Skip to main content
SpringerLink
Log in

Linear and Nonlinear Optical Properties of Graphene: A Review

  • Review Article
  • Published:
Journal of Electronic Materials Aims and scope Submit manuscript

Abstract

This article gives a brief overview of the linear and nonlinear optical response of graphene and its applications. Graphene exhibits unique physical properties. The charge carriers in graphene follow the relativistic massless Dirac equation; thus, they are known as the Dirac fermions. These Dirac fermions in graphene exhibit peculiar linear band structure at the Dirac point in the first Brillouin zone. These carriers exhibit novel linear and nonlinear optical properties in the presence of an intense electromagnetic field. The unique optical properties (linear and nonlinear) are a consequence of the unusual low-energy electronic band structure of graphene. The linear and nonlinear optical response of graphene can be tuned in the terahertz regime by the application of magnetic field. The uniqueness of graphene is shown by different findings in nonlinear optics such as four-wave mixing, saturation and reverse saturation absorption, two-photon absorption and optical limiting, among others. Therefore, the present review article describes the recent development in the field of linear and nonlinear optics of graphene. The different applications of graphene in the context of optics have been highlighted.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Adapted from Ref. 118 under the terms of the Creative Commons CC BY license.

Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

© The Optical Society.

Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

© The Optical Society.

Fig. 26

Similar content being viewed by others

References

  1. A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K. Geim, Rev. Mod. Phys. 81, 109 (2009).

    Article  CAS  Google Scholar 

  2. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, and A.A. Firsov, Science 306, 666 (2004).

    Article  CAS  Google Scholar 

  3. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, and A.A. Firsov, Nature 438, 197 (2005).

    Article  CAS  Google Scholar 

  4. P.R. Wallace, Phys. Rev. 71, 622 (1947).

    Article  CAS  Google Scholar 

  5. M.I. Katsnelson, K.S. Novoselov, and A.K. Geim, Nat. Phys. 2, 620 (2006).

    Article  CAS  Google Scholar 

  6. O. Klein, Z. Angew. Phys. 53, 157 (1929).

    CAS  Google Scholar 

  7. K.I. Bolotin, K.J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H.L. Stormer, Solid State Commun. 146, 351 (2008).

    Article  CAS  Google Scholar 

  8. J.H. Chen, C. Jang, S. Xiao, M. Ishigami, and M.S. Fuhrer, Nat. Nanotechnol. 3, 206 (2008).

    Article  CAS  Google Scholar 

  9. A.K. Geim, and K.S. Novoselov, Nat. Mater. 6, 183 (2007).

    Article  CAS  Google Scholar 

  10. F. Xia, D.B. Farmer, Y.M. Lin, and P. Avouris, Nano Lett. 10, 715 (2010).

    Article  CAS  Google Scholar 

  11. F. Schwierz, Nat. Nanotechnol. 5, 487 (2010).

    Article  CAS  Google Scholar 

  12. Y. Zhang, Y.W. Tan, H.L. Stormer, and P. Kim, Nature 438, 201 (2005).

    Article  CAS  Google Scholar 

  13. V.P. Gusynin, and S.G. Sharapov, Phys. Rev. Lett. 95, 146801 (2005).

    Article  CAS  Google Scholar 

  14. K.S. Novoselov, Z. Jiang, Y. Zhang, S.V. Morozov, H.L. Stormer, U. Zeitler, J.C. Maan, G.S. Boebinger, P. Kim, and A.K. Geim, Science 315, 1379 (2007).

    Article  CAS  Google Scholar 

  15. N.M.R. Peres, F. Guinea, and A. H. , Phys. Rev. B 73, 125411 (2006).

    Article  CAS  Google Scholar 

  16. J. Cserti, A. Csordás, and G. Dávid, Phys. Rev. Lett. 99, 066802 (2007).

    Article  CAS  Google Scholar 

  17. K. Ziegler, Phys. Rev. B 75, 233407 (2007).

    Article  CAS  Google Scholar 

  18. I.F. Herbut, V. Juricic, and O. Vafek, Phys. Rev. Lett. 100, 046403 (2008).

    Article  CAS  Google Scholar 

  19. J. Martin, N. Akerman, G. Ulbricht, T. Lohmann, J.H. Smet, K. von Klitzing, and A. Yacoby, Nat. Phys. 4, 144 (2008).

    Article  CAS  Google Scholar 

  20. A. Rycerz, J. Tworzydło, and C.W.J. Beenakker, Nat. Phys. 3, 172 (2007).

    Article  CAS  Google Scholar 

  21. J.L. Garcia-Pomar, A. Cortijo, and M. Nieto-Vesperinas, Phys. Rev. Lett. 100, 236801 (2008).

    Article  CAS  Google Scholar 

  22. J.M. Pereira, F.M. Peeters, R.N. Costa Filho, and G.A. Farias, J. Phys. Condensed Matter 21, 045301 (2009).

    Article  CAS  Google Scholar 

  23. D. Gunlycke, and C.T. White, Phys. Rev. Lett. 106, 136806 (2011).

    Article  CAS  Google Scholar 

  24. H. Min, G. Borghi, M. Polini, and A.H. MacDonald, Phys. Rev. B 77, 041407 (2008).

    Article  CAS  Google Scholar 

  25. P. San-Jose, E. Prada, E. McCann, and H. Schomerus, Phys. Rev. Lett. 102, 247204 (2009).

    Article  CAS  Google Scholar 

  26. L. Majidi, and M. Zareyan, Phys. Rev. B 83, 115422 (2011).

    Article  CAS  Google Scholar 

  27. M. Trushin, and J. Schliemann, Phys. Rev. Lett. 107, 156801 (2011).

    Article  CAS  Google Scholar 

  28. L. Majidi, and M. Zareyan, Phys. Rev. B 86, 075443 (2012).

    Article  CAS  Google Scholar 

  29. M. Ezawa, Phys. Rev. B 73, 045432 (2006).

    Article  CAS  Google Scholar 

  30. L. Brey, and H.A. Fertig, Phys. Rev. B 73, 235411 (2006).

    Article  CAS  Google Scholar 

  31. M.Y. Han, B. Ozyilmaz, Y. Zhang, and P. Kim, Phys. Rev. Lett. 98, 206805 (2007).

    Article  CAS  Google Scholar 

  32. C.H. Park, Y.W. Son, L. Yang, M.L. Cohen, and S.G. Louie, Nano Lett. 8, 2920 (2008).

    Article  CAS  Google Scholar 

  33. C.H. Park, L. Yang, Y.W. Son, M.L. Cohen, and S.G. Louie, Nat. Phys. 4, 213 (2008).

    Article  CAS  Google Scholar 

  34. C.H. Park, L. Yang, Y.W. Son, M.L. Cohen, and S.G. Louie, Phys. Rev. Lett. 101, 126804 (2008).

    Article  CAS  Google Scholar 

  35. S.V. Morozov, K.S. Novoselov, M.I. Katsnelson, F. Schedin, L.A. Ponomarenko, D. Jiang, and A.K. Geim, Phys. Rev. Lett. 97, 016801 (2006).

    Article  CAS  Google Scholar 

  36. H. Suzuura, and T. Ando, Phys. Rev. Lett. 89, 266603 (2002).

    Article  CAS  Google Scholar 

  37. D.V. Khveschenko, Phys. Rev. Lett. 97, 036802 (2006).

    Article  CAS  Google Scholar 

  38. A.A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C.N. Lau, Nano Lett. 8, 902 (2008).

    Article  CAS  Google Scholar 

  39. P. Wei, W. Bao, Y. Pu, C.N. Lau, and J. Shi, Phys. Rev. Lett. 102, 166808 (2009).

    Article  CAS  Google Scholar 

  40. D. Dragoman, and M. Dragoman, Appl. Phys. Lett. 91, 203116 (2007).

    Article  CAS  Google Scholar 

  41. C.L. Kane, and E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005).

    Article  CAS  Google Scholar 

  42. R. Nandkishore, L.S. Levitov, and A.V. Chubukov, Nat. Phys. 8, 158 (2012).

    Article  CAS  Google Scholar 

  43. A.Y. Sin, Q. Chen, and C. Zhang, Front. Optoelectron. 8, 3 (2015).

    Article  Google Scholar 

  44. B.L. Zhi, L.Z. Xiao, Y.X. Qing, C.Y. Sheng, and T.J. Guo, Chin. Sci. Bull. 57, 2971 (2012).

    Article  CAS  Google Scholar 

  45. J.W. You, S.R. Bongu, Q. Bao, and N.C. Panoiu, Nanophotonics 8, 63 (2019).

    Article  Google Scholar 

  46. M.K. Kavitha, and M. Jaiswal, Asian J. Phys. 25, 809 (2016).

    Google Scholar 

  47. P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M.C. Asensio, A. Resta, B. Ealet, and G. Le Lay, Phys. Rev. Lett. 108, 155501 (2012).

    Article  CAS  Google Scholar 

  48. A. Fleurence, R. Friedlein, T. Ozaki, H. Kawai, Y. Wang, and T.Y. Yamada, Phys. Rev. Lett. 108, 245501 (2012).

    Article  CAS  Google Scholar 

  49. Y. Xu, B. Yan, H.J. Zhang, J. Wang, G. Xu, P. Tang, W. Duan, and S.C. Zhang, Phys. Rev. Lett. 111, 136804 (2013).

    Article  CAS  Google Scholar 

  50. E. Bianco, S. Butler, S. Jiang, O.D. Restrepo, W. Windl, and J.E. Goldberger, ACS Nano 7, 4414 (2013).

    Article  CAS  Google Scholar 

  51. M. Naguib, M. Kurtoglu, V. Presser, J. Lu, J. Niu, M. Heon, L. Hultman, Y. Gogotsi, and M.W. Barsoum, Adv. Materials 23, 4248 (2011).

    Article  CAS  Google Scholar 

  52. M. Naguib, V.N. Mochalin, M.W. Barsoum, and Y. Gogotsi, Adv. Materials 26, 992 (2013).

    Article  CAS  Google Scholar 

  53. A. Eftekhari, J. Mater. Chem. A 5, 18299 (2017).

    Article  CAS  Google Scholar 

  54. A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.Y. Chim, G. Galli, and F. Wang, Nano Lett. 10, 1271 (2010).

    Article  CAS  Google Scholar 

  55. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, Nat. Nanotechnol. 6, 147 (2011).

    Article  CAS  Google Scholar 

  56. R.S. Sundaram, M. Engel, A. Lombardo, R. Krupke, A.C. Ferrari, Ph. Avouris, and M. Steiner, Nano Lett. 13, 1416 (2013).

    Article  CAS  Google Scholar 

  57. O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, Nat. Nanotechnol. 8, 497 (2013).

    Article  CAS  Google Scholar 

  58. S.A. Mikhailov, Euro Phys. Lett. 79, 27002 (2007).

    Article  CAS  Google Scholar 

  59. S.A. Mikhailov, and K. Ziegler, J. Phys. Condens. Matte 20, 384204 (2008).

    Article  CAS  Google Scholar 

  60. A.R. Wright, X.G. Xu, J.C. Cao, and C. Zhang, Appl. Phys. Lett. 95, 072101 (2009).

    Article  CAS  Google Scholar 

  61. M. Dragoman, D. Neculoiu, G. Deligeorgis, G. Konstantinidis, D. Dragoman, A. Cismaru, A.A. Muller, and R. Plana, Appl. Phys. Lett. 97, 093101 (2010).

    Article  CAS  Google Scholar 

  62. E. Hendry, P.J. Hale, J. Moger, A.K. Savchenko, and S.A. Mikhailov, Phys. Rev. Lett. 105, 097401 (2010).

    Article  CAS  Google Scholar 

  63. S. Giancarlo, W. Gang, R. Habib, G.P. David, De. F. Domenico, M. Teng, L. Birong, W. Junjia, K.O. Anna, Y. Duhee, A.B. Sean, E.M. Jakob, G. Ilya, D.C. Stefano, C. Michele, T. Andrea, P. Marco, C. Giulio, and C.F. Andrea, Nat. Nanotechnol. 13, 583 (2018).

    Article  CAS  Google Scholar 

  64. J. Wang, Y. Hernandez, M. Lotya, J.N. Coleman, and W.J. Blau, Adv. Mater. 21, 2430 (2009).

    Article  CAS  Google Scholar 

  65. A.Y. Bykov, T.V. Murzina, M.G. Rybin, and E.D. Obraztsova, Phys. Rev. B 85, 121413 (2012).

    Article  CAS  Google Scholar 

  66. Y.Q. An, F. Nelson, J.U. Lee, and A.C. Diebold, Nano Lett 13, 2104 (2013).

    Article  CAS  Google Scholar 

  67. Y.Q. An, J.E. Rowe, D.B. Dougherty, J.U. Lee, and A.C. Diebold, Phys. Rev. B 89, 115310 (2014).

    Article  CAS  Google Scholar 

  68. G.E. Fernandes, J.H. Kim, R. Osgood III., and J. Xu, Nanotechnology 29, 105201 (2018).

    Article  CAS  Google Scholar 

  69. R.R. Nair, P. Blake, A.N. Grigorenko, K.S. Novoselov, T.J. Booth, T. Stauber, N.M.R. Peres, and A.K. Geim, Science 320, 1308 (2008).

    Article  CAS  Google Scholar 

  70. H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, Appl. Phys. Lett. 95, 41103 (2009).

    Article  CAS  Google Scholar 

  71. H. Zhang, D.Y. Tang, L.M. Zhao, Q.L. Bao, and K.P. Loh, Opt. Express 17, 17630 (2009).

    Article  CAS  Google Scholar 

  72. G.K. Lim, Z.L. Chen, J. Clark, R.G.S. Goh, W.H. Ng, H.W. Tan, R.H. Friend, P.K.H. Ho, and L.L. Chua, Nat. Photonics 5, 554 (2011).

    Article  CAS  Google Scholar 

  73. S. Wu, L. Mao, A.M. Jones, W. Yao, C. Zhang, and X. Xu, Nano Lett. 12, 2032 (2012).

    Article  CAS  Google Scholar 

  74. S.Y. Hong, J.I. Dadap, N. Petrone, P.C. Yeh, J. Hone, and R.M. Osgood, Phys. Rev. X 3, 021014 (2013).

    Google Scholar 

  75. K.L. Ishikawa, Phys. Rev. B 82, 201402 (2010).

    Article  CAS  Google Scholar 

  76. I. Gierz, J.C. Petersen, M. Mitrano, C. Cacho, I.C.E. Turcu, E. Springate, A. Stöhr, A. Köhler, U. Starke, and A. Cavalleri, Nat. Mater. 12, 1119 (2013).

    Article  CAS  Google Scholar 

  77. L.A.C. Lucas, G. M. de-Sa Thiago, W. Kenji, T. Takashi, C. C. Leonardo, J. Ado and M. M. Leandro, Nano Lett. 17, 3447 (2017).

    Article  CAS  Google Scholar 

  78. J. Guo, H. Wang, X. Dai, Y. Xiang, and D. Tang, Opt. Express 27, 32746 (2019).

    Article  CAS  Google Scholar 

  79. F. Nasehnia, S.M. Lima, M. Seifi, and E. Mehran, Comp. Mater. Sci. 114, 112 (2016).

    Article  CAS  Google Scholar 

  80. F. Hipolito, D. Dimitrovski, and T.G. Pedersen, Phys. Rev. B 99, 195407 (2019).

    Article  CAS  Google Scholar 

  81. T.G. Pedersen, Phys. Rev. B 98, 165425 (2018).

    Article  CAS  Google Scholar 

  82. S.R.K.C. Sharma, M. Yamijala, and S.K. Mukhopadhyay, J. Phy. Chem. C 119, 12079 (2015).

    Article  CAS  Google Scholar 

  83. W.H. Cao, and Y.S. Ang, Euro phys. Lett. 107, 37007 (2014).

    Article  CAS  Google Scholar 

  84. J.L. Cheng, N. Vermeulen, and J.E. Sipe, New J. Phys. 16, 53014 (2014).

    Article  CAS  Google Scholar 

  85. J.L. Cheng, N. Vermeulen, and J.E. Sipe, Opt. Express 22, 15868 (2014).

    Article  CAS  Google Scholar 

  86. J.L. Cheng, N. Vermeulen, and J.E. Sipe, Phys. Rev. B 91, 235320 (2015).

    Article  CAS  Google Scholar 

  87. J.L. Cheng, N. Vermeulen, and J.E. Sipe, Phys. Rev. B 92, 235307 (2015).

    Article  CAS  Google Scholar 

  88. J.L. Cheng, N. Vermeulen, and J.E. Sipe, Sci. Rep. 7, 43843 (2017).

    Article  CAS  Google Scholar 

  89. I. Al-Naib, J.E. Sipe, and M.M. Dignam, Phys. Rev. B 90, 245423 (2014).

    Article  CAS  Google Scholar 

  90. I. Al-Naib, J.E. Sipe, and M.M. Dignam, New J. Phys. 17, 113018 (2015).

    Article  CAS  Google Scholar 

  91. I. Al-Naib, M. Poschmann, and M.M. Dignam, Phys. Rev. B 91, 205407 (2015).

    Article  CAS  Google Scholar 

  92. D.A. Smirnova, I.V. Shadrivov, A.E. Miroshnichenko, A.I. Smirnov, and Y.S. Kivshar, Phys. Rev. B 90, 35412 (2014).

    Article  CAS  Google Scholar 

  93. V.A. Margulis, E.E. Muryumin, and E.A. Gaiduk, J. Opt. 16, 125203 (2014).

    Article  CAS  Google Scholar 

  94. P. Bowlan, E. Martinez-Moreno, K. Reimann, T. Elsaesser, and M. Woerner, Phys. Rev. B 89, 41408 (2014).

    Article  CAS  Google Scholar 

  95. S. Sekwao, and J.-P. Leburton, Appl. Phys. Lett. 106, 63109 (2015).

    Article  CAS  Google Scholar 

  96. B. Semnani, A.H. Majedi, and S. Safavi-Naeini, J. Opt. 18, 35402 (2016).

    Article  CAS  Google Scholar 

  97. R. McGouran, L. Al-Naib, and M.M. Dignam, Phys. Rev. B 94, 235402 (2016).

    Article  Google Scholar 

  98. Y. Wang, and D.R. Andersen, J. Phys. D. Appl. Phys. 49, 46 (2016).

    CAS  Google Scholar 

  99. A. Marini, J.D. Cox, and F.J. García de Abajo, Phys. Rev. B 95, 125408 (2017).

    Article  Google Scholar 

  100. H. Rostami, and M. Polini, Phys. Rev. B 93, 161411 (2016).

    Article  CAS  Google Scholar 

  101. F. Hipolito, A. Taghizadeh, and T.G. Pedersen, Phys. Rev. B 98, 205420 (2018).

    Article  CAS  Google Scholar 

  102. BM Matthias, A. Marini, JD. Cox, T. Zhu, F. Silva, S. Teichmann, M. Massicotte, F. Koppens, L. S. Levitov, F. JavierGarcíadeAbajo, BJ Jens (2018) Nat. Commun.; 9:1018 .

  103. Z. Sun, D.N. Basov, and M.M. Fogler, PNAS 115, 3285 (2018).

    Article  CAS  Google Scholar 

  104. J. Wang, Y. Wang, T. Wang, G. Li, R. Lou, G. Cheng, and J. Bai, Nanomaterials 9, 640 (2019).

    Article  CAS  Google Scholar 

  105. S.-E. Zhu, S. Yuan, and G.C.A.M. Janssen, Euro Phys. Lett. 108, 17007 (2014).

    Article  CAS  Google Scholar 

  106. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, and A.A. Firsov, Nature (London) 438, 197 (2005).

    Article  CAS  Google Scholar 

  107. Y. Zhang, V.-W. Tan, H.L. Störmer, and P. Kim, Nature (London) 438, 201 (2005).

    Article  CAS  Google Scholar 

  108. A.W.W. Ludwig, M.P.A. Fisher, R. Shankar, and G. Grinstein, Phys. Rev. B 50, 7526 (1994).

    Article  CAS  Google Scholar 

  109. K. Ziegler, Phys. Rev. B 55, 10661 (1997).

    Article  CAS  Google Scholar 

  110. E.V. Gorbar, V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. B 66, 045108 (2002).

    Article  CAS  Google Scholar 

  111. S. Ryu, C. Mudry, A. Furusaki, and A.W.W. Ludwig, Phys. Rev. B 75, 205344 (2007).

    Article  CAS  Google Scholar 

  112. K. Ziegler, Phys. Rev. Lett. 80, 3113 (1998).

    Article  CAS  Google Scholar 

  113. E.V. Gorbar, V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. Lett. 95, 146801 (2005).

    Article  CAS  Google Scholar 

  114. E.V. Gorbar, V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. B 73, 245411 (2006).

    Article  CAS  Google Scholar 

  115. M.I. Katsnelson, Eur. Phys. J. B 51, 157 (2006).

    Article  CAS  Google Scholar 

  116. J. Tworzydlo, B. Trauzettel, M. Titov, A. Rycerz, and C.W.J. Beenakker, Phys. Rev. Lett. 96, 246802 (2006).

    Article  CAS  Google Scholar 

  117. K. Nomura, and A.H. MacDonald, Phys. Rev. Lett. 96, 256602 (2006).

    Article  CAS  Google Scholar 

  118. L.A. Falkovsky, J. Phys: Conf. Ser. 129, 012004 (2008).

    Google Scholar 

  119. L.A. Falkovsky, and A.A. Varlamov, Eur. Phys. J. B 56, 281 (2007).

    Article  CAS  Google Scholar 

  120. M. Weismann, and N.C. Panoiu, Phys Rev B 94, 035435 (2016).

    Article  CAS  Google Scholar 

  121. F. Léonard, C.D. Spataru, M. Goldflam, D.W. Peters, and T.E. Beechem, Sci. Rep. 7, 45873 (2017).

    Article  CAS  Google Scholar 

  122. G.L. Klimchitskaya, and V.M. Mostepanenko, Phys. Rev. B 93, 245419 (2016).

    Article  Google Scholar 

  123. N.M.R. Peres, and T. Stauber, Int. J. Mod. Phys. B 22, 2529 (2008).

    Article  CAS  Google Scholar 

  124. J. Horng, C.-F. Chen, B. Geng, C. Girit, Y. Zhang, Z. Hao, H.A. Bechtel, M.C. Martin, A. Zettl, M.F. Crommie, Y.R. Shen, and F. Wang, Phys. Rev. B 83, 165113 (2011).

    Article  CAS  Google Scholar 

  125. T. Stauber, N.M.R. Peres, and A.K. Geim, Phys. Rev. B 78, 085432 (2008).

    Article  CAS  Google Scholar 

  126. T. Stauber, and N.M.R. Peres, J. Phys.: Condens. Matter 20, 055002 (2008).

    Google Scholar 

  127. T. Stauber, N.M.R. Peres, and A.H. Castro Neto, Phys. Rev. B 78, 085418 (2008).

    Article  CAS  Google Scholar 

  128. N.M.R. Peres, T. Stauber, and A.H. CastroNeto, EuroPhys. Lett. 84, 38002 (2008).

    Google Scholar 

  129. F. Hipolito, A. Taghizadeh, and T.G. Pedersen, Phys. Rev B 98, 205420 (2018).

    Article  CAS  Google Scholar 

  130. T Basak., H. Chakraborty, and A. Shukla, , Phys. Rev. B 92, 205404 (2015).

    Article  CAS  Google Scholar 

  131. H. Dakhlaoui, J. Appl. Phys. 117, 135705 (2015).

    Article  CAS  Google Scholar 

  132. E. Al, F. Ungan, U. Yesilgul, E. Kasapoglu, H. Sari, and I. Sokmen, Opt. Mater. 47, 1 (2015).

    Article  CAS  Google Scholar 

  133. U. Yesilgul, E.B. Al, J.C. Martinez-Orozco, R.L. Restrepo, M.E. Mora-Ramos, C.A. Duque, F. Ungan, and E. Kasapoglu, Opt. Mater. 58, 107 (2016).

    Article  CAS  Google Scholar 

  134. C.V. Nguyen, N.N. Hieu, C.A. Duque, D.Q. Khoa, N.V. Hieu, L.V. Tung, and H.V. Phuc, J. Appl. Phys. 121, 045107 (2017).

    Article  CAS  Google Scholar 

  135. C.V. Nguyen, N.N. Hieu, C.A. Duque, N.A. Poklonski, V.V. Ilyasov, N.V. Hieu, L. Dinh, Q.K. Quang, L.V. Tung, and H.V. Phuc, Opt. Mater. 69, 328 (2017).

    Article  CAS  Google Scholar 

  136. A. Khavasi, Opt. Lett. 38, 3009 (2013).

    Article  CAS  Google Scholar 

  137. E.P. Franken, A.E. Hill, C.E. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).

    Article  Google Scholar 

  138. A. Autere, H. Jussila, Y. Dai, Y. Wang, H. Lipsanen, and Z. Sun, Adv. Mater. 30, 1705963 (2018).

    Article  CAS  Google Scholar 

  139. J.L. Cheng, N. Vermeulen, and J.E. Sipe, N J Phys. 16, 053014 (2014).

    Article  CAS  Google Scholar 

  140. J.D. Cox, I. Silveiro, and F.J. Garcia de Abajo, ACS Nano 10, 1995 (2016).

    Article  CAS  Google Scholar 

  141. J.L. Cheng, J.E. Sipe, N. Vermeulen, and C. Guo, J. Phys.: Photonics 1, 015002 (2019).

    CAS  Google Scholar 

  142. L.Z. Zheng, C. Zhang, and J.C. Cao, Phys. Rev. B 96, 035206 (2017).

    Article  Google Scholar 

  143. S.R. Bongu, P.B. Bisht, R.C. Namboodiri, P. Nayak, S. Ramaprabhu, T.J. Kelly, C. Fallon, and J.T. Costello, J. Appl. Phys. 116, 073101 (2014).

    Article  CAS  Google Scholar 

  144. U. Kurum, B. Liu, K. Zhang, Y. Liu, and H. Zhang, Appl. Phys. Lett. 98, 141103 (2011).

    Article  CAS  Google Scholar 

  145. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z.-X. Shen, K.P. Loh, and D.Y. Tang, Adv. Funct. Mater. 19, 3077 (2009).

    Article  CAS  Google Scholar 

  146. Z. Zheng, C. Zhao, S. Lu, Y. Chen, Y. Li, H. Zhang, and S. Wen, Opt. Express 20, 23201 (2012).

    Article  CAS  Google Scholar 

  147. H. Zhang, D. Tang, R.J. Knize, L. Zhao, Q. Bao, and K.P. Loh, Appl. Phys. Lett. 96, 111112 (2010).

    Article  CAS  Google Scholar 

  148. S. Yamashita, APL Photonics 4, 034301 (2019).

    Article  CAS  Google Scholar 

  149. I.I. Rabi, Phys. Rev. 51, 652 (1937).

    Article  CAS  Google Scholar 

  150. L. Allen, and J.H. Eberly, Optical Resonances and Two-Level Atoms (New York: Wiley and Sons, 1975).

    Google Scholar 

  151. H. Haug, and S.W. Koch, Quantum Theory of Optical and Electronic Properties of Semiconductors, 4th ed., (Singapore: World Scientific, 2004).

    Book  Google Scholar 

  152. M. Lindberg, and S.W. Koch, Phys. Rev. B 38, 3342 (1988).

    Article  CAS  Google Scholar 

  153. R. Binder, S.W. Koch, M. Lindberg, N. Peyghambarian, and W. Schafer, Phys. Rev. Lett. 65, 899 (1990).

    Article  CAS  Google Scholar 

  154. M. Welkowsky, and R. Braunstein, Phys. Rev. B 5, 497 (1972).

    Article  Google Scholar 

  155. L. Banyai, I. Galbraith, C. Ell, and H. Haug, Phys. Rev. B 36, 6099 (1987).

    Article  CAS  Google Scholar 

  156. M. Sinada, and S. Sigano, J. Phys. Soc. Jpn 21, 1936 (1966).

    Article  Google Scholar 

  157. S. Schmitt-Rink, D.S. Chemla, and H. Haug, Phys. Rev. B 37, 941 (1988).

    Article  CAS  Google Scholar 

  158. N. Kosugi, S. Matsuo, K. Konno, and N. Hatakenaka, Phys. Rev. B 72, 172509 (2005).

    Article  CAS  Google Scholar 

  159. A. Schulzgen, R. Binder, M.E. Donovan, M. Lindberg, K. Wundke, H.M. Gibbs, G. Khitrova, and N. Peyghambarian, Phys. Rev. Lett. 82, 2346 (1999).

    Article  CAS  Google Scholar 

  160. M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J.M. Raimond, and S. Haroche, Phys. Rev. Lett. 76, 1800 (1996).

    Article  CAS  Google Scholar 

  161. M. Hirtschulz, F. Milde, E. Malic, S. Butscher, C. Thomsen, S. Reich, and A. Knorr, Phys. Rev. B 77, 035403 (2008).

    Article  CAS  Google Scholar 

  162. E.G. Mishchenko, Phys. Rev. Lett. 103, 246802 (2009).

    Article  CAS  Google Scholar 

  163. S.A. Mikhailov, Microelectron. J. 40, 712 (2009).

    Article  CAS  Google Scholar 

  164. S.A. Mikhailov, and K. Ziegler, J. Phys.: Condens. Matter 20, 384204 (2008).

    CAS  Google Scholar 

  165. S.A. Mikhailov, Phys. E. 40, 2626 (2008).

    Article  CAS  Google Scholar 

  166. H.K. Avetissian, A.K. Avetissian, G.F. Mkrtchain, and Kh.V. Sedrakian, Phys. Rev. B 85, 115443 (2012).

    Article  CAS  Google Scholar 

  167. P.N. Romanets, and F.T. Vasko, Phys. Rev. B 81, 241411 (2010).

    Article  CAS  Google Scholar 

  168. B. Dora, K. Ziegler, P. Thalmeier, and M. Nakamura, Phys. Rev. Lett. 102, 036803 (2009).

    Article  CAS  Google Scholar 

  169. Enamullah, and V.G.S. Kumar Setlur, Phys. B 407, 4600 (2012).

    Article  CAS  Google Scholar 

  170. V. Kumar, Enamullah, U.. Kumar, and G.S. Setlur, Pramana J. . Phys. 83, 597 (2014).

    Article  CAS  Google Scholar 

  171. U. Kumar, V. Kumar, Enamullah, and G.S. Setlur, JOSA B 31, 3042 (2014).

    Article  CAS  Google Scholar 

  172. Enamullah, V. Kumar, U. Kumar, and G.S. Setlur, JOSA B 31, 484 (2014).

    Article  CAS  Google Scholar 

  173. S.A. Jafari, J. Phys.: Condens. Matter 24, 205802 (2012).

    CAS  Google Scholar 

  174. T.G. Pedersen, A.P. Jauho, and K. Pedersen, Phys. Rev. B 79, 113406 (2009).

    Article  CAS  Google Scholar 

  175. V. Kumar, Enamullah, U. Kumar, and G.S. Setlur, Physica B 436, 140 (2014).

    Article  CAS  Google Scholar 

  176. V. Kumar, Enamullah, U. Kumar, and G.S. Setlur, Eur. Phys. J. B 87, 70 (2014).

    Article  CAS  Google Scholar 

  177. U. Kumar, and V. Kumar, Phys. E. 108, 288 (2019).

    Article  CAS  Google Scholar 

  178. U. Kumar, V. Kumar, Enamullah, and G.S. Setlur, Eur. Phys. J. B 91, 86 (2018).

    Article  CAS  Google Scholar 

  179. Enamullah, V. Kumar, U. Kumar, and G.S. Setlur, Adv. Sci. Lett. 20, 1459 (2014).

    Article  Google Scholar 

  180. V. Kumar, Enamullah, U. Kumar, and G.S. Setlur, Adv. Sci. Lett. 24, 5666 (2018).

    Article  Google Scholar 

  181. J. Shang, Z. Luo, C. Cong, J. Lin, T. Yu, and G.G. Gurzadyan, Appl. Phys. Lett. 97, 163103 (2010).

    Article  CAS  Google Scholar 

  182. P.A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M.G. Spencer, Nano Lett. 8, 4248 (2008).

    Article  CAS  Google Scholar 

  183. D. Sun, Z.-K. Wu, C. Divin, X. Li, C. Berger, W.A. de Heer, P.N. First, and T.B. Norris, Phys. Rev. Lett. 101, 157402 (2008).

    Article  CAS  Google Scholar 

  184. B.A. Ruzicka, L.K. Werake, H. Zhao, S. Wang, and K.P. Loh, Appl. Phys. Lett. 96, 173106 (2010).

    Article  CAS  Google Scholar 

  185. J.M. Dawlaty, S. Shivaramam, M. Chandrashekhar, F. Rana, and M.G. Spencer, Appl. Phys. Lett. 92, 042116 (2008).

    Article  CAS  Google Scholar 

  186. M. Breusing, S. Kuehn, T. Winzer, E. Malic, F. Milde, N. Severin, J.P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, Phys. Rev. B 83, 153410 (2011).

    Article  CAS  Google Scholar 

  187. S. Kumar, M. Anija, N. Kamaraju, K.S. Vasu, K.S. Subrahmanyam, A.K. Sood, and C.N.R. Rao, Appl. Phys. Lett. 95, 191911 (2009).

    Article  CAS  Google Scholar 

  188. H. Wang, J.H. Strait, P.A. George, S. Shivaraman, V.B. Shields, M. Chandrashekhar, J. Hwang, F. Rana, M.G. Spencer, C.S. Ruiz-Vargas, and J. Park, Appl. Phys. Lett. 96, 081917 (2010).

    Article  CAS  Google Scholar 

  189. Enamullah, V. Kumar, U. Kumar, and G.S. Setlur, Pramana J. Phys. 82, 1085 (2014).

    Article  CAS  Google Scholar 

  190. H. Zhang, S. Virally, Q. Bao, L.K. Ping, S. Massar, N. Godbout, and P. Kockaert, Opt. Lett. 37, 1856 (2012).

    Article  CAS  Google Scholar 

  191. A. Saynatjoki, L. Karvonen, J. Riikonen, W. Kim, S. Mehravar, R.A. Norwood, N. Peyghambarian, H. Lipsanen, and K. Kieu, ACS Nano 7, 8441 (2013).

    Article  CAS  Google Scholar 

  192. H. Zhang, S. Virally, Q. Bao, K.P. Loh, S. Massar, N. Godbout, and P. Kockaert, Opt. Lett. 37, 1856 (2012).

    Article  CAS  Google Scholar 

  193. T. Gu, N. Petrone, J.F. McMillan, A. van der Zande, M. Yu, G.-Q. Lo, D.-L. Kwong, J. Hone, and C.W. Wong, Nat. Photonics 6, 554 (2012).

    Article  CAS  Google Scholar 

  194. B. Semnani, A.H. Majedi, and S. Safavi-Naeini, J. Opt. 18, 035402 (2016).

    Article  CAS  Google Scholar 

  195. J.L. Cheng, N. Vermeulen, and J.E. Sipe, New J. Phys. 16, 053014 (2014).

    Article  CAS  Google Scholar 

  196. D.B.S. Soh, R. Hamerly, and H. Mabuchi, Phys. Rev. A 94, 023845 (2016).

    Article  CAS  Google Scholar 

  197. X. Zheng, B. Jia, X. Chen, and M. Gu, Adv. Mater. 26, 2699 (2014).

    Article  CAS  Google Scholar 

  198. J. Ren, X. Zheng, Z. Tian, D. Li, P. Wang, and B. Jia, Appl. Phys. Lett. 109, 221105 (2016).

    Article  CAS  Google Scholar 

  199. E. Dremetsika, B. Dlubak, S.-P. Gorza, C. Ciret, M.B. Martin, S. Hofmann, P. Seneor, D. Dolfi, S. Massar, P. Emplit, and P. Kockaert, Opt. Lett. 41, 3281 (2016).

    Article  CAS  Google Scholar 

  200. W. Chen, G. Wang, S. Qin, C. Wang, J. Fang, J. Qi, X. Zhang, L. Wang, H. Jia, and S. Chang, AIP Adv. 3, 042123 (2013).

    Article  CAS  Google Scholar 

  201. L. Miao, Y. Jiang, S. Lu, B. Shi, C. Zhao, H. Zhang, and S. Wen, Photon. Res. 3, 214 (2015).

    Article  CAS  Google Scholar 

  202. S.A. Mikhailov, Phys. Rev. B 93, 085403 (2016).

    Article  CAS  Google Scholar 

  203. N.A. Savostianova, and S.A. Mikhailov, Phys. Rev. B 97, 165424 (2018).

    Article  CAS  Google Scholar 

  204. U. Khan, B. Amin, K. Ullah, and A. Ullah, Phys. Lett. A 383, 125998 (2019).

    Article  CAS  Google Scholar 

  205. K.J.A. Ooi, J.L. Cheng, J.E. Sipe, L.K. Ang, and D.T.H. Tan, APL Photonics 1, 46101 (2016).

    Article  CAS  Google Scholar 

  206. J. Li, J. Tao, Z.H. Chen, and X.G. Huang, Opt. Express 24, 22169 (2016).

    Article  CAS  Google Scholar 

  207. H. Nasari, and M.S. Abrishamian, J. Opt. Soc. Am. B 31, 1691 (2014).

    Article  CAS  Google Scholar 

  208. Z.B. Liu, X.L. Zhang, X.Q. Yan, Y.S. Chen, and J.G. Tian, Chin. Sci. Bull. 57, 2971 (2012).

    Article  CAS  Google Scholar 

  209. L. Zheng, S. Matthew, C. Zhang, and J.C. Cao, J. Appl. Phys. 118, 043106 (2015).

    Article  CAS  Google Scholar 

  210. S. Fraser, X. Zheng, L. Qiu, D. Li, and B. Jia, Appl. Phys. Lett. 107, 031112 (2015).

    Article  CAS  Google Scholar 

  211. S. Biswas, A.K. Kole, C.S. Tiwary, and P. Kumbhakar, RSC Adv. 6, 10319 (2016).

    Article  CAS  Google Scholar 

  212. M. Yue, J. Si, Y. Lihe, Y. Yu, and X. Hou, Opt. Mater. Express 8, 698 (2018).

    Article  CAS  Google Scholar 

  213. S.A. Jafari, T. Tohyama, and S. Maekawa, J. Phys. Soc. Japan 75, 054703 (2006).

    Article  CAS  Google Scholar 

  214. S.A. Jafari, T. Tohyama, and S. Maekawa, J. Phys. Soc. Japan 75, 083706 (2006).

    Article  CAS  Google Scholar 

  215. W. Choi, K.H. Lee, and Y.B. Kim, Phys. Rev. Lett. 124, 117205 (2020).

    Article  CAS  Google Scholar 

  216. S.A. Jafari, Opt. Commun. 282, 317 (2009).

    Article  CAS  Google Scholar 

  217. S.A. Jafari, J. Phys.: Condens. Matter 24, 305601 (2012).

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India

    Vipin Kumar

Authors
  1. Vipin Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vipin Kumar.

Ethics declarations

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumar, V. Linear and Nonlinear Optical Properties of Graphene: A Review. J. Electron. Mater. 50, 3773–3799 (2021). https://doi.org/10.1007/s11664-021-08904-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11664-021-08904-w

Keywords

Search

Navigation