1. R.W. Boyd, Nonlinear optics, Academic press, 2020.
2. H. Gibbs, Optical bistability: controlling light with light, Elsevier, 2012.
3. V.E. Zakharov and L.A. Ostrovsky, "Modulation instability: the beginning," Physica D, Vol. 238, pp. 540-548, 2009. [
DOI:10.1016/j.physd.2008.12.002]
4. V.E. Zakharov and A.A. Gelash, "Nonlinear stage of modulation instability," Phys. Rev. Lett. Vol. 111, pp. 054101 (1-5), 2013. [
DOI:10.1103/PhysRevLett.111.054101]
5. M.A. Sharif, "Modulation instability of optical nonlinear media, a route to chaos," IEEE. Asia Communications and Photonics Conference and Exhibition (ACP), pp. 1-8, Nov. 2011. [
DOI:10.1364/ACP.2011.83080G]
6. R.P. Sharma, K. Batra, and A.D. Verga, "Nonlinear evolution of the modulational instability and chaos using one-dimensional Zakharov equations and a simplified model," Phys. Plasmas, Vol. 12, pp. 022311 (1-7), 2005. [
DOI:10.1063/1.1850477]
7. M.A. Sharif, M. Borjkhani, and B. Ghafary, "Temporal modulation instability, transition to chaos in non-feedback biased photorefractive media," Opt. Commun. Vol. 319, pp. 17-24, 2014. [
DOI:10.1016/j.optcom.2013.12.064]
8. J.M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, "Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation," Opt. Express, Vol. 17, pp. 21497-21508, 2009. [
DOI:10.1364/OE.17.021497]
9. A. Demircan and U. Bandelow, "Supercontinuum generation by the modulation instability," Opt. Commun. Vol. 244, pp. 181-185, 2005. [
DOI:10.1016/j.optcom.2004.09.049]
10. M. Conforti, A. Mussot, A. Kudlinski, and S. Trillo, "Modulational instability and pulse generation in dispersion oscillating fiber ring cavities," J. Opt. Soc. Am. Vol. 27, pp. NTh4A.3, 2014. [
DOI:10.1364/NP.2014.NTh4A.3]
11. D.Y. Tang, S. Fleming, W.S. Man, H.Y. Tam, and M.S. Demokan, "Subsideband generation and modulational instability lasing in a fiber soliton laser," J. Opt. Soc. Am. B, Vol. 18, pp. 1443-1450, 2011. [
DOI:10.1364/JOSAB.18.001443]
12. S. Mosca, M. Parisi, I. Ricciardi, F. Leo, T. Hansson, M. Erkintalo, P. Maddaloni, P. De Natale, S. Wabnitz, and M. De Rosa, "Modulation instability induced frequency comb generation in a continuously pumped optical parametric oscillator," Phys. Rev. Lett, Vol. 121, pp. 093903 (1-19), 2018. [
DOI:10.1103/PhysRevLett.121.093903]
13. R. Haldar, A. Roy, P. Mondal, V. Mishra, and S.K. Varshney, "Free-carrier-driven Kerr frequency comb in optical microcavities: Steady state, bistability, self-pulsation, and modulation instability," Phys. Rev. A, Vol. 99, pp. 033848 (1-14), 2019. [
DOI:10.1103/PhysRevA.99.033848]
14. M.A. Sharif, "Modulation instability-enhanced frequency comb generation in graphene-based electro-optical modulator at terahertz frequency range," J. Opt. Vol. 22, pp. 095503 (1-9), 2020. [
DOI:10.1088/2040-8986/abaa20]
15. P.T.S. DeVore, D. Borlaug, and B. Jalali, "Enhancing electrooptic modulators using modulation instability," Phys. status solidi RRL, Vol. 7, pp. 566-570, 2013. [
DOI:10.1002/pssr.201307174]
16. M. A. Sharif, B. Ghafary, and M.H.M. Ara, "A novel graphene-based electro-optical modulator using modulation instability," IEEE. Photon. Technol. Lett. Vol. 28, pp. 2897-2900, 2016. [
DOI:10.1109/LPT.2016.2624562]
17. X. Du, I. Skachko, A. Barker, and E.Y. Andrei, "Approaching ballistic transport in suspended grapheme," Nat. Nanotechnol, Vol. 3, pp. 491-495, 2008. [
DOI:10.1038/nnano.2008.199]
18. K.I. Bolotin, K.J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H.L. Stormer, "Ultrahigh electron mobility in suspended grapheme," Solid state Commun, Vol. 146, pp. 351-355, 2008. [
DOI:10.1016/j.ssc.2008.02.024]
19. H. Deng, F. Ye, B.A. Malomed, X. Chen, and N.C. Panoiu, "Optically and electrically tunable Dirac points and Zitterbewegung in graphene-based photonic superlattices," Phys. Rev. B, Vol. 91, pp. 201402 (1-5), 2015. [
DOI:10.1103/PhysRevB.91.201402]
20. M.F. Craciun, S. Russo, M. Yamamoto, and S. Tarucha, "Tuneable electronic properties in grapheme," Nano Today, Vol. 6, pp. 42-60, 2011. [
DOI:10.1016/j.nantod.2010.12.001]
21. A. Ciattoni and C. Rizza, "Graphene-nonlinearity unleashing at lasing threshold in graphene-assisted cavities," Phys. Rev. A, Vol. 91, pp. 053833 (1-7), 2015. [
DOI:10.1103/PhysRevA.91.053833]
22. N.A. Savostianova and S.A. Mikhailov, "Giant enhancement of the third harmonic in graphene integrated in a layered structure," Appl. Phys. Lett, Vol. 107, pp. 181104 (1-4), 2015. [
DOI:10.1063/1.4935041]
23. F. Shi, Y. Chen, P. Han, and P. Tassin - Small, "Broadband, Spectrally Flat, Graphene‐based Terahertz Modulators," Small, Vol. 11, pp. 6044-6050, 2015. [
DOI:10.1002/smll.201502036]
24. C.T. Phare, Y.H.D. Lee, J. Cardenas, and M. Lipson, "Graphene electro-optic modulator with 30 GHz bandwidth," Nat. Photonics, Vol. 9, pp. 511-514, 2015. [
DOI:10.1038/nphoton.2015.122]
25. S. Luo, Y. Wang, X. Tong, and Z. Wang "Graphene-based optical modulators," Nanoscale Res. Lett. Vol. 10, pp. 1-11, 2015. [
DOI:10.1186/s11671-015-0866-7]
26. B. Sensale-Rodriguez, R. Yan, M.M. Kelly, T. Fang, K. Tahy, W.S. Hwang, D. Jena, L. Liu, and H.G. Xing, "Broadband graphene terahertz modulators enabled by intraband transitions," Nat. Commun. Vol. 3, pp. 1-7, 2012. [
DOI:10.1038/ncomms1787]
27. Ch. Ye, S. Khan, Zh. R. Li. E. Simsek, and V. J. Sorger, "λ-size ITO and graphene-based electro-optic modulators on SOI," IEEE. J. Sel. Top. Quantum Electron, Vol. 20, pp. 40-49, 2014. [
DOI:10.1109/JSTQE.2014.2298451]
28. Sh. Yu, X. Wu, K. Chen, B. Chen, X. Guo, D. Dai, L. Tong, W. Liu, and Y. Ron Shen "All-optical graphene modulator based on optical Kerr phase shift," Optica, Vol. 3, pp. 541-544, 2016. [
DOI:10.1364/OPTICA.3.000541]
29. D. Ansell1, I.P. Radko, Z. Han, F.J. Rodriguez, S.I. Bozhevolnyi, and A.N. Grigorenko, "Hybrid graphene plasmonic waveguide modulators," Nat. Commun. Vol. 6, pp. 1-6, 2015. [
DOI:10.1038/ncomms9846]
30. X. Peng, R. Hao, Z. Ye, P. Qin, W. Chen, H. Chen, X. Jin, D. Yang, and E. Li, "Highly efficient graphene-on-gap modulator by employing the hybrid plasmonic effect," Opt. Lett. Vol. 42, pp.1736-1739, 2017. [
DOI:10.1364/OL.42.001736]
31. F. Zhou and W. Du, "Ultrafast all-optical plasmonic graphene modulator," Appl. Opt. Vol. 57, pp. 6645-6650, 2018. [
DOI:10.1364/AO.57.006645]
32. F. Sun, L. Xia, Ch. Nie, C. Qiu, L. Tang, J. Shen, T. Sun, L. Yu, P. Wu, Sh. Yin, Sh. Yan, and Ch. Du "An all-optical modulator based on a graphene-plasmonic slot waveguide at 1550 nm," Appl. Phys. Express, Vol. 12, pp. 042009 (1-12), 2019. [
DOI:10.7567/1882-0786/ab0a89]
33. C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, "All-plasmonic Mach-Zehnder modulator enabling optical high-speed communication at the microscale," Nat. Photonics, Vol. 9, pp. 525-528, 2015. [
DOI:10.1038/nphoton.2015.127]
34. X. Guo, R. Liu, D. Hu, H. Hu, Zh. Wei, R.Wang, Y. Dai, Y. Cheng, K. Chen, K.Liu, G. Zhang, X. Zhu, Zh. Sun, X. Yang, and Q. Dai, "Efficient All‐Optical Plasmonic Modulators with Atomically Thin Van Der Waals Heterostructures," Adv. Mater, Vol. 32, pp. 1907105 (1-8), 2020. [
DOI:10.1002/adma.201907105]
35. H. Vahed and S.S. Ahmadi, "Hybrid plasmonic optical modulator based on multi-layer grapheme," Opt. Quantum Electron. Vol. 52, pp. 1-2, 2020. [
DOI:10.1007/s11082-019-2118-z]
36. J. Wang, X. Zhang, Y. Chen, Y. Geng, Y. Du, and X. Li, "Design of a graphene-based silicon nitride multimode waveguide-integrated electro-optic modulator," Opt. Commun. Vol. 481, pp. 126531 (1-5), 2021. [
DOI:10.1016/j.optcom.2020.126531]
37. C. Ma, B. Xiao, D. Zhou, and L. Xiao, "A novel tunable terahertz wave modulator based on graphene and frequency selective surface (FSS)," Opt. Commun, Vol. 478, pp. 126375 (1-6), 2021. [
DOI:10.1016/j.optcom.2020.126375]
38. S. Wagner, C. Weisenstein, A.D. Smith, M. Östling, S. Kataria, and M.C. Lemme, "Graphene transfer methods for the fabrication of membrane-based NEMS devices," Microelectron. Eng, Vol. 159, pp. 108-113, 2016. [
DOI:10.1016/j.mee.2016.02.065]
39. M. Chen, R.C. Haddon, R. Yan, and E. Bekyarova, "Advances in transferring chemical vapour deposition graphene: a review," Mater Horizons, Vol. 4, pp. 1054-1063, 2017. [
DOI:10.1039/C7MH00485K]
40. H. Cheun Lee, W.-W. Liu, S.-P. Chai, A.R. Mohamed, A. Aziz, Ch.-S. Khe, N. M.S. Hidayah, and U. Hashim, "Review of the synthesis, transfer, characterization and growth mechanisms of single and multilayer grapheme," RSC Adv, Vol. 7, pp. 15644-15693, 2017. [
DOI:10.1039/C7RA00392G]
41. A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, "Electrical Control of Silicon Photonic Crystal Cavity by Graphene," Nano Lett. Vol. 13, pp. 515−518, 2013. [
DOI:10.1021/nl3039212]
42. S. Liu, P. Zhang, C. Lou, F. Xiao, and J. Zhao, "Numerical simulations of discrete propagations of light waves in optically induced planar waveguide arrays," J. Mod. Opt. Vol. 56, pp. 677-684, 2009. [
DOI:10.1080/09500340902745385]
43. S.A. Mikhailov, "Quantum theory of the third-order nonlinear electrodynamic effects of graphene," Phys. Rev. B, Vol. 93, pp. 085403 (1-31), 2016. [
DOI:10.1103/PhysRevB.93.085403]
44. J.L. Cheng, N. Vermeulen, and J.E. Sipe, "Third order optical nonlinearity of graphene," New J. Phys. Vol. 16, pp. 053014 (1-17), 2014. [
DOI:10.1088/1367-2630/16/5/053014]
45. E. Hendry, P.J. Hale, J. Moger, A.K. Savchenko, and S.A. Mikhailov, "Coherent Nonlinear Optical Response of Graphene," Phys. Rev. Lett. Vol. 105, pp. 097401 (1-4), 2010. [
DOI:10.1103/PhysRevLett.105.097401]
46. V.E. Zakharov and L.A. Ostrovsky, "Modulation instability: the beginning," Physica D. Vol. 238, pp. 540-548, 2009. [
DOI:10.1016/j.physd.2008.12.002]
47. A.A. Balyakin and N.M. Ryskin, "A change in the character of modulation instability in the vicinity of a critical frequency," Tech. Phys. Lett. Vol. 30, pp. 175-177, 2004. [
DOI:10.1134/1.1707158]
48. M.A. Sharif, M. Khodavirdizadeh, S. Salmani, S. Mohajer, and M.H. MajlesAra, "Difference Frequency Generation-based ultralow threshold Optical Bistability in graphene at visible frequencies, an experimental realization," J. Mol. Liq, Vol. 284, pp. 92-101, 2019. [
DOI:10.1016/j.molliq.2019.03.167]
49. M.A. Alejo, L. Fanelli, and C. Muñoz, "Review on the Stability of the Peregrine and Related Breathers," Front. Phys. Vol. 8, pp. 404 (1-8), 2020. [
DOI:10.3389/fphy.2020.591995]
50. J.M. Dudley, F. Dias, M. Erkintalo, and G. Genty, "Instabilities, breathers and rogue waves in optics," Nat. Photonics, Vol. 8, pp. 755-764, 2014. [
DOI:10.1038/nphoton.2014.220]
51. G. Mu, Z. Qin, and R. Grimshaw, "Dynamics of rogue waves on a multisoliton background in a vector nonlinear Schrodinger equation," SIAM J. Appl. Math. Vol. 75, pp. 1-20, 2015. [
DOI:10.1137/140963686]
52. B.F. Feng, L. Ling, and D.A. Takahashi, "Multi‐breather and high‐order rogue waves for the nonlinear Schrödinger equation on the elliptic function background," Stud. Appl. Math. Vol. 144, pp.46-101, 2020. [
DOI:10.1111/sapm.12287]
53. L.L. Feng and T.T. Zhang, "Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation," Appl. Math. Lett. Vol. 78, pp. 133-140, 2018. [
DOI:10.1016/j.aml.2017.11.011]
54. G.T. Adamashvili and D.J. Kaup, "Optical surface breather in graphene," Phys. Rev. A, Vol. 95, pp.053801, 2017. [
DOI:10.1103/PhysRevA.95.053801]
55. M.A. Sharif, "Spatio-temporal modulation instability of surface plasmon polaritons in graphene-dielectric heterostructure," Physica E Low Dimens. Syst. Nanostruct. Vol. 105, pp.174-181, 2019. [
DOI:10.1016/j.physe.2018.09.011]
56. P.‐H. Ho, Ch.‐H. Chen, F.‐Y. Shih, Y.‐R. Chang, Sh.‐S. Li, W.‐H. Wang, M.‐Ch. Shih, W.‐T. Chen, Y‐P. Chiu, M.‐K. Li, Y‐S. Shih, and Ch.‐W. Chen, "Precisely Controlled Ultrastrong Photoinduced Doping at Graphene-Heterostructures Assisted by Trap‐State‐Mediated Charge Transfer," Adv Mater. Vol. 27, pp. 7809-7815, 2015. [
DOI:10.1002/adma.201503592]
57. L. Misseeuw, T. Ciuk, A. Krajewsk, I. Pasternak, W. Strupinski, B. Feigel, M. Khoder, I. Vandriessche, J. Van Erps, S.Van Vlierberghe, H. Thienpont, P. Dubruel, and N. Vermeulen, "Localized optical-quality doping of graphene on silicon waveguides through a TFSA-containing polymer matrix," J. Mater. Chem. C, Vol. 6, pp. 10739-10750, 2018. [
DOI:10.1039/C8TC03198C]