya, Dubinov A A, Ryzhii V 2009 JETP Letters 89 63
[17] Wu S Q, Liu J S, Wang S L, Hu B 2013 Chin. Phys. B 22 104207
[18] Hanson G W 2008 J. Appl. Phys. 103 064302
[19] Vafek O 2006 Phys. Rev. Lett. 97 266406
[20] Falkovsky L A, Varlamov A A 2007 Eur. Phys. J. B 56 281
[21] Jablan M, Buljan H, Solijacic M 2009 Phys. Rev. B 80 245435
[22] Watanabe T, Fukushima T, Yabe Y, Boubanga-Tombet S A, Satou A, Dubinov A A, Aleshkin V Ya, Mitin V, Ryzhii V, Otsuji T 2013 New J. Phys. 15 075003
[23] Dubinov A A, Aleshkin V Ya, Mitin V Otsji T, Ryzhii V 2010 J. Phys. 23 145302
[24] Vakil A 2011 Science 332 1291
[25] Chen P Y, Alu A 2011 ACS Nano 5 5855
[26] Lin C, Tian Z, Xun L, Guoping W 2013 Optics Express 21 28628
[27] Rana F 2008 IEEE Trans. Nanotechnol. 7 91
[28] Zhang Y P, Liu L Y, Zhang X, Zhang H Y, Zhang H Y 2012 Journal of Optoelectronics. Laser 23 832 (in Chinese)[张玉萍, 刘陵玉, 张晓, 张洪艳, 张会云2012 光电子 激光23 832]
[29] Satou A, Otsuji T, Ryzhii V 2011 J. Appl. Phys 50 070116
[30] Satou A, Ryzhii V, Kurita Y, Otsuji T 2013 J. Appl. Phys. 113 143108
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